كتاب Harris' Shock and Vibration Handbook 6th Edition

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Harris’ Shock and Vibration Handbook
Allan G. Piersol
Thomas L. Paez
Sixth Edition

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CONTENTS
Contributors xi
Preface xiii
Chapter 1. Introduction to the Handbook 1.1
Cyril M. Harris and Allan G. Piersol
Chapter 2. Basic Vibration Theory 2.1
Ralph E. Blake
Chapter 3. Vibration of a Resiliently Supported Rigid Body 3.1
Harry Himelblau and Sheldon Rubin
Chapter 4. Nonlinear Vibration 4.1
C. Nataraj and Fredric Ehrich
Chapter 5. Self-Excited Vibration 5.1
Fredric Ehrich
Chapter 6. Dynamic Vibration Absorbers and Auxiliary
Mass Dampers 6.1
Sheldon Rubin
Chapter 7. Vibration of Systems Having Distributed Mass
and Elasticity 7.1
Ronald G. Merritt
Chapter 8. Transient Response to Step and Pulse Functions 8.1
Thomas L. Paez
Chapter 9. Mechanical Impedance/Mobility 9.1
Elmer L. Hixson
Chapter 10. Shock and Vibration Transducers 10.1
Anthony S. Chu
viiChapter 11. Calibration of Shock and Vibration Transducers 11.1
Jeffrey Dosch
Chapter 12. Strain Gage Instrumentation 12.1
Patrick L. Walter
Chapter 13. Shock and Vibration Data Acquisition 13.1
Strether Smith
Chapter 14. Vibration Analyzers and Their Use 14.1
Robert B. Randall
Chapter 15. Measurement Techniques 15.1
Cyril M. Harris
Chapter 16. Condition Monitoring of Machinery 16.1
Ronald L. Eshleman
Chapter 17. Shock and Vibration Standards 17.1
David J. Evans and Henry C. Pusey
Chapter 18. Test Criteria and Specifications 18.1
Allan G. Piersol
Chapter 19. Vibration Data Analysis 19.1
Allan G. Piersol
Chapter 20. Shock Data Analysis 20.1
Sheldon Rubin and Kjell Ahlin
Chapter 21. Experimental Modal Analysis 21.1
Randall J. Allemang and David L. Brown
Chapter 22. Matrix Methods of Analysis 22.1
Stephen H. Crandall and Robert B. McCalley, Jr.
Chapter 23. Finite Element Methods of Analysis 23.1
Robert N. Coppolino
Chapter 24. Statistical Energy Analysis 24.1
Richard G. DeJong
viii CONTENTSChapter 25. Vibration Testing Machines 25.1
David O. Smallwood
Chapter 26. Digital Control Systems for Vibration Testing Machines 26.1
Marcos A. Underwood
Chapter 27. Shock Testing Machines 27.1
Vesta I. Bateman
Chapter 28. Pyroshock Testing 28.1
Vesta I. Bateman and Neil T. Davie
Chapter 29. Vibration of Structures Induced by Ground Motion 29.1
William J. Hall, Billie F. Spencer, Jr., and Amr S. Elnashai
Chapter 30. Vibration of Structures Induced by Fluid Flow 30.1
Robert D. Blevins
Chapter 31. Vibration of Structures Induced by Wind 31.1
Alan G. Davenport and J. Peter C. King
Chapter 32. Vibration of Structures Induced by Sound 32.1
John F. Wilby
Chapter 33. Engineering Properties of Metals 33.1
M. R. Mitchell
Chapter 34. Engineering Properties of Composites 34.1
Keith T. Kedward
Chapter 35. Material and Slip Damping 35.1
Peter J. Torvik
Chapter 36. Applied Damping Treatments 36.1
David I. G. Jones
Chapter 37. Torsional Vibration in Reciprocating and
Rotating Machines 37.1
Ronald L. Eshleman
Chapter 38. Theory of Shock and Vibration Isolation 38.1
Michael A. Talley
CONTENTS ixChapter 39. Shock and Vibration Isolation Systems 39.1
Herbert LeKuch
Chapter 40. Equipment Design 40.1
Karl A. Sweitzer, Charles A. Hull, and Allan G. Piersol
Chapter 41. Human Response to Shock and Vibration 41.1
Anthony J. Brammer
Index follows Chapter 41
absolute measurements, 11.3
absorber, mass ratio, 6.11
accelerated test, 18.15
acceleration:
definition of, 1.9
vibration, 1.26
acceleration response, 2.2
accelerometers, 10.2, 16.4
definition of, 1.9
flesh-mounted, effect of size on, 41.3
flesh-mounted, effect of weight on, 41.3
hand-held, 15.12
acceptance test, 18.5
acronyms, 1.5
action, 7.2, 7.4
active vibration isolation systems, 39.46
added mass, 30.1
adhesive, damping in, 36.3, 36.7, 36.10
admissible functions, 7.8
admittance, 6.3, 10.30
aerodynamic excitation, 31.1, 32.7
air bags, inflatable, 41.43
air guns, 27.8
air springs, 39.10
aliasing, 13.5, 14.11, 19.17, 26.4
diagram, 13.7
rejection, 13.8
alloy systems, damping, 36.2
almost-periodic vibrations, 19.5
ambient vibration, definition of, 1.9
American National Standards Institute
(ANSI), 17.1
American Petroleum Institute (API), 37.17
American Society for Testing and Materials
(ASTM), 17.1
amplitude, 1.7
amplitude demodulation, 14.34
analog, 1.16
analog filters, 13.7
analog-to-digital converters (ADCs), 19.16,
26.3
analogy, definition of, 1.16
analysis, 22.1
matrix methods, 26.6,
transient, by statistical energy analysis,
24.20
(See also specific analysis types)
analytical modeling procedures, classical,
32.1, 18.7
finite element method, 23.1, 40.17
analytical tests, 18.4
anchoring, free-layer damping, 36.7
angular frequency, 1.7, 1.17, 2.3
angular mechanical impedance, 1.16
anisotropic conditions, 7.33
anti-aliasing filters, 14.11
antinode, 1.16
antiresonance, 1.16
aperiodic motion, 1.16
apparent mass, 10.30
arches, 7.1
Arrhenius model, 36.5
assumed modes method, 7.7, 7.9
ASTM (see American Society for Testing
and Materials)
asymmetric shafting, 5.2, 5.16, 5.22
asymmetric stiffness, 4.5, 4.9
asynchronous excitation, 4.17
asynchronous quenching, 4.17
attenuation, 6.4
audiofrequency, 1.16
autocorrelation, 19.6, 24.3
autocorrelation coefficient, 1.16
autocorrelation function, 1.16
automobile vibration, 18.15, 25.20
autonomous system, 4.18
1
INDEXautospectral density, 1.16, 19.8
auxiliary mass damper, 6.1
coulomb friction damping, 6.12
cutting tool chatter, 6.28
gear vibration reduction, 6.28
optimum damping, 6.11
rotating machinery, 6.16
torsional vibration, 6.18
transient and self-excited vibration, 6.28
turbine fatigue reduction, 6.28
average value, 19.3, 19.17, 19.21
averaging time, 14.6, 19.17
optimum, 19.26
background noise, 1.16
backward whirl, 5.4, 5.11, 5.22
balancing, definition of, 1.16
ballistic pendulum calibrator, 11.18
ball-passing frequency, 16.16
bandpass filter, 1.16, 14.2
bandwidth, 2.18
desired, 13.6
effective, 1.19
nominal, 1.22
optimum resolution, 19.23, 19.27
bars, 7.1, 7.11
base-bend sensitivity, 10.15
beams, 7.1
bearings, 16.1, 24.15
beat frequency, 1.17
beats, 1.17
belt friction system, 4.4
Bessel filter, 13.7
biodynamic models:
ATB and MADYMO, 41.14
dynamic response index (DRI) for,
41.20
hand and arm for, 41.13
head and neck of human body, 41.14
lumped parameter, 41.7, 41.11
mechanical impedance of hand-arm
system for, 41.13
mechanical impedance of whole body for,
41.8
neural network, 41.14
seat-to-head transmissibility for, 41.8
spine for, 41.13
biofidelity of human surrogates, 41.4
Bishop theory, 7.17
bistable vibration, 5.2, 5.20
blade-tip-clearance induced instability, 5.2,
5.5, 5.12, 5.22
blocked force, 6.4
bluff bodies, 30.8
body:
mechanical characteristics of, 41.5
mechanical impedance of, 41.8, 41.12
mechanical resonances of, 41.7
motion sickness, 41.3
physical properties of, 41.6
posture and vibration injury, 41.16
skull vibration, 41.13
survivable shocks to, 41.33
thorax-abdomen subsystem, 41.9
transmissibility from seat to head, 41.8
body-induced vibration, 3.47
Bogoliuboff’s method, 4.34
bolted joints, 40.12
bolts, 24.15, 40.12
bone:
compressive strength of, 41.6
density of, 41.6
elastic moduli of, 41.6
tensile strength of, 41.6
boundary conditions, damping and, 36.7,
36.18, 36.19
boundary value problem, 7.2
branched systems, 37.6
broadband random vibration, 1.17
building vibration, acceptability of, 41.29
built-up structure, damping in, 36.2
Butterworth filter, 13.7
cables, 7.35, 15.18
noise generation in, 15.19
calibration:
comparison method of, 11.4
field techniques for, 15.13
random excitation method of, 11.5
shields, use of, 15.19
standards 17.2–17.3
transverse sensitivity, 11.24
voltage substitution method of, 15.16
calibration factor, 11.1
calibration traceability, 11.2
calibrator:
ballistic pendulum, 11.18
centrifuge, 11.9
drop-ball, 11.19
earth’s gravitational field, 11.8
Fourier-transform shock, 11.22
high-acceleration, 11.15
impact-force shock, 11.20
interferometer, 11.10
2 INDEXcalibrator (Cont.):
pendulum, 11.8
reciprocity, 11.5
resonant-bar, 11.15
resonant-beam, 11.25
rotating table, 11.9
shock excitation, 11.16
sinusoidal excitation, 11.15
(See also calibration)
Campbell diagram, 14.27
carpal tunnel syndrome, 41.16
cascade plot, 14.27, 19.25
cement, 15.9
cement mounting, 15.9
CEN (see European Committee for
Standardization)
CENELEC (see European Committee for
Electrotechnical Standardization)
center of twist, 7.18
center of gravity, 1.17, 3.26
center of mass, 1.17, 3.14
central limit theorem, 24.19
centrifuge, 27.12
centrifuge calibrator, 11.9
cepstrum, 14.33
cepstrum analysis, 14.33, 16.17, 16.19
ceramic matrix composites, 34.2
chaotic dynamics, 4.28
characteristic equation, 7.15
characteristic space, 21.20
charge amplifier, 13.2
charge sensitivity, 10.21
chatter, 5.2, 5.19, 5.22
circuit boards, 40.13
circular frequency, 1.17
classical plate theory, 7.31
classification of vibrations, 19.1–19.3, 40.3
coefficient condensation, 21.37
coherence function, 19.10, 21.51
coil springs, 39.42
comfort, in public transportation, 41.28
comparison method of calibration, 11.4
complex amplitude, 6.3
complex angular frequency, 1.17
complex cepstrum, 14.33
complex frequency, 20.13
complex function, 1.17
complex modulus, 35.4
methods for measuring, 36.18
model, 36.4
complex shock, 27.5, 27.10
complex vibration, 1.17, 19.5
compliance, 1.17
composite beam, 7.29
composite materials, 34.1
damping 34.26
design, 34.2, 34.14
failure criteria, 34.9
fatigue performance, 34.15
properties 34.6
types of, 34.1
wearout model 34.24
compound pendulum, 2.31
compressional wave, 1.17
compressors, 17.4
computers, 26.1
experimental applications of, 26.3
personal, 7.1, 26.2
condition monitoring of machinery, 16.1
intermittent, 16.2
off-line, 16.2
on-line, 16.2
permanent, 16.2
relation to spectrum changes in, 16.6
confidence coefficient, 18.9
conjugate even, 14.10
constant-bandwidth analysis, 14.9
constant-percentage bandwidth analysis,
14.9, 19.23
constrained-layer damping, 24.15
continuous beams, 7.27
continuous fiber composites, 34.2
continuous systems, 1.17, 7.1
continuum mechanics, 7.2
control systems:
mixed-mode, 26.19
random vibration, 26.15
sine-wave, 26.17
transient/shock, 26.18
waveform, 26.20
convolution integral, 8.11
coordinate modal assurance criterion, 21.5
coordinate system, 3.1
correction methods, 16.23
correlation coefficient, 1.17
correlation function, 1.17, 19.7
coulomb damping, 1.17, 4.40
coupled modes, 1.17
coupling factor, electromechanical, 1.17
coupling loss factor, 24.10, 24.16, 24.18
couplings, elastic, 37.6
crack propagation, 33.23
Craig-Bampton reduction, 23.19
crankshaft, 37.4
INDEX 3crash:
flailing in, 41.42
helmets for, 41.45
test dummies, 41.4
crest factor, 1.17
criteria, test, 18.1
critical damping, 36.14
fraction of, 1.17, 2.5
critical damping coefficient, 6.6
critical damping ratio, 24.2
critical speeds, 1.18, 37.10
critical strain velocity, 33.11
cross-axis (transverse) sensitivity, 11.25
cross-spectral density function, 19.8, 21.23
computation of, 19.24
cross talk, 15.16
cumulative damage, 34.18
curved beams, 7.35
cycle, 1.18
cycle counting, 33.20
cylindrical shells, 7.36
D’Alembert’s principle, 7.2
damage potential of dynamic load, 40.2
damage rules, in metals, 33.21
damped natural frequency, 1.18
damped systems, 2.27
damper, 1.18, 2.2
applied to rotating systems, 37.21
damper-controlled system, 2.1
damping, 5.3, 5.4, 5.6, 5.12, 5.15, 5.19, 5.20,
7.5, 36.1–36.3, 36.5, 36.6, 36.8,
36.10–36.12, 36.17
acoustic radiation, 36.2
aluminum tape, 36.10
amorphous materials, 36.2
analytical modeling, 36.1, 36.4, 36.5
base structure, 36.8
beam, 36.6–36.8, 36.13, 36.18, 36.19
behavior, 36.4, 36.9
benefits, 36.1, 36.5
blanketing, 36.5
by bolts, rivets, and bearings, 24.15, 36.9,
40.12
bonding layer, 36.7
characteristics of isolators, 39.2, 39.13
commercial test systems, 36.1, 36.22
complex modulus, 36.3, 36.4, 36.18, 36.22
complex structures, 36.2
in computer codes, 36.4
constrained layer, 24.15, 36.1, 36.8, 36.9,
36.10
shear parameter, 36.8, 36.9
damping (Cont.):
coulomb, 1.17, 4.40
coulomb friction, 36.2
critical, 1.18, 2.5
cyclic strain, 36.17
cyclic stress, 36.2
deadness, 36.2
deep drawing, 36.9
definition of, 1.18
design, 36.1, 36.5
dissipation, 36.1, 36.2, 36.8
effect of initial, 36.9
elastic moduli of layers, 36.6, 36.7
energy dissipation, 36.1, 36.2, 36.6
epoxy cure cycle, 36.22
equivalent viscous, 1.19
failure control, 36.5
fiber, imaginary, 36.6
fluid medium, 36.2
fluid pumping, 36.2
free layer, 24.15, 36.1, 36.6, 36.7
equation limitations, 36.7
friction, 36.2
Geiger plate test, 36.18–36.20
generalized Hooke’s law, 36.12
hysteretic, 36.13, 36.15
impedance test, 36.21
integral, 36.1, 36.9, 36.10
intermetallic compounds, 36.2
isotropic characteristics, 36.7
layer dimensions, 36.6, 36.9
linear velocity, 4.32
logarithmic decrement, 36.12, 36.14, 36.16
mass, 2.27
material element, 36.1, 36.2
measures of, 36.1, 36.8, 36.11–36.17
mechanisms of, 21.12
metals, 36.2
in a mode, 36.5
molecular chains, 36.3
noise, 36.1, 36.5
noise control, 36.5
noise radiation control, 36.1, 36.5
nonlinear, 1.22, 36.2, 36.17
nonlinear materials, 36.17
nonproportional, 21.12
Oberst equations, 36.7, 36.22
plastic, 35.5
and product acceptance, 36.5
proportional, 21.12
recovery of molecular chains, 36.3
relaxation of molecular chains, 36.3
in riveted joints, 36.9
4 INDEXdamping (Cont.):
Ross-Kerwin-Ungar (RKU) equations,
36.10, 36.22
shape memory, 35.6
slip, 35.19
sources of, 36.2
specific damping capacity, 36.12, 36.17
spot weld, 36.9
structural, 2.18
test methods, 36.16, 36.18, 36.19
test system, 36.22
thermal effects, 36.2
thermoelastic, 35.12
treatment thickness, 36.6, 36.9, 36.10
tuned damper, 36.1, 36.11
uniform mass, 2.29
uniform structural, 2.29
uniform viscous, 2.27
vibration control, 36.1, 36.2
in vibration isolators, 39.2
viscoelastic, 35.10, 36.2, 36.8, 36.9, 36.13
viscous, 1.26, 2.5, 2.9, 4.3, 4.4, 7.1,
36.13–36.15
viscous dashpot, 36.4
in welded joints, 24.15, 36.9, 40.12
Williams-Landel-Ferry (WLF) model,
36.4
Young’s modulus model, 36.3, 36.4, 36.6
damping coefficient, 2.2, 2.5
(See also fraction of critical damping)
damping criteria, 36.1, 36.11
damping impedance, 6.6, 36.21
damping links, 36.1, 36.11
damping loss factor, 24.14, 24.16, 32.14
damping materials, 36.1, 36.4
acrylic rubber, 36.3
amount of, 36.7
behavior of, 36.4
butadiene rubber, 36.3
butyl rubber, 36.4
chloroprene, 36.3
composites, 34.26
creep, 36.20
cured polymers, 36.3
elastomeric, 36.1, 36.2, 36.11
fluorocarbon, 36.3
fluorosilicone, 36.3
glassy, 36.2
laminates, 36.3, 36.9, 36.19
mastic, 36.3
natural rubber, 36.3
neoprene, 36.3
nitrile rubber, 36.3
damping materials (Cont.):
nylon, 36.3
Plexiglas, 36.3
polyisoprene, 36.3
polymeric, 36.1, 36.2
polymethyl methacrylate, 36.3
polysulfide, 36.3
polysulfone, 36.3
polyvinyl chloride, 36.3
pressure-sensitive adhesives, 36.3, 36.10
shear modulus, 36.4
silicone rubber, 36.3
styrene-butadiene (SBR), 36.3
tapes, 36.3, 36.10
urethane, 36.3
vinyl, 36.3
damping measurements, 35.2, 35.22
comparisons, 36.17
damping mechanisms, 36.2, 36.8
damping model:
fractional derivative, 36.4
shift factor, 36.4, 36.5
damping parameter, 36.15
damping ratio, 36.12, 36.14
damping treatment, 36.1, 36.5–36.10
types, 36.6
damping values, comparison of, 24.15,
40.12
data analysis
digital, 19.16, 21.16, 26.6
matrix methods, 22.1
statistical sampling errors, 19.21
data domain, 21.18
data reduction
to frequency domain, 20.5
to response domain, 20.5
for vibration data, 19.1 (See also data
analysis)
data window, 14.11, 14.13, 14.15
dc accelerometer, 10.13
decibel (dB), definition of, 1.18
deflection, static, 2.4
degrees of freedom (DOF), 1.18, 2.19, 7.2,
21.3
(See also multiple-degree-of-freedom
systems; single-degree-of-freedom
structures and systems)
delamination of composites, 34.5
delta function, 7.26, 20.2
design criteria, 40.14
design issues using composites, 34.3
design life, 40.16
design margins, 40.17
INDEX 5design procedure equipment, 40.2
final design, 40.23
preliminary, 40.2
design requirements, 40.7
design reviews, 40.24
design verification, 40.25
desired bandwidth, 13.6
deterministic force field, 7.6
deterministic function, 1.18, 19.4, 19.10
analysis of, 19.17, 19.26
deterministic signal, stationary, 14.19
deterministic vibration, 1.1
development tests, 18.4
differential geometry, 7.36
digital analysis of data, 19.16, 21.16, 26.6
digital computers, 26.1
experimental applications of, 26.3
digital control systems, 26.12
digital filters, 14.2
digital signal processing, 21.16, 26.3
digital-to-analog conversion (DAC), 26.3
digitizer, 13.1
director approach, 7.35
discrete Fourier transform (DFT), 14.9,
19.18, 21.15
discrete mass moment of inertia, 7.16
displacement:
definition of, 1.18
as design requirement, 40.6
distortion, 1.18
displacement pickup, 1.18
displacement shock, 27.5, 27.6
displacement transducers, 16.4
distributed systems, 1.18
driving point impedance, 1.18, 10.29
hand-arm system, 41.12
human body, 41.8
drop-ball shock calibrator, 11.19
drop tables, 27.7
drop-test calibrator, 11.19
dry friction whip, 5.2, 5.5, 5.11, 5.19, 5.22
ductility of metals, 33.10
Duffing’s method, 4.32
Duhamel’s integral, 7.1, 20.12
dummies:
crash test, 41.4
dynamic, 41.4
durability test, 18.16
duration of shock pulse, 1.18
dynamic absorber, 6.13
pendulum, 6.20
tuned to orders of vibration, 6.20
untuned, 6.25
dynamic disturbances, types of, 39.2
dynamic environment, 39.2
dynamic load factors (DLFs), 39.6
dynamic mass, 10.3
dynamic range, 13.4
dynamic response index (DRI), 41.2,
41.33
dynamic stiffness, 1.18, 10.3
of isolators, 39.13
dynamic vibration absorber, 1.18, 6.1
earth’s gravitational field method of
calibration, 11.8
effective bandwidth, 1.19
effective mass, 1.19
eigenfrequencies, 7.5
eigenvalues, 22.13
eigenvectors, 7.5
expansions, 22.15
elastic axis, 3.22
elastic center, 3.23
elastic couplings, 37.6
elastic foundation, 7.34
elastomer cup mounts, 39.32
elastomeric seismic bearings, 39.43
electrodynamic exciters, 11.23
electrodynamic vibration machines, 25.7
controls for, 26.12, 26.13
electromechanical coupling factor, 1.19
electrostatic shields, 15.2
electrostriction, 1.19
elliptical filters, 13.10, 13.11
elliptical coordinate system, 7.32
elliptic function, first king, 6.23
end dynamic mass, 10.31
endurance limit of metals, 33.12
energy balance method, 37.13
energy dissipation, 6.3
energy-equivalent vibration total value,
41.31
energy functional, 7.2
energy spectral density, 24.4
engines, 37.1
ensemble, 1.19
entrainment of frequency, 4.18
envelope detectors, 16.18
environment:
active, 39.2
aeroacoustic, 18.11, 32.1
as design concern, 40.1
dynamic (summary), 23.9, 39.2
induced, 1.2
natural, 1.22
6 INDEXenvironment (Cont.):
types of, 18.2
wind, 31.1
environmental test specifications, 18.1
equal sensation contours, 41.17
equation condensation, 21.38
equipment design:
practice of, 40.1
for shock, 40.2
for vibration, 40.2
equipment loading effects, 18.12, 40.15
equivalent static acceleration, 20.11
equivalent static force, 20.13
equivalent system, 1.19
equivalent viscous damping, 1.19, 1.26
ergodic process, 1.19
Euler Bernoulli beam theory, 7.19
European Committee for Electrotechnical
Standardization (CENELEC), 17.1
European Committee for Standardization
(CEN), 17.1
excitation:
aeroacoustics, 32.1
definition of, 1.19
engine, 37.11
multiple-axis, 18.18
types of, 18.17, 40.3
experimental modal analysis, 21.1, 21.14
extrapolation procedures, 18.8
failure:
criteria for, 40.6
definition of, 18.13
false alarms, 16.6,
fast Fourier transform (FFT), 14.9, 19.17
fatigue:
acoustic, 32.17
tests for, 33.11, 33.15
fatigue diagram, 33.2
fatigue failure, 40.24
of bone, 41.5
of cartilage, 41.5
model for bone, 41.33
fatigue performance:
of bone, 41.6
of cartilage, 41.6
of composites, 34.15
fault detection in machinery, 16.5
fault diagnosis in machinery, 16.8
FFT (see fast Fourier transform)
FFT analyzers, 14.9
FFT spectrum analysis, 14.9, 14.11, 14.16,
14.22
field calibration techniques, 15.13
filter(s):
bandwidth of, 14.3, 14.4, 19.22, 19.27
definition of, 1.19
digital, 14.2
effective noise bandwidth of, 14.3
high-pass, 1.20
impulsive response of, 14.4
low-pass, 1.21
properties of, 14.3
relative bandwidth of, 14.4
response time of, 14.3
(See also specific filter types)
finite element analysis, 21.47, 32.14, 40.18
finite element method (FEM), 18.7, 23.1,
37.8, 40.18
finite element programs, 23.1
finite impulse response (FIR) filters, 13.9
fixed-reference transducer, 10.2
flattest spectrum rule, 15.4, 16.4
flattop window, 14.14
floating shock platform, 27.10
flow-induced vibration, 30.2, 32.7
fluid bearing instability, 5.2, 5.5, 5.12, 5.22
fluid elastic instability, 30.14
fluid flow, 30.1
in pipes, 30.18
over structures, 30.8, 32.7
fluidic elastomer mounts, 39.32
fluid-structure interaction, 23.5
fluid trapped in the rotor, 5.2, 5.4, 5.9, 5.22
flutter, 31.3
flutter mechanisms, 31.20
flywheel, 6.22
force factor, 1.19
forced motion, 2.23
forced oscillation, 1.19
forced vibration, 1.1, 1.19
forced vibration, 1.1, 1.19, 2.7–2.9, 5.1, 5.2,
5.5, 5.7, 5.10, 5.16, 5.19
forces:
biodynamic, 41.13
feed or thrust, 41.13
grip, 41.13
force transmissibility, 2.7
force transmission, 2.12
forcing frequency, 1.2
FORTRAN, 7.1
forward whirl, 5.4, 5.7, 5.9, 5.12, 5.13, 5.22
foundation, 1.19
motion of, 2.16, 2.26
foundation-induced vibration, 3.42, 40.21
foundation mass, 7.29
INDEX 7Fourier coefficients, 19.4
Fourier integral, 7.6
Fourier series, 7.6, 7.26, 19.4
Fourier spectrum, 20.5
acceleration impulse, 20.6
acceleration step, 20.6
applications, 20.9
complex shock example, 20.9
decaying sinusoidal acceleration, 20.9
examples, 20.7
half-sine acceleration, 20.8
relation to shock response spectrum,
20.13, 20.22
Fourier transform, 14.9
discrete, 19.18, 21.15
finite, 19.4
shock calibration, 11.22
fraction of critical damping, 1.19, 2.5, 6.6,
10.2
relation to Q, 20.14
fracture mechanics, 33.23
free-fall calibration, 15.13
free velocity, 6.3, 6.9
free vibration, 1.1, 1.2, 2.21, 4.6
with damping, 2.5
without damping, 2.3
free vibration problem, 7.5
frequency:
angular, 1.7, 1.16, 2.3
audio, 1.16
circular, 1.16
critical, 32.11
definition of, 1.7, 1.20
entrainment of, 4.18
forcing, 1.2
fundamental, 1.2
natural, 1.22, 2.3
normalized, 32.5
Nyquist, 13.5, 19.18
resonance, 1.24
transversal, 7.26
frequency domain, 19.4, 19.6
frequency equation, 2.21
frequency resolution, 19.22
frequency response function (FRF), 19.9,
20.9, 21.7, 40.25
frequency response procedures, 18.8
frequency sampling, 14.12
frequency weighted acceleration, 41.23
for building vibration, 41.29
for comfort, 41.23
component of, 41.2
frequency weighted acceleration (Cont.):
for hand-arm response, 41.31
for motion sickness, 41.3
for perception, 41.29
sum, 41.28
for whole-body response, 41.23
friction damping, 35.18
fringe-counting interferometer, 11.10
fringe-disappearance interferometer, 11.12
full-bridge configuration, 10.24
functional, 7.2
functional test, 18.16
fundamental frequency, 1.2
fundamental mode of vibration, 1.2
g, definition of, 1.2
gage factor, 10.24
Galerkin series, 7.33
galloping, 31.3
galloping oscillations, 31.3
gaussian distribution, 19.7, 24.3
gearbox, 16.7
geared systems, 37.6
generalized coordinates, 2.22, 2.24, 7.9, 7.1
generalized force, 2.24
generalized foundation, 7.29
generalized mass, 2.24
generators, 17.4
ghost components in vibration spectra, 16.15
Goodman diagram, 33.16
gravity, center of, 1.17, 3.26
grounding, 15.21
ground loops, 15.21
ground motions, 29.1
gust factor, 31.12
Guyan reduction, 23.17
gyro stabilizer, 6.16
half-bridge configuration, 10.24
half-power point, 2.18
Hamilton’s variational principle (HVP), 7.1,
7.2, 23.2
Hamming window, 14.14
hand-arm vibration syndrome (HAVS),
41.16
hand-held accelerometer, 15.12
hand-transmitted vibration:
biodynamic force, 41.13
effects of, 41.16
hand-arm vibration syndrome (HAVS),
41.16
mechanical impedance for, 41.12
8 INDEXhand-transmitted vibration (Cont.):
mechanical resonances, 41.13
numbness, 41.16
physiological response to, 41.17
transmission to shoulder, 41.13
white fingers, 41.16
Hanning window, 14.14
hardening, definition of, 4.2
hardening spring, 19.6
hard failure, 18.13
harmonic, 1.2
harmonic motion, 1.7 (See also simple
harmonic motion)
harmonic response, 1.2
head:
concussion from rotation of, 41.21
injury from shock and impact, 41.18, 41.21,
41.45
mechanical resonances of, 41.8
protective helmets, 41.45
skull fracture, 41.22
skull vibration, 41.13
transmissibility from seat to, 41.8
headroom, 13.4
helical cable, 39.10
helical cable mounts, 39.38
helical isolators, 39.40
heterodyne interferometer, 11.15
HIDAMETS, 35.13
high-acceleration methods of calibration,
11.15
high-deflection elastomer shock mounts,
39.33
high-frequency shock, 27.7
high-impact shock machines, 27.10, 27.11
high-pass filter, 1.20
Hilbert transform, 14.35
homodyne interferometer, 11.15
homogeneous equation solution part, 7.6
Hooke’s law, 4.2
Hopkinson bar, 7.16, 27.10, 28.7
Hopkinson bar calibrator, 11.17
H-type elements, 23.2
human surrogates, 41.3
biofidelity, 41.4
control of objects, 41.22
visual acuity, 41.22
human tissue:
density of, 41.6
elastic moduli of, 41.6
injury by shock and vibration, 41.14, 41.16
mechanical impedance of, 41.13
human tissue (Cont.):
nonlinearity of, 41.5
resistance and stiffness of, 41.5, 41.13
tensile strength of, 41.6
human tolerance criteria:
boundary for severe injury, 41.2, 41.33
boundary for voluntary exposure, 41.33
in buildings, 41.29
comfort, 41.28
hand-arm system, 41.31
head injury criterion, 41.37
health, 41.27
health caution zone, 41.27
motion sickness, 41.3
multiple shocks and impacts, 41.33
survivable single shocks, 41.33
Wayne State concussion tolerance curve,
41.37
hydraulic vibration machines, 25.16, 25.15
hysteresis, 2.16
hysteresis loss, 2.18
hysteretic whirl, 5.2, 5.4, 5.5, 5.22, 16.8
IEC (see International Electrotechnical
Commission)
IEPE (see internal electronic piezoelectric
system)
image impedance, 1.20
impact, 1.20, 38.16, 38.17, 38.27
excitation of, 25.19
with rebound, 38.12, 38.13
without rebound, 38.14
impact-force shock calibrator, 11.20
impedance, 6.3
definition of, 1.20
image, 1.20
of SDOF TVA, 6.5
transfer, 1.25
(See also mechanical impedance)
impedance matrix, 6.5
impulse, 1.2
impulse response function (IRF), 21.7
impulsive response, of filters, 14.4
induced environments, 1.20
inertia:
moment of, 3.15
product of, 3.15
inertial frame of reference, 3.1
inflated membrane, 7.19
initial conditions, 2.4
initial value problem, 7.2
in-plane forces, 7.34
INDEX 9insertion loss, 1.20
instability/instabilities, 5.1
in forced vibrations, 5.2, 5.19, 5.22
parametric, 5.2, 5.16, 5.22
instantaneous line spectrum, 19.12
computation of, 19.26
instantaneous power spectrum, 19.12
computation of, 19.27
interferometer calibrators, 11.10
intermittent monitoring system, 16.2
internal electronic piezoelectric (IEPE)
system, 13.2, 13.3
International Electrotechnical Commission
(IEC), 17.1
International Organization for
Standardization (ISO), 17.1, 20.13
inverse power law, 18.14
ISO (see International Organization for
Standardization)
isochronous system, 4.6
isolation:
analysis methods, 38.3
areas, 38.1, 38.2,
definition of, 1.20
of force, 38.1, 38.3
shock, 38.3–38.6, 38.9
of support motion, 38.1, 38.3, 38.12
system, 38.8, 38.10, 38.11, 38.17, 38.18,
38.23, 38.25, 38.28, 38.31–38.35, 38.38
vibration, 1.3, 38.1, 38.3, 38.29, 38.35, 38.38,
38.39, 39.7
isolators (see shock isolators; vibration
isolators)
jerk, definition of, 1.20
joint acceptance, 30.10
joint acceptance function, 32.11
joints:
bolted, 40.12
damping in, 36.2, 36.9
welded, 24.15, 40.11
jump phenomena, 4.9, 4.41
Kaiser-Bessel window, 14.14
kinematic boundary conditions, 7.3
kinetic energy, 7.8
Kirchhoff’s laws, 7.32
Kryloff’s method, 4.34
Lagrange’s equations, 2.3, 7.2
Lagrangian energy functional, 7.2, 7.3
laminate design, 34.8
Laplace domain, 21.8
Laplace’s equation, 7.19
Laplace variable, 20.13
laser Doppler vibrometer, 10.32
leaf springs, 39.26
leakage, 14.11, 19.19
least squares, 21.16
Leibniz’s rule, 8.14
level, 1.20
life cycle analysis, 40.5
limit cycle, 4.22
linear mechanical impedance, 1.21
linear resilient support, 3.22
linear spring, 7.16
linear system, definition of, 1.21
linear variable differential transformer,
10.35
linear velocity damping, 4.32
line spectrum, 1.21, 19.5, 19.19
load deflection, 39.7
loading, 18.12, 40.15
variable-amplitude, 33.20, 33.23
load system, 6.4
logarithmic decrement, 1.21, 2.6
longitudinal wave, 1.21
loss factor, 24.10, 35.4, 36.3, 36.6, 36.11, 36.12
coupling, 24.16
damping, 24.14
low-cycle fatigue in metals, 33.16
low-pass filter, 1.21, 13.1
lumped mass, 7.16
lumped parameter systems, 2.1, 40.18
machinery:
monitoring of, 16.1
reciprocating, 16.22
rotating, 37.1
types of, 17.4
vibration, 17.3
machinery vibration:
rotating faults, 16.9
spectrum analysis of, 16.17
stationary faults in, 16.9
MacNeal-Rubin reduction, 23.19
magnetic shields, 15.20
magnetic tape recorder, 1.21
magnetoelastic damping, 35.8
magnetostriction, 1.21
maintenance costs, reduction, 36.5
manikin:
anthropometric, 41.4
for crash testing, 41.4
10 INDEXmass, 2.2
center of, 3.14
mass computation, 3.3
mass controlled system, 2.1
mass damping, 2.27
mass loading, 15.13, 40.16
mass-spring transducer (seismic transducer),
10.2
MATEMATICA, 7.1
Mathieu’s equation, 5.16, 4.41
MATLAB, 7.1
matrix:
definition of, 22.2
diagonal, 22.3
identity, 22.3
null, 22.3
spectral, 22.13, 26.6, 26.7
symmetric, 22.4
types of, 22.3
unit, 22.3
zero, 22.3
matrix eigenvalues, 22.13
matrix methods of analysis, 22.1
matrix operations, 22.4
maximum environment, 18.4
maximum expected environment, 18.9, 40.15
maximum transient vibration value, 41.24
maximum value, 1.21
MDOF (see multiple-degree-of-freedom
systems)
mean phase deviation, 21.47
mean-square value, 19.3, 24.3
computation of, 19.25
mean value, 19.3, 24.6
computation of, 19.25
mean wind velocity, 31.5
measurement:
absolute, 11.3
comparison, 11.4
procedures, 21.21, 26.10
synthesis, 21.47
measuring instrument, 10.1
measuring system, 10.1
mechanical circuit theorems, 9.6
mechanical elements, combination, 9.4
mechanical exciters, 11.23
mechanical impedance, 9.1, 1.2, 1.21, 10.3
applications of, 9.12, 40.16
definition of, 9.1
of hand-arm system, 41.12
of human body, 41.8
measurement, 9.11
mechanical impedance (Cont.):
shock source and load, 20.10
of soft tissue, 41.14
mechanical mobility, 9.1, 9.12
mechanical properties of materials:
aluminum alloys, 33.7, 33.8
bone, 41.5
cast iron, 33.11
composites, 34.4
soft tissue, 41.5
steels, 33.5, 33.6
mechanical shock, 1.21
(See also shock)
mechanical 2-ports, 9.1
membranes, 7.1, 7.35
metal matrix composites, 34.2
metals:
ductility in, 33.10
effects of temperature on, 33.8
endurance limit in, 33.12
engineering properties of, 33.1
equipment design using, 40.1
fatigue in, 33.11
physical properties of, 33.2
static properties of, 33.2
tensile strength of, 33.2, 33.8
toughness of, 33.10
metal springs, 39.2
metal strain gage, 12.1
micromachining, 10.26
microstrain, 10.15
Mindlin theory, 7.31
Miner’s rule, 33.21
mixed-mode testing control, 26.19
mixed vibration environments, 19.3
mobility, 6.3, 10.3
mobility matrix, 6.5
modal analysis, 21.1
applied to rotary systems, 37.16
effect of environment, 21.5
measurements in, 21.3
parameter estimation, 21.2
theory of, 21.5
modal complexity, 21.51
modal coupling, 3.27
modal damping, 21.13
modal damping ratio, 7.5
modal data acquisition, 21.15
modal data presentation/validation, 21.46
modal density, 23.9, 24.13
modal excitation, 24.18
modal force, 7.26
INDEX 11modal identification:
algorithms, 21.41, 21.42
concepts, 21.39
models, 21.22
modal mass, 21.13
modal matrices, 22.13
modal modification prediction, 21.47
modal numbers, 1.21
modal overlap factor, 24.11
modal parameter estimation, 21.16
modal phase colinearity, 21.51
modal power potential, 24.11
modal scaling, 21.13
modal superposition, 24.5
modal testing, 21.1
configurations, 21.16
control systems for, 26.30
modal truncation, 23.13
modal vector consistency, 21.49
modal vector orthogonality, 21.48
modal viscous damping factor, 7.5
mode counts, 24.13
model, shock and vibration:
single-degree-of-freedom, 40.2
structural, 40.17
mode natural frequency, 2.24
of rotors, 37.7
modes:
of driven machinery, 37.2
failure, 18.14
identification, 21.41, 21.42
mode shapes, 21.1
modes of vibration, 1.21
fundamental, 1.2
natural frequency of, 1.22
normal, 1.22 (See also modes)
modulation, 1.21
moments, temporal, 28.6
moments of inertia, 3.15
experimental determination of, 3.17, 37.4
polar, 37.3
monitoring of machinery, 16.1
motion:
periodic, 1.1
rigid body, 3.1
rotational, 2.2
transitional, 2.1
undamped, 2.3
motion response, 2.7
motion sickness, 41.3
motion transmissibility, 2.7
motors, 17.4
multical mounts, 39.40
multiple-axis excitation, 18.18, 25.2, 25.20
multiple-degree-of-freedom (MDOF)
systems, 1.21, 2.19, 2.27, 6.2, 21.11
absorber applications, 6.27
multivibrator, 5.20
response of, 24.4
narrowband damping, 6.7
narrowband random vibration, 1.22
natural boundary conditions, 7.3
natural environment, 1.22
natural frequency, 1.22, 2.3, 6.6, 7.8
angular, 2.3
damped, 1.18
undamped, 1.26
of vibration isolators, 39.5
natural mode of vibration, 1.22, 2.22
neoprene, 39.18
neutral surface, 1.22
Newkirk effect, 5.21
Newton’s laws, 7.2
nodal lines, 7.32
node, 1.22
noise, 1.22
background, 1.17
in diesel engine, control of, 36.5
generation of, in cable, 15.19
suppression, 15.2
white, 1.27
nominal bandwidth, 1.22
nominal passband center frequency, 1.22
nominal upper and lower cutoff frequencies,
1.22
nonisochronous system, 4.6
nonlinear damping, 1.22
nonlinear systems, 4.1, 4.8, 23.8, 32.15
nonlinear vibration, 4.1, 4.6, 4.31, 4.32, 4.36,
4.41
nonstationary vibration environment, 18.3,
19.2, 19.11
normal distribution, 24.3
(See also gaussian distribution)
normalizing condition, 2.22
normal mode, 7.6
normal modes of vibration, 1.22, 2.22, 21.1,
24.4
Nyquist frequency, 13.5, 19.17
octave, 1.22
one-dimensional wave equation, 7.4
on-line/off-line monitoring systems, 16.2
12 INDEXorder of disturbance, 6.23
order of vibration, 6.20
orthogonality condition, 2.22
oscillation, 1.22
galloping, 31.2
turbulence-induced, 31.2, 32.7
wake-induced, 31.3
out-of-band energy, 13.14
overall vibration value, 41.28
oversampling, 13.8
parallel, dashpots in, 36.4
parametric instability, 5.2, 5.16, 5.22
partial node, 1.22
particle velocity, 7.16
particular equation solution part, 7.6
passive-circuit type, 10.1
peakness methods, 16.20
peak-to-peak value, 1.22
peak value, 1.22
pendulum, 2.31, 4.2, 4.3
dampers, 37.21
equivalent moment of inertia, 6.22
nonlinear, 4.3
pendulum absorber:
linear vibration, 6.26
types, 6.2, 6.24, 6.25
period, 1.22, 2.3
periodic functions, 19.4
periodic motion, 1.1
periodic quantity, 1.22
permanent monitoring system, 16.2
personal computer (PC), 7.1, 26.2
perturbation method, 4.32
phase angle, 2.4
phase coherent signal, 14.35
phase coherent vibrations, 19.1
phase demodulation, 14.35
phase of periodic quantity, 1.22
picket fence corrections, 14.14
pickup (sensor), 10.1
piezoelectric accelerometers:
calibration of, 11.1
mounting of, 15.5
selection of, 15.4
piezoelectric exciters, 11.23, 25.18
piezoelectricity, 1.23
piezoelectric material, 10.1, 13.2
piezoelectric strain gage, 12.1
piezoelectric vibration exciters, 11.5, 25.18
piezoresistive, 10.1
pipes, fluid flow in, 30.19
plastic damping, 35.5
plastic isolators, 39.10
plates, 1.14, 7.1
lateral vibration of, 1.14
pneumatic-elastomeric mount, 39.37
pneumatic isolators, 39.36
point mass, 2.19
Poisson operator, 7.31
Poisson ratio, 7.17
polar moments of inertia, 37.3
measurement of, 37.4
polar orthotropy, 7.33
polycal mounts, 39.40
polymeric materials, 34.6
polymer matrix composites, 34.1
potential energy, 7.8
power spectral density, 1.23, 14.8
power spectral density function, 18.11, 19.8,
24.3
computation of, 19.22
instantaneous, 19.27
power spectral density level, 1.23
power spectrum, 1.23, 14.8, 14.33
Prandtl’s membrane analogy, 7.17
preventive maintenance, machinery, 16.1
primary shock response spectrum, 20.13
primary standard, 11.3
principal elastic axes, 3.22
principle of minimum complementary
energy, 7.5
principle of minimum potential energy, 7.5
principle of stationary Reissner energy, 7.5
principle of virtual work, 7.2
printed wiring assembly, 40.13
probability density function, 19.6, 24.20
computation of, 19.22
process, 1.23
production test, 18.5
product of inertia, 3.15
experimental determination of, 3.19
propellers, 37.4
propeller whirl, 5.2, 5.5, 5.15, 5.22
proportional damping, 21.12
protection from shock and vibration:
body support and restraints for, 41.41
collapsing structures for crash, 41.41
dynamic preload for crash, 41.45
energy absorption for crash, 41.42
gloves for, 41.41
harnesses for, 41.42
helmets for, 41.45
inflatable air bags for, 41.43
INDEX 13protection from shock and vibration (Cont.):
preventive measures against HAVS,
41.41
vibration-isolation for power tools, 41.4
proximity probe, 10.36
proximity probe transducer, 16.4
pseudo velocity, 40.20
pseudo-velocity response, 20.11
P-type element, 23.2
pulsating longitudinal loading, 5.2, 5.16, 5.18,
5.22
pulsating torque, 5.2, 5.16, 5.22
pulse, 38.1, 38.2, 38.22
acceleration, 38.6, 38.1, 38.11, 38.22
half-sine, 38.6, 38.1, 38.11, 38.13
rectangular, 38.6, 38.1, 38.11, 38.13
versed, 38.1, 38.11
pulse rise time, 1.23
pumps, 17.4
pyroshock:
characteristics of, 28.2
definition of, 28.1, 28.4
measurement techniques, 28.21
simulation of, 28.4, 28.8
testing techniques, 28.11
test specifications for, 28.7
Q (quality factor), 1.23, 2.18, 6.6
quadratic forms, 22.7
qualification test, 18.5, 40.27
quality control test, 18.5
quantization, 19.17
quasi-ergodic process, 1.23
quasi-periodic signal, 1.23
quasi-periodic vibrations, 19.5
quasi-sinusoid, 1.23
quasi-static acceleration, 40.3
quefrency, 14.33
quenching, 4.17
radius of gyration, 3.4
rahmonic, 14.33
rainflow counting method, 33.20
random excitation, 18.17, 40.4, 40.22
by jet and rocket exhausts, 32.3
by turbulent boundary layer, 32.7
by vortices, 31.17
by wind, 31.1
random process:
nonstationary, 19.24
stationary, 19.6
random response, 23.22, 24.2, 40.22
random signal:
broadband, 19.9, 24.2
narrowband, 19.9, 24.2
stationary, 14.19, 19.6
random test, 18.17
random vibration, 1.23
analysis of, 19.21, 24.1
broadband, 1.17
control systems for, 26.15
laboratory test exciters for, 25.7, 25.9
narrowband, 1.22
statistical parameters, 19.6, 24.1
testing, 18.17, 25.2, 25.12
Rayleigh beam theory, 7.17, 7.19
Rayleigh Ritz method, 7.6, 7.9
Rayleigh’s equation, 4.35
Rayleigh’s method, 7.5
Rayleigh’s principle, 7.8
Rayleigh’s quotient, 7.8, 22.16
Rayleigh wave, 1.23
real-time analysis, 14.20
real-time digital analysis of transients, 14.23
real-time frequency, 14.21
real-time parallel filter analysis, 19.22
receptance, 10.3
reciprocating machinery, 16.22, 17.4, 37.1
reciprocity method of calibration, 11.5
recording channel, 1.24
recording system, 1.24
rectangular orthotropy, 7.33, 7.34
rectangular shock pulse, 1.24
rectangular weighting, 14.22
reference standard, 11.4
regular polygonal prismatic shells, 7.36
relaxation oscillations, 4.17
relaxation oscillator, 5.2
relaxation time, 1.24
reliability factor, 10.23
reliability growth test, 18.6, 40.27
reliability test, statistical, 18.6
repetitive motion injury, 41.16
re-recording, 1.24
residual shock response spectrum, 20.13
residues, 21.10
resilient elements, elastic center of, 3.23
resilient supports:
linear, 3.22
orthogonal, 3.36
resonance, 1.24, 2.18
resonance frequency, 1.24
acceleration, 2.18
body organs for, 41.7
14 INDEXresonance frequency (Cont.):
damped natural, 2.18
displacement, 2.18
hands for, 41.13
head for, 41.8, 41.22
spine for, 41.8
velocity, 2.18
resonance gain (Q), 20.13
resonant bar, 28.16, 28.17
resonant-bar calibrator, 11.15
resonant beam, 28.14, 28.17
resonant-beam calibrator, 11.25
resonant magnification, 6.6
resonant plate, 28.11, 28.15
resonant vibration, 5.1, 5.6
resonant whirl, 16.8
response, 1.24
subharmonic, 4.15
superharmonic, 4.10
response curves, 4.7
response minimization, 6.10
response optimization, 6.10
response spectrum, 1.24
alternative for shock response spectrum,
20.11
rigid-body motion, 3.1
ringing, 10.8
Ritz coefficients, 7.9
Ritz method, 4.36, 4.38
riveted joints, 24.16, 40.12
rms value, 19.3
road simulator, 25.21
rods, 7.1
Ross-Kerwin-Ungar (RKU) equations,
36.10, 36.22
rotary accelerator, 27.12
rotary inertia, 7.17
rotating machinery, 17.4, 37.1
condition monitoring of, 16.1
fault detection in, 16.5
rotating table (centrifuge) calibrator, 11.9
rotational mechanical impedance, 1.24
rotational motion, 2.2
rotational speed, low harmonics of, 16.9
safety, in design, 40.8
sampling, 21.20, 26.3
frequency, 14.12
rate of, 19.16, 26.4
theorem, 21.20
scaling, 14.8
scan averaging, 14.24
screening test, 18.6
SDOF (see single-degree-of-freedom
structures; single-degree-of-freedom
systems)
SEA (see statistical energy analysis)
seal-induced instability, 5.2, 5.5, 5.11, 5.22
seats:
cushions, 41.39
protective harnesses for, 41.42
transmissibility of, 41.39
vibration reduction for, 41.39
secondary standard, 11.4
seismic design, 29.13
seismic design spectra, 29.9
seismic energy dissipation devices, 29.15
seismic ground motions, 29.5
seismic inelastic spectra, 29.11
seismic response spectra, 29.6
seismic risk, 29.17
seismic system, 1.24
seismic transducer, 1.24
self-excited vibration, 1.24, 4.17, 5.1
self-generating type, 10.1
semiconductor strain gage, 12.2
sensing element, 1.24
sensitivity, 1.24, 10.21
series, dashpots in, 36.4
servo-controlled isolation systems, 39.1
shafts, 7.1
Shannon’s theorem, 13.5
shape memory damping, 35.6
shear correction factor, 7.3
shear wave, 1.24
shells, 7.1, 7.36
shielding, 15.2
shipboard vibration, 17.6
ship roll reduction, 6.14, 6.15
shock:
acceleration impulse, 20.2
acceleration step, 20.4
complex, 27.5, 27.10
complex motion example, 20.5
control methods, 1.2
data reduction concepts, 20.5
data reduction methods, 20.1, 20.5
data reduction to frequency domain, 20.5
data reduction to response domain, 20.5,
20.10
decaying sinusoidal acceleration, 20.5
definition of, 1.2
displacement, 27.5
Fourier spectrum, 20.6
INDEX 15shock (Cont.):
half-sine acceleration, 20.4
high-frequency, 27.7
laboratory simulation, 20.2
mechanical, 1.21 (See also mechanical
shock)
motion examples, 20.2, 20.3
pyrotechnic, 28.1
response of SDOF systems, 20.10
simple pulse, 27.7
step velocity, 20.2
structural response calculation, 20.2
velocity, 27.5, 27.7, 28.1, 28.2, 28.5, 28.10
(See also mechanical shock)
shock absorber, 1.24
shock and impact exposure:
crash protection for, 41.41
effect of duration, 41.19
examples of, 41.37
flailing of body parts, 41.42
health effects, 41.18
longitudinal accelerations, 41.19
lower extremity injuries, 41.19
neck and spinal injuries, 41.18
soft tissue injuries, 41.18
survivable shocks, 41.33
transverse accelerations, 41.21
whiplash, 41.18
shock calibration, Fourier transform, 11.22
shock calibrator, impact-force, 11.20
shock data analysis, 20.1
digital filter method, 20.2
shock environment, 18.2, 27.1, 40.3
shock excitation, 27.3, 40.21
shock interpretation, 20.1
shock isolation, 38.3–38.6, 38.9
shock isolators, 39.1
response spectra, 39.11, 39.24
selection of, 39.2, 39.4
specification of, 39.8
shock machines, 27.1, 27.3, 27.9, 27.10, 27.12,
28.10
calibration of, 27.3, 27.5
characteristics of, 27.2, 27.3
standards for, 17.3
types of shocks produced by, 27.5
shock motion, 1.24, 20.1
shock pulse, 1.24
duration of, 1.18
shock response spectra (SRS), 20.2, 20.10,
24.3, 27.2, 27.6, 27.10, 28.5, 28.11, 40.21
acceleration impulse, 20.15
acceleration step, 20.15
shock response spectra (SRS) (Cont.):
amplitude scaling, 8.18
calculation, 20.12
complex shock example, 20.20
decaying sinusoidal acceleration, 20.19
definition, 8.17
examples, 20.15
frequency scaling, 8.18
half-sine, 8.2
half-sine acceleration, 20.18
haversine, 8.7, 8.20
impulsive region, 20.21
ISO standard for calculation, 20.13
limiting values, 20.20
maximax, definition, 8.19
noninvertability, 8.18
parameters for, 20.11
positive/negative directions, 20.13
primary, 20.13
pseudo-velocity, definition, 8.2
relation to Fourier spectrum, 20.13, 20.22
residual, 20.13
roll-off, 8.18
square-wave, 8.23
static region, 20.21
triangle, 8.21
wavelet (wavsyn), 8.22
shock response using SEA, 24.20
shock sources, 20.1
shock spectra, 1.24
alternative for shock response spectra, 20.11
shock testing, 27.1, 27.5, 28.10
digital control systems for, 26.18
specifications for, 18.7, 27.1, 27.9, 28.7
standards for, 17.3
shock time history, 20.1
short fiber/particulate composites, 34.2
sideband patterns, 16.15, 19.13
sigma delta, 13.9
signal, 1.25
signal averaging, 21.23
signal conditioning, 13.1
signal enhancement, 14.31
signal processing, digital, 14.1, 14.2,
19.17–19.20, 21.16
signal-nulling interferometer, 11.14
signal-to-noise ratio (S/N), 19.17
simple harmonic motion, 1.7, 1.25
simple pendulum, 4.2
simple spring-mass system, 4.2
sine-sweep tests, 18.4
sine-wave control systems, 26.17
sine-wave test, 18.17
16 INDEXsingle-degree-of-freedom (SDOF)
structures, 8.1
base-excited, 8.3
classical approach, 8.4
convolution integral, 8.11
damping factor, 8.2
force-excited, 8.2
free vibration, 8.4
homogeneous equation, 8.4
impulse response function, 8.12
numerical computation of response, 8.15
particular solution, 8.7
response to complex pulse, 8.15
response to square pulse, 8.11
response to square wave, 8.16
undamped natural frequency, 8.2
single-degree-of-freedom (SDOF) systems,
1.25, 2.3, 2.9, 6.1, 21.6
response of, 24.1, 40.22
singular points, 4.19
sinusoidal excitation methods, 11.15
sinusoidal motion, 1.25
foundation-induced, 3.42
skew coordinate system, 7.32
slip damping, 35.19
snubber, 1.25, 39.42
softening, definition of, 4.2
soft failure, 18.13
sound pressure level, 32.2
sound sources, 32.1
jet and rocket exhausts, 32.3
propellers and fans, 32.6
turbulent boundary layers, 32.7
specialized processors, 26.2
specifications:
environmental, 18.1
test, 18.1 (See also standards)
specific damping energy, 35.2
specifying isolator requirements, 38.5
spectral analysis, 14.1, 16.17, 19.19, 26.6
spectral density functions, 19.8–19.11
spectral matrices, 22.13, 26.6, 26.7
spectrum, 1.25, 18.3
instantaneous, 19.12
line, 1.21, 19.5
maximax, 18.4, 40.15
response, 1.24
(See also specific spectra)
spectrum analysis, speed of, 14.6
nonstationary signals, 14.26
real-time, 14.21
time-window effect in, 14.12
zoom, 14.17, 14.19, 16.16
spectrum analyzers, 14.1
spectrum density, 1.25
spectrum interpretation, 16.8
spherical shells, 7.36
spine:
dynamic response index (DRI) for, 41.20
injury from shock and impact, 41.18, 41.33
mechanical resonances of, 41.8
predicting injury from shock, 41.20, 41.33
spring, 39.2
coil, 39.42
hardening, 19.6
ideal, 2.1
leaf, 39.26
metal, 39.2
parallel combination of, 39.17
selection of, 39.4
series combination of, 39.12
spring-controlled system, 2.1
spring-mass system, 4.2
SRS (see shock response spectra)
stability diagram, 21.28
standard deviation, 1.25, 18.1, 19.3
standards, 17.1
ANSI, 27.4
DOD, 17.6, 37.17
human tolerance to building vibration,
41.29
human tolerance to hand-arm vibration,
41.31
human tolerance to repeated shocks and
impacts, 41.33
human tolerance to vibration, 41.23
international, 17.3
NASA, 17.5
organizations, 17.7
primary, 11.3
terminology, 17.2
testing, 17.5
transfer, 11.4
for vibration, 17.1
for vibration isolators, 17.3
working reference, 11.4
standards laboratories, 11.3
standing wave, 1.25
static deflection, 2.4
stationary deterministic signals, 14.19
stationary faults, 16.9
stationary process, 1.25
stationary random process, 19.1, 24.3
stationary random signals, 14.19
stationary signal, 1.25
stationary vibration environment, 18.3
INDEX 17statistical energy analysis (SEA), 24.1, 24.4,
24.6, 32.13, 32.14
statistical methods of analysis, 24.1
statistical reliability test, 18.6
statistical sampling errors, 19.21
steady-state vibration, 1.1, 1.25
steel, properties of, 33.5, 33.6
stick-slip rubs, 5.2, 5.19, 5.22
stiffness:
asymmetric, 4.5, 4.9
coefficient of, 2.2
definition of, 1.25
dynamic, 1.19
isolators, 39.2
vs. static, 39.12
symmetric, 4.7
torsional, 37.4
strain:
in composites, 34.6
in metals, 33.2
strain gage, 12.1
bridge configurations, 12.9
materials, 12.4
temperature compensation, 12.4
strain-hardening modulus, 33.4
strain-life method, 33.16
strain sensitivity, 10.15
stress, 7.16
stress intensity factor, 33.23
stress-life method, 33.12
stress-strain relationship:
in composites, 34.6
in metals, 33.2
stress-velocity relationship, 27.2, 40.2
stretched string, 4.3
strings, 7.1, 7.35
Strouhal number, 30.9
structural damping, 2.18
uniform, 2.29
structural-gravimetric calibrator, 11.8
structural model, 40.17
structural vibration:
sound-induced, 32.1
vortex-induced, 30.10
wind-induced, 31.1
structure, 7.1
structure mass matrix, 7.9
structure stiffness matrix, 7.9
subharmonic response, 1.25, 4.14, 4.15
subsynchronous components of vibration,
16.8
superharmonic response, 1.25, 4.1, 4.10
survivability, 10.9
swept sine-wave testing, 18.4, 18.17
symbols, 1.5
symmetric stiffness, 4.7
synchronization, 30.10
synchronous averaging, 14.31
system, 7.1
system response distribution, 24.18
TEDS (see transducer electronic data sheet)
temporal moments, 28.6
tensile strength, ultimate, 33.2, 33.8
tension loading of isolators, 39.30
terminology, standards, 17.2
test:
accelerated, 18.15
acoustic, 32.18
durability, 18.16
functional, 18.16
random, 18.17
sine-wave, 18.17
swept-sine-wave, 18.17
test criteria, 18.1
test duration, 18.13
test failures, 18.16, 40.6
test fixture, 18.18, 25.21, 25.1
testing standards, 17.5
test level, 18.7, 18.11
test load, definition of, 25.1
test specifications, 18.1
theory, 7.11
thermoelastic damping, 35.12
three-degrees-of-freedom (3-DOF) system,
2.31
tilting support calibrator, 11.8
time-dependent failure mechanism, 18.13
time domain, 21.7
time history:
analysis of, 19.1
definition of, 1.25
time-varying functions, 19.2
time-window effect, 14.12
Timoshenko beam theory, 7.19
Timoshenko-Gere theory, 7.17
Timoshenko paradox, 7.26
tolerance limit, 18.9
torsional rigidity, 7.17
torsional spring, 7.16
torsional vibration, 7.11
in machinery, 37.1
model of, 37.2
testing, 37.18
18 INDEXtorsion loading of isolators, 39.33
total least squares (TLS), 21.16
traceability of calibrations, 11.2
tracking analysis, 14.27
trajectories, 4.22, 4.28, 4.34
transducer:
cables for, 15.18
definition of, 1.25
displacement, 16.4
frequency response, 11.1
hand-held, 15.12
mountings for, 15.5, 15.1
selection of, 15.4, 16.4
sensitivity, 11.1
torque, 37.18
torsional, 37.4
velocity-type, 16.4
transducer calibration, 11.1
ballistic pendulum method of, 11.18
centrifuge method of, 11.9
comparison method, 11.4, 15.13
drop-ball method, 11.19
earth’s gravitational method, 11.8, 15.14
electrodynamic exciter method, 11.23
field methods, 15.13
Fourier transform method, 11.22
free-fall method, 15.13
heterodyne interferometer method, 11.15
high-acceleration method, 11.15
impact-force shock method, 11.20
interferometer method, 11.10
inversion method, 15.14
pendulum calibrator method, 11.8
reciprocity method, 11.5
rotating table method, 11.8
shaker excitation method, 11.23
shock excitation method, 11.20
signal-nulling interferometer method,
11.14
sinusoidal-excitation method, 11.15
structural-gravimetric method, 11.8
techniques, 15.13
tilting-support method, 11.8
transfer function method, 11.5
vibration exciter method, 11.22
transducer electronic data sheet (TEDS),
13.3
transducing element, 10.1
transfer function, SDOF system, 20.13
transfer impedance, 1.25, 10.29
transfer matrix method, 7.7, 7.27, 37.7
transfer standard, 11.4
transient analysis, 14.22, 24.20
transient response, 24.20
transient vibration, 1.1, 1.25
translational motion, 2.1
transmissibility:
calculation, 2.9
force, 2.7, 2.12
motion, 2.7
from seat to head, 41.8
transmission loss, 1.25
transportation environments, 17.4, 18.14,
40.5
transpose of a matrix, 22.3
transversal frequency, 7.26
transverse sensitivity, 11.24
transverse wave, 1.26
trend analysis, 16.7, 16.23
triboelectricity, 15.19
tuned damper, 1.1
tuned mass damper, 6.1
tuned resonant fixtures, 28.13
tuned vibration absorber (TVA), 6.1
semiactive/active, 6.31
turbulence, excitation by, 32.7
turbulence-induced oscillations, 31.2
TVA (see tuned vibration absorber)
two-degrees-of-freedom (2-DOF) system,
37.12
two-stage snubbing, 39.18
ultimate tensile strength, 33.2, 33.8
ultra-subharmonic response, 4.12, 4.14
unbalance, centrifugal machinery, 6.16
sources of, 37.1, 37.10
uncoupled mode, 1.26
undamped motion, 2.3
undamped natural frequency, 1.26, 20.13
unified matrix polynomial approach, 21.42
uniform beams, 7.24
uniform mass damping, 2.27, 2.29
uniform structural damping, 2.29
uniform viscous damping, 2.27
United States National Committee of the
International Electotechnical
Commission (USNC/IEC), 17.1
unit step function, 20.4
unstable imbalance, 5.2, 5.20
upsampling, 13.12
U-tube, 2.32
Van der Pol’s equation, 4.17, 4.33,
variable-amplitude loading, 33.13
INDEX 19variance, 1.26, 19.3, 24.6
computation of, 19.17
for nonstationary data, 19.1
variation operator, 7.2, 7.3
vector cancellation method, 37.20
vehicle vibration, 18.15, 25.21
discomfort from, 41.28
velocity, 1.26
velocity pickup, 1.26, 16.4
velocity response, 2.1
velocity shock, 3.51, 27.5, 27.7, 28.1, 28.2,
28.5, 28.10
(See also mechanical shock)
velocity-squared damping, 4.33
vibration:
ambient, 1.16
back pain and, 41.16
body-induced, 3.47
chronic effects from, 41.16
classification, 19.1, 40.3
comfort in public transportation, 41.28
complex, 1.17
control methods, 1.2
coordinate axes for, 41.26
definition of, 1.26
deterministic, 1.1
discomfort from, 41.17, 41.28
effect on task performance, 41.22
effect on visual acuity, 41.22
effects on manual control, 41.22
equipment design to withstand, 40.1
flow-induced, 30.2, 32.7
forced, 1.1, 1.19, 2.7–2.9, 5.1, 5.2, 5.5, 5.7,
5.10, 5.16, 5.19
foundation-induced, 3.42
free, 1.1, 1.2, 2.2, 4.6
health caution zone, 41.27
health effects from, 41.16
longitudinal, 41.7
measurement of, 41.23
mechanical damage from, 41.15
mechanical impedance for, 41.8, 41.12
motion sickness from, 41.3
nonlinear, 4.1, 4.6
periodic, 1.1
physiological responses to, 41.7
random, 1.1
self-excited, 4.17, 5.1
ship, 17.6
skull, 41.13
sound-induced, 32.1
steady-state, 1.1, 1.25
vibration (Cont.):
subsynchronous components, 16.8
systems with damping, 22.21
systems without damping, 22.18
thorax-abdomen subsystem, 41.9
transient, 1.1, 1.25
transmissibility from seat to head, 41.8
transverse, 41.11
vortex-induced, 30.1, 30.8, 30.10, 31.2
wave-induced, 30.6
white fingers, 41.16
wind-induced, 31.1
vibration absorber, activated, 6.31
vibration acceleration, 1.26
vibration acceleration level, 1.26
vibration amplitude, 5.1, 5.3, 5.6, 5.16, 5.20
control of, 36.1, 36.5, 36.11, 36.17
vibration analysis:
cepstrum, 16.19
envelope, 16.18
peakness, 16.20
techniques, 16.17
vibration data analysis, 19.1
vibration dose value (VDV), 41.24
vibration environment, 18.2
vibration exciters, 25.1, 25.15
electrodynamic, 11.23, 25.7
hydraulic, 25.16
impact, 25.19
mechanical, 11.23, 25.2
piezoelectric, 11.23, 25.18
vibration exposure,
acceptability of buildings, 41.29
hand/arm, 41.16, 41.31, 41.4
health caution zone for, 41.27
maximum transient vibration value for,
41.24
overall vibration value for, 41.28
running rms acceleration for, 41.23
total daily exposure, 41.28
transient events, 41.23
vibration dose value for, 41.24
vibration total value for, 41.31
for whole body, 41.15, 41.23, 41.39
vibration isolation:
efficiency of, 39.7
function of, 1.3
theory, 38.1, 38.3, 38.29, 38.35, 38.38, 38.39
vibration isolation systems for seats, 41.39
active, 39.3
semiactive, 39.3
servo-controlled, 39.1
20 INDEXvibration isolators:
air, 39.8
applications for, 39.1
coil spring, 39.42
commercial, 39.1
damping characteristics of, 39.26
definition of, 1.26
dynamic stiffness, 39.2
elastomeric, 39.1, 39.27
fail-safe installation, 39.2
fatigue failure in, 39.27
helical cable, 39.10
installation of, 39.26
leaf, 39.26
location of, 39.13
materials for, 39.26
metal spring, 39.2
natural frequency of, 39.5
plastic, 39.10
pneumatic, 39.36
selection of, 39.1
service life, 39.34
shear loading of, 39.13
specifications for, 39.2
standards for, 17.3
static stiffness of, 39.12
stiffness of, 39.2
tension loading of, 39.30
torsion loading of, 39.33
types of, 39.26
vibration machines, 25.1
circular motion machine, 25.4
direct-drive, 25.2
electrodynamic, 25.7
hydraulic, 25.16
impact, 25.19
piezoelectric, 25.18
reaction type, 25.4
rectilinear, 25.5
vibration measurements, 15.1
considerations in, 15.3
data sheets for, 15.22
false alarms in, 16.6
field calibration techniques in, 15.13
on soft tissue, 41.3, 41.23
parameters for, 15.2, 16.4
planning of, 15.1
techniques in, 15.1
time interval between measurements, 16.5
torsional, 37.18
transducer locations for, 16.5
transducer selection in, 15.4
vibration measurement system:
calibration of, 15.14
wiring considerations for, 15.18
vibration meter, 1.26
vibration monitoring of machinery, 16.1
vibration problems, matrix forms of, 22.9
vibration spectra:
of machinery, 16.17, 16.8
sideband patterns, 16.17
vibration standards, 17.1
for exposure to building vibration, 41.28
for exposure to multiple shocks, 41.33
for whole-body exposure, 41.23
vibration test codes, 17.1
vibration testing, 18.4, 25.1, 40.26
criteria for, 18.1
digital control systems for, 26.15
duration of, 18.13
magnitude of, 18.11
multiple-exciter applications, 25.2, 25.20,
26.11, 26.24
specifications, 18.1
vibration troubleshooting in machinery,
16.10, 16.14
vibrograph, 1.26
virtual mass effect, 30.1
virtual work, 23.2
viscoelastic damping, 35.10, 36.2, 36.8, 36.9,
36.13
viscous damping, 1.26, 2.5, 2.9, 4.3, 4.4, 7.1,
36.13–36.15
equivalent, 1.19
uniform, 2.27
viscous damping coefficient, 6.7
voltage sensitivity, 10.21
voltage substitution method, 15.16
volume-stress function, 35.16
vortex shedding, 30.8, 30.10, 31.15
vortex-induced oscillation, 31.15
wake buffeting, 31.2
wake-induced oscillation, 31.3
warping function, 7.17
waterfall plot, 14.26, 19.25
wave, 1.27
wave, compressional, 1.17
wave interference, 1.27
wavelength, 1.27
wave number, 32.5
wave propagation, 7.17
Wayne State concussion tolerance curve,
41.37
INDEX 21weighting, rectangular, 14.13
weighting functions, 21.39
for spectrum averaging, 14.22
welded joints, 24.15, 40.11
Wheatstone bridge with equations, 12.7
whip:
dry friction, 5.2, 5.5, 5.11, 5.19, 5.22
fluid bearing, 5.2, 5.5, 5.12, 5.22
whipping in rotating shafts, 5.2, 5.22
whirl:
propeller, 5.2, 5.5, 5.15, 5.22
resonant, 16.8
in rotating shafts, 5.2, 5.22
speed/frequency, 5.4, 5.6, 5.8, 5.10, 5.12,
5.16, 5.17, 5.22
white fingers, 41.16
predicting development of, 41.31
white noise, 1.27
Wigner distribution, 19.12
wind:
characteristics of, 31.4
fluctuating components of, 31.6
wind (Cont.):
gradient, 31.5
gustiness of, 31.7
mean velocity, 31.5
wind-induced vibration, 31.1
windows, 14.11, 14.13, 14.15
Hanning, 14.14
working reference standard, 11.4
workstations, 26.2
yield strength, metals, 33.2
zero acceleration output, 10.11
zero-offset, 10.11
zero output bias, 10.11
zero shift, 10.9
zone, 18.9
zone limit, 18.9
zoom analysis, 14.16
zoom FFT analysis, 14.23
zoom spectrum, 16.15
z-transform, SDOF response, 20.14
22 INDEX

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