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 |  موضوع: كتاب Engineering Vibration Analysis with Application to Control Systems الخميس 03 مايو 2012, 12:48 am | |
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أحضرت لكم كتاب
Engineering Vibration Analysis with Application to Control Systems
C. F. Beards BSc, PhD, C Eng, MRAeS, MIOA
Consultant in Dynamics, Noise and Vibration
Formerly of the Department of Mechanical Engineering
Imperial College of Science, Technology and Medicine
University of London
و المحتوى كما يلي :
Contents
Preface xi
Acknowledgements xiii
General notation xv
1 Introduction 1
2 The vibrations of systems having one degree of freedom
Free undamped vibration
2.1.1 Translational vibration
2.1.2 Torsional vibration
2.1.3 Non-linear spring elements
2.1.4 Energy methods for analysis
Free damped vibration
2.2.1 Vibration with viscous damping
2.2.2 Vibration with Coulomb (dry friction) damping
2.2.3 Vibration with combined viscous and Coulomb damping
2.2.4 Vibration with hysteretic damping
2.2.5 Energy dissipated by damping
Forced vibration
2.3.1 Response of a viscous damped system to a simple harmonic
exciting force with constant amplitude
2.3.2 Response of a viscous damped system supported on a
foundation subjected to harmonic vibration
55 viii Contents
2.3.2.1 Vibration isolation 56
Response of a Coulomb damped system to a simple harmonic
exciting force with constant amplitude 69
Response of a hysteretically damped system to a simple harmonic
exciting force with constant amplitude 70
Response of a system to a suddenly applied force 71
Shock excitation 72
Harmonic analysis 74
Random vibration 77
2.3.8.1 Probability distribution 77
2.3.8.2 Random processes 80
2.3.8.3 Spectral density 84
The measurement of vibration 86
3 The vibrations of systems having more than one degree of freedom 88
The vibration of systems with two degrees of freedom 92
3.1.1 Free vibration of an undamped system 92
3.1.2 Free motion 94
3.1.3 Coordinate coupling 96
3.1.4 Forced vibration 102
3.1.5 The undamped dynamic vibration absorber 104
3.1.6 System with viscous damping 113
The vibration of systems with more than two degrees of freedom 115
3.2.1 The matrix method 115
3.2.1.10rthogonality of the principal modes of vibration 118
3.2.2 The Lagrange equation 121
3.2.3 Receptances 125
3.2.4 Impedance and mobility 135
4 The vibrations of systems with distributed mass and elasticity 141
Wave motion 141
4.1.1 Transverse vibration of a string 141
4.1.2 Longitudinal vibration of a thin uniform bar 142
4.1.3 Torsional vibration of a uniform shaft 143
4.1.4 Solution of the wave equation 144
Transverse vibration 147
4.2.1 Transverse vibration of a uniform beam 147
4.2.2 The whirling of shafts 151
4.2.3 Rotary inertia and shear effects 152
4.2.4 The effects of axial loading 152
4.2.5 Transverse vibration of a beam with discrete bodies 153
4.2.6 Receptance analysis 155
The analysis of continuous systems by Rayleigh's energy method 159
4.3.1 The vibration of systems with heavy springs 159
4.3.2 Transverse vibration of a beam 160 Contents ix
4.3.3 Wind or current excited vibration
4.4 The stability of vibrating systems
4.5 The finite element method
5 Automatic control systems
5.1 The simple hydraulic servo
5.1.1 Open loop hydraulic servo
5.1.2 Closed loop hydraulic servo
5.2.1 Derivative control
5.2.2 Integral control
5.3 The electric position servomechanism
5.3.1 The basic closed loop servo
5.3.2 Servo with negative output velocity feedback
5.3.3 Servo with derivative of error control
5.3.4 Servo with integral of error control
5.2 Modifications to the simple hydraulic servo
5.4 The Laplace transformation
5.5 System transfer functions
5.6 Root locus
5.6.1 Rules for constructing root loci
5.6.2 The Routh-Hurwitz criterion
5.7 Control system frequency response
5.7.1 The Nyquist criterion
5.1.2 Bode analysis
6 Problems
6.1 Systems having one degree of freedom
6.2 Systems having more than one degree of freedom
6.3 Systems with distributed mass and elasticity
6.4 Control systems
7 Answers and solutions to selected problems
Bibliography 419
Index
Index
absorber, dynamic vibration, 104, 128, 296
acceleration feedback, 315
accelerometer, 315
amplitude frequency response, 49, 106
asymptotes, 231
auto-correlation function, 80
automatic control systems, 2, 6, 171
axial loading, 152
beam equation, 148
beam,
hinged structure, 156
transverse vibration, 147
with axial load, 152
with discrete bodies, 153
block diagram, 6, 172
Bode analysis, 271
Bode diagram, 184, 272, 325
breakaway points, 233
break frequency, 274
bridge vibration, 285
building vibration, 26
cantilever, 163
characteristic equation, 93
closed loop, 180, 192, 194, 195
electric servo, 194, 195, 311,313
hydraulic servo, 180, 192, 311
system, 172
transfer function, 225
with feedback, 192
column matrix, 116
complex modulus, 42
complex roots, 231,234
complex stiffness, 42
compressibility, 312
computer control, 172
conservative system, 169
continuous systems, 141,309
co-ordinate coupling, 96
co-ordinate generalised, 122
corner frequency, 274
Coulomb damping, 69
equivalent viscous, 43, 44
critical speed, 103, 151
critical viscous damping 30, 284
cross receptance, 125
damping,
combined viscous and Coulomb, 40
Coulomb (dry friction), 37, 69
critical viscous, 30, 284
energy dissipated, 43
equivalent viscous, 43, 44, 45
factor, 248, 251
free vibration, 28
hysteretic, 68, 70
joints, 34
ratio, 30, 65, 241,246, 248
root locus study of, 37
viscous, 29, 46, 55, 67
dead zone, 38 424 Index
decay, 31,32
delta function, 73
derivative control, 185
derivative of error control servo, 185
design, 2
direct receptance, 125
D-operator, 37,71
dry friction damping, 37, 69
Duhamel integral, 74
Dunkerley's method, 153
dynamic magnification factor, 49
dynamic vibration absorber, 104, 128, 296
earthquake model, 100
effective mass, 52
Eigenvalue, 117
Eigenvector, 117
electric servo, 194, 195, 199, 203, 207, 239, 313
energy dissipated by damping, 43
energy methods, 19
ensemble, 77
equations of motion, 8
ergodic process, 79
Euler buckling load, 166
excitation, 54
periodic, 74
shock, 72
fatigue, 2
feedback, 172
final value theorem, 223
finite elements, 170
flexibility matrix, 171
flow equation, 179
fluid leakage, 312
force,
suddenly applied, 71,176, 192, 199, 287
transmitted, 56
forced vibration, 46, 102, 288, 190
foundation vibration, 55
Fourier series, 75
frame vibration, 158
free motion, 94
free vibration,
damped, 28
undamped, 11, 92
frequency,
bandwidth, 65
corner, 274
equation, 93, 227, 229, 230
natural, 88
response of control system, 255
gain margin, 259, 325
Gaussian process, 80
geared system torsional vibration, 17
generalised co-ordinate, 122
half power points, 64
harmonic analysis, 74
hydraulic servo, 178, 185, 188, 311
hysteretic damping, 41, 68
equivalent viscous, 45
impedance, 135, 308
impulse, 73, 176
influence coefficient, 117, 305
integral control, 188
integral of error control, 207
isolation, 54, 56, 58, 62, 124, 287
iteration, 117
Kennedy-Pancu diagram, 68
Lagrange equation, 115, 121, 301, 304
Lanchester damper, 108
Laplace,
operator, 222
transformation, 221
transforms, list of, 222
logarithmic decrement, 31
longitudinal vibration, 142, 309
loss factor, 42, 43
machine tool vibration, 5, 113, 297
magnification factor, 49
margin gain, 259, 325
margin phase, 259, 325
mathematical model, 3
matrix method for analysis, t 15
mobility, 135, 308
mode of vibration, 93, 118, 141,295
model parameter, 7
modelling, 3
multi degree of freedom system, 88, 115,
292
narrowband process, 84
natural frequency, 88
negative output velocity feedback, 203
node, 21
noise, 1
non-linearities, 8
notation, xiii
Nyquist,
criterion, 255, 323
diagram, 68, 256 Index 425
open loop,
hydraulic servo, 178,311
system, 172
transfer function, 225
orthogonality of principal modes, 118
output velocity feedback, 203, 313, 314, 315
overshoot, 177, 196,
periodic excitation, 46, 74
phase frequency response, 49
phase lag network, 325
phase lead network, 326
phase margin, 259, 325
pole, 228
portal frame analysis, 158
power amplifier, error actuated, 178
primary system, 104
principal modes, 141
probabalistic quantity, 77
probability,
distribution, 77
density function, 78
Q-factor, 51, 63, 285
ramp input, 176, 183, 196
random,
variable, 77
vibration, 77
Rayleigh's method, 159, 309, 311
reaction time, 171
receptance, 125, 155, 306
cross, 125
direct, 125
reciprocating unbalance, 51
reciprocity principle, 127
relative stability, 259
remote position control, 178
resonance, 251
Reynold's number, 168
root locus, 43, 228, 318
rules, 230
summary, 236
rotary inertia and shear, 152
rotating unbalance, 51,288
Routh-Hurwitz, 242, 321
s-plane, 114, 227, 241
servo, electric position, 194, 195, 239, 313
comparison of main forms, 210
response to sudden load, 199
with derivative of error control, 207
with integral of error control, 207
with output velocity feedback, 203
servo, simple hydraulic, 178
closed loop, 180, 192, 311
open loop, 178
with derivative control, 185
with integral control, 188
shaft, stepped, 17
shear frame, 90,293
shock excitation, 72
single degree of freedom system, 11, 159,
280
sinusoidal input, 183, 196
spectral density, 84
spool valve, 178
springs,
elastic soil, 27
heavy, 159
in parallel, 15
in series, 14
non-linear, 18
square wave, 75
stability,
absolute, 259
of control systems, 208, 218, 228, 242,
318
of vibrating systems, 169, 228, 242, 318
relative, 259
stable response, 28
standard deviation, 80
stationary process, 79
steady state error, 176, 183, 187, 194, 196,
207, 208, 215, 223
step input, 176, 182, 195
stiffness,
complex, 42
equivalent torsional, 17
string vibration, 141
Strouhal number, 167
structure, conservative, 169
subsystem analysis, 127
sweeping matrix, 120
system,
closed loop, 172
open loop, 172
matrix, 116
time constant, 181
torsional vibration, 15, 143
geared systems, 17
trailer motion, 103, 281, 291
transfer function,
closed loop, 225
open loop, 225
system, 173, 224, 312
transient motion, 48 426 Index
translation vibration, 11
with rotation, 96, 293
transmissibility, 56, 289, 290, 292
frequency response, 57
transverse beam vibration, 147, 160
axial load, 152
with discrete bodies, 153
transverse string vibration, 141
two degree of freedom system, 89, 92
dynamic absorber, 104
forced, 102
free undamped, 92
viscous damped, 104, 113
unstable response, 115,
vibration,
beam, 147
hinged, 156
bridge, 285
buildings, 26
combined viscous and Coulomb
damping, 40
continuous system with distributed mass,
141
Coulomb (dry friction) damping, 69
decay, 31, 32
distributed mass systems, 141, 309
dynamic absorber, undamped, 104, 128,
296
floor, 61
foundation, 55
forced, 46, 102
forced, damped, 46,69, 290
free damped, 28
free, undamped, torsional, 15
free, undamped, torsional, geared system,
17
free, undamped, translation, 11
hysteretic damping, 68, 70
isolation, 54, 56, 58, 62, 124, 287
longitudinal bar, 142, 309
machine tool, 5, 113, 297
mode of, 93, 118
measurement, 86, 289
multi degree of freedom system, 88, 115,
292
principal mode, 141
random, 77
rotation with translation, 96
single degree of freedom, 10, 11, 159, 280
systems with heavy springs, 159
systems stability, 115
torsional vibration of shaft, 143
transverse beam, 147, 160
with discrete bodies, 153
transverse string, 141
two degrees of freedom systems, 88, 92
viscous damping, 29, 55, 284
vibrometer, 87, 288
viscous damped system with vibrating
foundation, 55
viscous damping, 29, 67, 113
critical, 30
equivalent coefficient, 43, 45
ratio, 30, 65
vortex shedding, 167
wave,
equation, 144
motion, 141
wheel shimmy, 228
whirling of shafts, 151
white noise, 84
wide band process, 84
wind excited oscillation, 167
zero, 228 Notes
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