Admin مدير المنتدى
عدد المساهمات : 19002 التقييم : 35506 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
| موضوع: كتاب Advanced Mechanical Vibrations - Physics, Mathematics and Applications السبت 10 أبريل 2021, 1:28 am | |
|
أخوانى فى الله أحضرت لكم كتاب Advanced Mechanical Vibrations Physics, Mathematics and Applications Paolo Luciano Gatti
و المحتوى كما يلي :
Contents Preface xi Acknowledgements xiii Frequently used acronyms xv 1 A few preliminary fundamentals 1 1.1 Introduction 1 1.2 Modelling vibrations and vibrating systems 1 1.3 Some basic concepts 3 1.3.1 The phenomenon of beats 5 1.3.2 Displacement, velocity, acceleration and decibels 6 1.4 Springs, dampers and masses 8 2 Formulating the equations of motion 13 2.1 Introduction 13 2.2 Systems of material particles 14 2.2.1 Generalised co-ordinates, constraints and degrees of freedom 15 2.3 Virtual work and d’Alembert’s principles – Lagrange and Hamilton equations 16 2.3.1 Hamilton’s equations (HEs) 20 2.4 On the properties and structure of Lagrange’s equations 24 2.4.1 Invariance in the form of LEs and monogenic forces 24 2.4.2 The structure of the kinetic energy and of Lagrange equations 24 2.4.3 The energy function and the conservation of energy 28 2.4.4 Elastic forces, viscous forces and Rayleigh dissipation function 29viii Contents 2.4.5 More co-ordinates than DOFs: Lagrange’s multipliers 32 2.5 Hamilton’s principle 34 2.5.1 More than one independent variable: continuous systems and boundary conditions 38 2.6 Small-amplitude oscillations 44 2.7 A few complements 48 2.7.1 Motion in a non-inertial frame of reference 48 2.7.2 Uniformly rotating frame 51 2.7.3 Ignorable co-ordinates and the Routh function 53 2.7.4 The Simple pendulum again: a note on non-small oscillations 56 3 Finite DOFs systems: Free vibration 59 3.1 Introduction 59 3.2 Free vibration of 1-DOF systems 59 3.2.1 Logarithmic decrement 65 3.3 Free vibration of MDOF systems: the undamped case 67 3.3.1 Orthogonality of eigenvectors and normalisation 68 3.3.2 The general solution of the undamped free-vibration problem 70 3.3.3 Normal co-ordinates 72 3.3.4 Eigenvalues and eigenvectors sensitivities 78 3.3.5 Light damping as a perturbation of an undamped system 80 3.3.6 More orthogonality conditions 82 3.3.7 Eigenvalue degeneracy 83 3.3.8 Unrestrained systems: rigid-body modes 84 3.4 Damped systems: classical and non-classical damping 87 3.4.1 Rayleigh damping 88 3.4.2 Non-classical damping 90 3.5 GEPs and QEPs: reduction to standard form 92 3.5.1 Undamped Systems 93 3.5.2 Viscously damped systems 94 3.6 Eigenvalues sensitivity of viscously damped systems 96 4 Finite-DOFs systems: Response to external excitation 99 4.1 Introduction 99 4.2 Response in the time-, frequency- and s-domains: IRF, Duhamel’s integral, FRF and TF 100Contents ix 4.2.1 Excitation due to base displacement, velocity or acceleration 105 4.3 Harmonic and periodic excitation 107 4.3.1 A few notes on vibration isolation 110 4.3.2 Eccentric excitation 112 4.3.3 Other forms of FRFs 114 4.3.4 Damping evaluation 116 4.3.5 Response spectrum 117 4.4 MDOF systems: classical damping 120 4.4.1 Mode ‘truncation’ and the mode-acceleration solution 122 4.4.2 The presence of rigid-body modes 125 4.5 MDOF systems: non-classical viscous damping, a state-space approach 126 4.5.1 Another state-space formulation 129 4.6 Frequency response functions of a 2-DOF system 133 4.7 A few further remarks on FRFs 137 5 Vibrations of continuous systems 139 5.1 Introduction 139 5.2 The Flexible String 140 5.2.1 Sinusoidal waveforms and standing waves 142 5.2.2 Finite strings: the presence of boundaries and the free vibration 143 5.3 Free longitudinal and torsional vibration of bars 148 5.4 A short mathematical interlude: Sturm–Liouville problems 150 5.5 A two-dimensional system: free vibration of a flexible membrane 156 5.5.1 Circular membrane with fixed edge 158 5.6 Flexural (bending) vibrations of beams 162 5.7 Finite beams with classical BCs 163 5.7.1 On the orthogonality of beam eigenfunctions 167 5.7.2 Axial force effects 168 5.7.3 Shear deformation and rotary inertia (Timoshenko beam) 170 5.8 Bending vibrations of thin plates 174 5.8.1 Rectangular plates 176 5.8.2 Circular plates 180 5.8.3 On the orthogonality of plate eigenfunctions 181 5.9 A few additional remarks 182x Contents 5.9.1 Self-adjointness and positive-definiteness of the beam and plate operators 182 5.9.2 Analogy with finite-DOFs systems 185 5.9.3 The free vibration solution 188 5.10 Forced vibrations: the modal approach 190 5.10.1 Alternative closed-form for FRFs 199 5.10.2 A note on Green’s functions 201 6 Random vibrations 207 6.1 Introduction 207 6.2 The concept of random process, correlation and covariance functions 207 6.2.1 Stationary processes 212 6.2.2 Main properties of correlation and covariance functions 214 6.2.3 Ergodic processes 216 6.3 Some calculus for random processes 219 6.4 Spectral representation of stationary random processes 223 6.4.1 Main properties of spectral densities 227 6.4.2 Narrowband and broadband processes 229 6.5 Response of linear systems to stationary random excitation 232 6.5.1 SISO (single input–single output) systems 233 6.5.2 SDOF-system response to broadband excitation 236 6.5.3 SDOF systems: transient response 237 6.5.4 A note on Gaussian (normal) processes 239 6.5.5 MIMO (multiple inputs–multiple outputs) systems 241 6.5.6 Response of MDOF systems 243 6.5.7 Response of a continuous system to distributed random excitation: a modal approach 245 6.6 Threshold crossing rates and peaks distribution of stationary narrowband processes 249 Appendix A: On matrices and linear spaces 255 Appendix B: Fourier series, Fourier and Laplace transforms 289 References and further reading 311 Index 31 Index accelerance 114, 138 acceleration 6 accelerometer 7 action integral 34 amplitude 3 complex 4 peak 3 angular frequency 3 asymptotically stable system 64 base excitation 105–106 basis 261 orthonormal 264–267 beams 162–167 axial-force effects 168–170 Euler-Bernoulli 163, 187, 197 Timoshenko 163, 170–174 Rayleigh 173 shear 172 beats 5–6, 76 biorthogonality 275 bode diagram 108 boundary condition (BC) 40, 143 geometric (or imposed) 40 natural (or force) 40 boundary-value problems (BVP) 150 broadband process 230–232 BVP see boundary-value problem Caughey series 89 Cholesky factorisation 83 Christoffel symbol 27 Clapeyron’s law 30 complete orthonormal system 154 condition number 287 configuration space 93 constraint bilateral16 equations 15 forces 16, 33 holonomic 15 non-holonomic 15 rheonomic 15 scleronomic 15 unilateral 16 continuous system 2 convolution 101, 225, 298 co-ordinates Cartesian 15 generalised 15 ignorable (or cyclic) 53 correlation function 209, 214–216 correlation matrix 241 covariance function 209, 214–216 critically damped system 62 dashpot 9 d’Alembert solution 141, 310 damping classical 87–90, 120–122 coefficient 9 critical 61 evaluation 116–117 matrix 47 non-classical 90–92, 126–133 light damping perturbation 80–81 ratio 61 decibel 7–8 degree of freedom (DOF) 2, 16 deterministic vibration 2 differential eigenvalue problem 186 dirac delta ‘function’ 300–304 discrete system 2318 Index displacement 6 Duhamel integral 101 DOF see degree of freedom dynamic coupling 77 dynamic magnification factor 107 dynamic potential 27 eccentric excitation 112–114 eigenfunction 145, 151 eigenvalue 67, 145, 151, 274 degeneracy 68, 83, 278 sensitivity 78–81, 96–97 eigenvector 67, 274 left 130, 275 right 130, 275 sensitivity 78–81 energy function 28 kinetic 18 potential 19 strain 30 ensemble 211 equation Bessel 159, 180 Helmholtz 157 ergodic random process 216–219 Euler’s buckling load 169 Euler relations 3 extended Hamilton’s principle 36 flexibility (or compliance) 9 force conservative 18 elastic 29–30 fictitious 50, 53 generalised 18 gyroscopic 27 inertia 19 monogenic 24 nonconservative 19 viscous 30–32 forced vibration 48 SDOF systems 100–103, 107–110 continuous systems 190–199 Fourier coefficients 289 series 289–294 transform 294–300 free vibration 48 SDOF systems 59–65 MDOF systems 67–68, 70–72 continuous systems 148–150, 156–167, 174–181, 188–190 frequency 3 equation 67, 144 fundamental 67, 289 natural 60 of damped oscillation 62 ratio 102 frequency response function (FRF) 102–103, 114–116, 137–138, 199–201 estimate 235 estimate 235 modal 121, 192, 244 FRF see frequency response function function Bessel 159, 180 coherence 236 complementary 99 Green 201–205 harmonic 3 Heaviside 302 periodic 109, 289 weight 151 Gaussian (or normal) processes 239–241 generalised momenta 20 generalised potential 24 generalised eigenvalue problem (GEP) 68, 92–96, 274 Gibbs’ phenomenon 294 Gram-Schmidt orthonormalisation process 267–268 Green’s formula 151 half-power bandwidth 116 Hamilton function (or Hamiltonian) 20 Hamilton equations 21 non-holonomic form 34 Hamilton’s principle 34–37 extended 36 harmonic excitation 107–108 Hermitian form 282 independent random variables 210 impulse response function (IRF) 100 modal 120, 191, 244 initial value problem (IVP) 14, 141Index 319 inner product 265, 268–269 IRF see impulse response function isomorphism 264 Lagrange’s equations 18 non-holonomic form 33 standard form 19 Lagrange function (or Lagrangian) 19 Lagrange identity 151 Lagrange’s multipliers 32–34 Lagrangian density 38, 157, 175 Laplace transform 304–310 linear system 1 logarithmic decrement 65–66 mass 9 apparent 116 coefficients 46 matrix 46 modal 69 matrix 255 defective 278 determinant 258 diagonal 257 diagonalisable 277 dynamic 93 exponential 282–283 Hermitian (or self-adjoint) 256, 279–281 Hermitian adjoint 256 inverse 259 negative-definite 282 negative-semidefinite 282 nondefective 278 nonsingular 259 normal 257 orthogonal 257 positive-definite 282 positive-semidefinite 282 rank 259 similar 270, 277 singular 259 skew-hermitian 256 skew-symmetric 256 spectral 70 symmetric 256, 279–281 trace 258 transpose 256 unitary 257 MDOF see multiple degree of freedom mean 210 mean square value 210, 291 matrix 245 mechanical impedance 116 membrane free vibration 156–157 circular 158–162 rectangular 157–158 multiple inputs-multiple outputs (MIMO) systems 241–243 mobility 114, 117 modal damping ratio 86 force vector 120 matrix 70, 281 participation factor 120 mode acceleration method 122–124 complex 81, 91–92 shape 67, 145 truncation 122 moments (in probability) 209 central 210 non-central 210 multiple degrees of freedom (MDOF) systems multiplicity algebraic 68, 275, 278 geometric 83, 278 narrowband process 229–230 peak distribution 251–254 threshold crossing rates 249–251 natural system 25, 28 Newton’s laws 13 non-inertial frame of reference 48–53 nonlinear system 1 non-natural system 25 norm matrix 285–288 vector 265–266 normal (or modal) co-ordinates 72–73, 120, 244 normalisation 68–70, 147, 274 mass 69 Nyquist plot 108, 117 operator beam 182–183 biharmonic 175 Laplace (also Laplacian) 157320 Index operator (Cont.) linear 263–267 mass 186 plate 183–185 stiffness 186 Sturm-Liouville 150 self-adjoint 152 orthogonality 68–70, 82, 92 mass 69 of beam eigenfunctions 167–168 of plate eigenfunctions 181–182 stiffness 69 overdamped system 62 Parseval’s relation 291, 296–297 pendulum compound (or physical) 44 double 23, 44 simple 21–23, 56–57 period 3 periodic excitation 109–110 Phase angle 3 phase space 93 phasor 4 plates 174–176 circular 180–181 flexural stiffness 175 Kirchhoff theory 174 Mindlin theory 174 rectangular 176–180 power spectral density (PSD) 223, 227–228 matrix 241 principle d’Alembert 17 of least action 35 of virtual work 17 superposition 1 uncertainty 299 probability density function (pdf) 208 distribution function (PDF) 208 progressive wave 141 PSD see power spectral density quadratic eigenvalue problem (QEP) 80, 92–96 quadratic form 282 random process 207, 219–223 variable (r.v.) 207 vibration 2, 207 Rayleigh damping 88 dissipation function 30–32 distribution 251, 253 quotient 154 receptance 114 reciprocity 122, 205 resonance 108, 110 response indicial 104 pseudo-static 123 resonant 109 spectrum 117–119 transient237–239 Riemann-Lebesgue lemma 292 rigid-body modes 83–87, 125, 149 rod vibration 148–150 root mean square 210 rotary (or rotatory) inertia 170, 173, 174 Routh function (or Routhian) 53–55 sample function 211 SDOF see single degree of freedom shaft vibration 148–150 shear deformation 163, 170, 172, 174, 187 single degree of freedom (SDOF) systems 92, 233, 236–239, 244, 251 singular value decomposition 283–285 single input-single output (SISO) systems 233–236 spectral density see power spectral density spectral matrix 70 spring 8 equivalent 9–11 stable system 64 standard deviation 210 standard eigenvalue problem (SEP) 68, 273–276 standing wave 142 stationary random process 212–214, 223–227 weakly stationary (WS) 214 state space 93–96, 126–133 stiffness 8 coefficients 45Index 321 coupling 77 dynamic 116 matrix 46 modal 69 stochastic process see random process string vibrations 140–148 Sturm-Liouville problem (SLp) 146, 150–156 regular 150 singular 161 theorem bandwidth 299–300 Bauer-Ficke 288 Betti’s 182 Dirichlet 292 Euler’s 29 Murnaghan-Wintner 284 Schur’s decomposition 283–284 spectral for normal matrices 281 transmissibility force 111 motion 110 transfer function (TF) 102 uncorrelated random variables 211 underdamped system 62 unstable system 64 variance 210 varied path 35 vector space 260–263 dimension 261–262 subspace 261 velocity 6 group 162, 173 phase 162, 173 vibration isolation 110–112 virtual displacement 16 viscous damper 8 wave equation 140, 148 wavelength 142 wavenumber 142, 309 Weibull distribution 253 white noise 231 band-limited 231 Wiener-Khintchine relations 224
كلمة سر فك الضغط : books-world.net The Unzip Password : books-world.net أتمنى أن تستفيدوا من محتوى الموضوع وأن ينال إعجابكم رابط من موقع عالم الكتب لتنزيل كتاب Advanced Mechanical Vibrations - Physics, Mathematics and Applications رابط مباشر لتنزيل كتاب Advanced Mechanical Vibrations - Physics, Mathematics and Applications
|
|