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أخواني في الله 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
![كتاب Engineering Vibration Analysis with Application to Control Systems E_v_a_10](https://i.servimg.com/u/f61/15/36/74/14/e_v_a_10.jpg) 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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