ISBN: 3540656618
TITLE: Nonlinear Dynamics of Active and Passive Systems of Vibration Protection
AUTHOR: Kolovsky, Michail Z.
TOC:

Preface 5
Translator's preface 8
1 Dynamic characteristics and efficiency of vibration protection systems 13
1.1 Statement of the problem of protection from dynamic excitations 13
1.1.1 One-dimensional dynamic vibration absorber 15
1.1.2 Multidimensional dynamic vibration absorber 17
1.1.3 Uniaxial vibration isolator 17
1.2 Dynamic characteristics of the vibration-isolated system and the base 20
1.2.1 Example 1: The dynamic compliance matrix for a free rigid body 35
1.2.2 Example 2. The dynamic compliance of a two degree-of-freedom system 36
1.3 Efficiency conditions in the case of harmonic excitation 39
1.4 Efficiency in case of polyharmonic, random and non-stationary excitations 56
2 Linear active systems 61
2.1. Structure and elements of active systems 61
2.1.1 Transfer functions of active systems 61
2.1.2 Sensors 64
2.1.3 Compensators and amplifiers 67
2.1.4 Actuators 70
2.2 One-dimensional linear active systems 81
2.3 Conditions for stability of active systems 108
2.4 Systems with several measurement points 122
2.5 Transient processes in active systems and protection from impacts 129
2.6 Work and power in active systems 147
2.7 Multidimensional systems 156
3 Nonlinear passive single degree-of-freedom systems 187
3.1 Methods of analysis for nonlinear system 167
3.2 Forced vibration-under harmonic excitation and linear damping 183
3.3 Forced vibrations under harmonic excitation and Coulomb friction 199
3.4 Forced vibration in a system with internal friction 208
3.5 Comparative study of the various types of damping 212
3.6 Forced vibration under polyharmonic excitation 218
3.6.1 System with nonlinear elastic force and linear damping 219
3.6.2 System with linear elastic force and dry friction 224
3.6.3 General solution for the problem of polyharmonic driving 227
3.7 Subharmonic resonances in vibration protection systems 230
3.8 Subharmonic resonance in systems with rigid stops 242
3.9 Forced random vibrations 249
4 Nonlinear passive multi-degree-of-freedorn systems 257
4.1 Static analysis of nonlinear elastic suspensions 257
4.2 Small vibration of elastically suspended rigid body 263
4.3 Vibration of an object mounted on nonlinear elastic isolators 272
4.4 Free vibration of a nonlinear vibration protection system 282
4.5 Resonant vibration 293
4.6 Forced vibration in systems with Coulomb friction 300
4.7 Forced vibration of elastic bodies 306
5 Nonlinear active systems 319
5.1 Resonant vibrations in nonlinear systems under harmonic excitation 319
5.2 Subharmonic vibrations 332
5.3 Influence of nonlinearities in feedback 342
5.4 Stability of vibration in nonlinear systems 354
6 Optimal systems of vibration protection 365
6.1 Statement of the optimisation problem 365
6.2 Determination of the optimal control 370
6.3 Optimal vibration isolation of a rigid body 390
6.4 Approximate synthesis of the optimal isolator characteristics 402
Bibliography 411
Index 423
ENDE
