Selected Topics in Vibrational Mechanics

by Blekhman, I. I.; Blekhman, I. I. (CON); Blekhman, L. I. (CON); Dresig, H. (CON); Duckstein, H. (CON); Ershova, O. A. (CON); Fidlin, A. (CON); Fradkov, A. L. (CON); Grishina, S. V. (CON); Indeitsev, D. A. (CON); Jensen, J. S. (CON); Landa, P. S.

• ISBN13: 9789812380555
• ISBN10: 9812380558
• Format: Hardcover
• Copyright: 2004-03-01
• Publisher: WORLD SCIENTIFIC PUB CO INC

Summary

Vibrational mechanics is a new, intensively developing section of nonlinear dynamics and of the theory of nonlinear oscillations. It presents a general approach to the study of the effects of vibration on nonlinear systems. This approach is characterized by simplicity of application and by physical clearness.In recent years a number of new, essential results have been obtained both on the development of the mathematical apparatus of vibrational mechanics and on the solution of certain applied problems. This book reflects those results through the ingenious presentation of the authors -- well-known scientists from Germany, Denmark and Russia. For the convenience of readers, the main content is preceded by a brief description of the main theses of vibrational mechanics.

Table of Contents

On some nonlinear oscillatory effects : the main idea of vibrational mechanics	p. 3
The main mathematical apparatus of vibrational mechanics and of the method of direct separation of motions	p. 9
On other methods of obtaining expressions for the vibrational forces and the main equations of vibrational mechanics	p. 35
A simplest example : solving the problem about a pendulum with a vibrating axis of suspension by different methods of the theory of nonlinear oscillations	p. 39
Conclusion : on the main peculiarities and advantages of the approaches of vibrational mechanics and of the method of direct separation of motions as compared to other methods of nonlinear mechanics	p. 55
Quasi-equilibrium positions and stationary rotations of the pendulums with a periodically vibrating axis	p. 65
Non-trivial effects of high-frequency excitation for pendulum systems	p. 73
On the theory of the Indian magic rope	p. 139
Conjugate resonances and bifurcations of pendulums under biharmonical excitation	p. 151
On the investigations of the electromechanical systems : on the behavior of the conductivity bodies of pendulum types in high-frequency magnetic fields	p. 167
On general definitions of synchronization	p. 179
A guide to solving certain self-synchronization problems	p. 189
The setting up of the self-synchronization problem of the dynamic objects with inner degrees of freedom and methods of its solution	p. 209
On the expansion of the field of applicability of the integral signs (extreme property) of stability in problems on the synchronization of the dynamic objects with almost uniform rotations	p. 235
On dynamic materials	p. 255
The active control of vibrations of composite beams by parametric stiffness modulation	p. 259
On vibrational hydrodynamics and hydraulics	p. 313
On the vibro-jet effect and on the phenomena of vibrational injection of the gas into fluid	p. 317
On asymptotic analysis of systems with fast excitation	p. 333
On the averaging of discontinuous systems	p. 357
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