Forced Oscillations of Multidimensional Highly Nonlinear Systems

This book highlights the presentation of methods for studying oscillations under external periodic influence and random changes in parameters in dynamic systems with nonlinearities that have discontinuities and kinks. The analysis of dynamic systems is based on effective approaches and algorithms of the method of point mappings of Poincaré surfaces, developed by the Nizhny Novgorod Scientific School of academician A.A. Andronov. Considerable attention is paid to the study of the general picture of the possible behavior of systems and their use in solving various applied problems. Using specific examples, it is found that this research approach allows not only to advance in the study of known nonlinear features but also to discover new effects and applications. The presentation is illustrated by numerous specific examples of oscillatory strongly nonlinear systems with discontinuous nonlinearities or piecewise-continuous nonlinearities. A separate chapter is devoted to the development and use of the point mapping method for random changes in the parameters of dynamic systems, as well as in dynamic systems subject to external seismic loads. The book is intended for scientists and engineers who are engaged in research and practice activities related to the theory of nonlinear oscillations and its applications, as well as graduate students and senior undergraduate students in relevant majors.

Presents semi-analytical methodology for studying multidimensional non-smooth dynamic systems Investigates in depth the chaotic regimes of non-smooth dynamic systems Introduces and uses the point mapping method to investigate the effect of random changes in parameters

Autorentext

Metrikin Vladimir Semenovich, doctoral candidate of physical and mathematical sciences, is Associate Professor, born on 03/26/1938. Metrikin Vladimir Semenovich's research interests include mathematical modeling of highly nonlinear dynamic systems, development of numerical analytical methods and software for describing complex periodic regimes and deterministic chaos.

Igumnov Leonid Aeksandrovich, Doctor of Physical and Mathematical Sciences, is Professor born on 11/04/1959. Igumnov Leonid Aeksandrovich is Head of the Department of Theoretical, Computer, and Experimental Mechanics at Lobachevsky State University of Nizhny Novgorod, Russia. Igumnov Leonid Aeksandrovich's research interests experimental models, methods, and hardware and software for monitoring and obtaining strength assessments of the operational states of materials and structures under extreme loading conditions. Igumnov Leonid Aeksandrovich is Editor-in-Chief of the journal "Problems of Strength and Plasticity."

Inhalt

1. Introduction.- 2. Dynamics of two-mass vibro-impact mechanisms with a fixed limiter.- 3. Research into multi-mass vibro-impact system.- 4. Investigating the effect of viscous friction forces on stability of vibro-impact systems.- 5. Dynamics of vibro-impact systems with randomly changing parameters.