Nonlinear dynamics and stochastic mechanics
著者
書誌事項
Nonlinear dynamics and stochastic mechanics
（Fields Institute communications, v. 9）
American Mathematical Society, c1996
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注記
Includes bibliographical references
内容説明・目次
内容説明
This volume contains the proceedings of the International Symposium on Nonlinear Dynamics and Stochastic Mechanics held at The Fields Institute for Research in Mathematical Sciences from August-September (1993) as part of the 1992-1993 Program Year on Dynamical Systems and Bifurcation Theory. In recent years, mathematicians and applied scientists have made significant progress in understanding and have developed powerful tools for the analysis of the complex behavior of deterministic and stochastic dynamical systems. By moving beyond classical perturbation methods to more general geometrical, computational, and analytical methods, this book is at the forefront in transferring these new mathematical ideas into engineering practice.This work presents the solutions of some specific problems in engineering structures and mechanics and demonstrates by explicit example these new methods of solution. The book joins problems in engineering science to recent developments in the mathematical theory of dynamical systems; offers novel applications of dynamical systems theory; presents numerical methods for stochastic systems; and, compares analytical and numerical studies near the onset of chaos. In one volume, it brings together and contrasts deterministic and stochastic models of 'chaos'.
目次
Chaotic responses in two degree-of-freedom systems with 1:2 internal resonances by B. Banerjee and A. K. Bajaj Robust numerical solution of the Fokker-Planck equation for second order dynamical systems under parametric and external white noise excitations by L. A. Bergman, B. F. Spencer, S. F. Wojtkiewicz, and E. A. Johnson Stochastic stability of systems with random properties by C. Bucher Oil whirl and oil whip, nonlinear limit-cycle phenomena by S. H. Crandall A basic explanation of homoclinic intersection in the twin-well duffing oscillator by E. H. Dowell and A. L. Katz Stability of superimplicit numerical methods for stochastic differential equations by N. Hofmann and E. Platen Response statistics of nonlinear systems to parametric filtered white noise by R. A. Ibrahim and Y. J. Yoon On robustness of some concepts in stability of stochastic differential equations by R. Z. Khasminskii Prediction of natural frequency and buckling load variability due to uncertainty in material properties by convex modeling by Y. W. Li, I. Elishakoff, J. H. Starnes, and M. Shinozuka Some results related to failure of stochastic structural systems by Y. Lin and G. Q. Cai Chaotic motion in a rotating body with internal energy dissipation by P. A. Meehan and S. F. Asokanthan Numerics for Lyapunov exponents of hypoelliptic linear stochastic systems by V. Wihstutz Vibration mode localization in large randomly disordered continuous beams by W.-C. Xie and S. T. Ariaratnam.
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