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Book DetailsFields Institute CommunicationsVolume: 9; 1996; 238 ppMSC: Primary 93; 70; Secondary 34
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.
Features:
- 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.
- Compares analytical and numerical studies near the onset of chaos.
- In one volume, brings together and contrasts deterministic and stochastic models of “chaos”.
Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
ReadershipGraduate students, applied mathematicians, and engineers working in nonlinear chaotic and stochastic behavior of mechanical systems and structures.
-
Table of Contents
-
Chapters
-
Bappaditya Banerjee and Anil Bajaj — Chaotic responses in two degree-of-freedom systems with 1:2 internal resonances
-
Lawrence Bergman, Billie Spencer, Steven Wojtkiewicz and Erik Johnson — Robust numerical solution of the Fokker-Planck equation for second order dynamical systems under parametric and external white noise excitations
-
Christian Bucher — Stochastic stability of systems with random properties
-
Stephen Crandall — Oil whirl and oil whip, nonlinear limit-cycle phenomena
-
Earl Dowell and Andrew Katz — A basic explanation of homoclinic intersection in the twin-well duffing oscillator
-
Norbert Hofmann and Eckhard Platen — Stability of superimplicit numerical methods for stochastic differential equations
-
R Ibrahim and Y Yoon — Response statistics of nonlinear systems to parametric filtered white noise
-
Rafail Khasminskii — On robustness of some concepts in stability of stochastic differential equations
-
Y Li, I Elishakoff, J Starnes and M Shinozuka — Prediction of natural frequency and buckling load variability due to uncertainty in material properties by convex modeling
-
Yuandan Lin and G Cai — Some results related to failure of stochastic structural systems
-
P Meehan and S Asokanthan — Chaotic motion in a rotating body with internal energy dissipation
-
Volker Wihstutz — Numerics for Lyapunov exponents of hypoelliptic linear stochastic systems
-
Wei-Chau Xie and S Ariaratnam — Vibration mode localization in large randomly disordered continuous beams
-
-
RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Requests
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.
Features:
- 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.
- Compares analytical and numerical studies near the onset of chaos.
- In one volume, brings together and contrasts deterministic and stochastic models of “chaos”.
Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Graduate students, applied mathematicians, and engineers working in nonlinear chaotic and stochastic behavior of mechanical systems and structures.
-
Chapters
-
Bappaditya Banerjee and Anil Bajaj — Chaotic responses in two degree-of-freedom systems with 1:2 internal resonances
-
Lawrence Bergman, Billie Spencer, Steven Wojtkiewicz and Erik Johnson — Robust numerical solution of the Fokker-Planck equation for second order dynamical systems under parametric and external white noise excitations
-
Christian Bucher — Stochastic stability of systems with random properties
-
Stephen Crandall — Oil whirl and oil whip, nonlinear limit-cycle phenomena
-
Earl Dowell and Andrew Katz — A basic explanation of homoclinic intersection in the twin-well duffing oscillator
-
Norbert Hofmann and Eckhard Platen — Stability of superimplicit numerical methods for stochastic differential equations
-
R Ibrahim and Y Yoon — Response statistics of nonlinear systems to parametric filtered white noise
-
Rafail Khasminskii — On robustness of some concepts in stability of stochastic differential equations
-
Y Li, I Elishakoff, J Starnes and M Shinozuka — Prediction of natural frequency and buckling load variability due to uncertainty in material properties by convex modeling
-
Yuandan Lin and G Cai — Some results related to failure of stochastic structural systems
-
P Meehan and S Asokanthan — Chaotic motion in a rotating body with internal energy dissipation
-
Volker Wihstutz — Numerics for Lyapunov exponents of hypoelliptic linear stochastic systems
-
Wei-Chau Xie and S Ariaratnam — Vibration mode localization in large randomly disordered continuous beams
