Titlebook: IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics; Proceedings of the I Francis C. Moon Conference proceed

宏伟

forthy

IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics978-94-011-5320-1Series ISSN 0925-0042 Series E-ISSN 2214-7764

Abrupt

Dynamics of a Quasiperiodically-Forced Mathieu OscillatorMathieu’s equation [6],.is the paradigm for problems in parametric excitation in which an autonomous linear structure is driven by a periodic forcer, usually in a direction perpendicular to the direction of motion (e.g., the vertically forced pendulum, dynamic buckling of an elastic column, water waves in a vertically driven channel).

prodrome

Improved Galerkin Method in the Dimension Reduction of Nonlinear Dynamical SystemsWe apply the Karhunen-Loeve modes to improve the usual Galerkin reduction and compare this result with various other choices of ansatz functions. Moreover we also compare results obtained from a flat Galerkin reduction with those from a nonlinear Galerkin reduction making use of the Approximate Inertial Manifold method.

深陷

Bifurcation in Stochastically Perturbed Dynamical Systemsn (1) around each of these solutions. The standard procedure for this purpose is the evaluation of the maximal Lyapunov exponent which determines the exponential rate of growth or decay of some norm of the solution; the sign of the maximal Lyapunov exponent determines the stability of the trivial solution.

混合,搀杂

合同

Jumps to Resonance Phenomena in Nonlinear Mechanics: Fractal Basins, Chaotic Transients and Unpredicisting attractor at the local bifurcation, jumps may be indeterminate in the sense that we cannot predict to which solution the system will settle upon. This is often a result fractal structure in the vicinity of the critical point resulting in chaotic transients until the settles onto one of the co-existing attractors

infelicitous

0925-0042 ry". From the very beginning, mechanics has been a central focus for modem nonlinear dynamical systems. Fluid, structural, machine and rigid body dynamics has been a fertile field for nonlinear phenomena and chaos in particular. Early experimental evidence for chaotic phenomena in mechanics gave the

adumbrate

Conference proceedings 1999the very beginning, mechanics has been a central focus for modem nonlinear dynamical systems. Fluid, structural, machine and rigid body dynamics has been a fertile field for nonlinear phenomena and chaos in particular. Early experimental evidence for chaotic phenomena in mechanics gave the new chaos

Shuttle

Nonstationary Responses in Two Degree-of-Freedom Nonlinear Systems with 1-to-2 Internal Resonanceequations are numerically studied for motions initiated in the vicinity of the stationary responses. An analytical technique, based on the . is then developed to explain the numerical observations for slow frequency sweep through the bifurcations, and the effects of system parameters on the dynamics near a Pitchfork Point are determined.