粘弹性矩形板的混沌和超混沌行为

CHAOTIC AND HYPERCHAOTIC BEHAVIORS OF VISCOELASTIC RECTANGULAR PLATES UNDER TRANSVERSE PERIODIC LOAD

摘要

摘要:从薄板Karman理论的基本假设出发；利用线性粘弹性理论中的Boltzman叠加原理，建立了粘弹性薄板非线性动力学分析的初边值问题，其运动方程是一组非线性积分──微分方程．在空间域上利用Galerkin平均化法之后，得到了变型的非线性积分──微分型的Duffing方程．综合利用动力系统中的多种方法，揭示了粘弹性矩形板在横向周期激励下的丰富的动力学行为，如不动点、极限环、混沌、奇怪吸引子、超混沌等，其中，混沌和超混沌是交替出现的．

Abstract:On the basis of the hypotheses of the Karman theory for elastic thin plates and the Boltzmann laws for linear isotropic viscoelastic materials, the constitutive equations for viscoelasticthin plates airs derived by using the "structure function" introduced in this paper. The initialboundary value problem of nonlinear dynamical analysis for viscoelastic thin plates is formulatedby using the procedure that is similar to the process deriving the Karman theory for elastic thinplates. If Poisson ration v of a ma...