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．
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 material does not depend on the time the forms of equations are the same as those in the Karman theory. But in fact, the equations are a set of integral-nonlinear,partial differential equations due to that the Boltzmann operator is involved in the equations. Fora simple-supported rectangUlar plate, an altered Duffing equation with nonlinear integral-ordinarydifferential type is obtained from the Galerkin method to the spatial domain. It may be reduced to a fourth-order nonlinear, non-autonomous, differential one and the corresponding autonomoussystems. Synthetically using several methods in dynamic systems, such as time-path curve, power spectrum, phase-trajectory diagram, stroboscopic observation, Lyapunov exponent spectrum and Lyapunov dimension etc., the dynamic properties of the viscoelastic thin plate with a transverseperiodic excitation are sufficiently revealed, for example, fixed point, limit cycle, chaos, strangeattractor, hyperchaos etc. One can see that when the load amplitude qo increajses from zero, themotion state of the plate will change from order (limit cycle) to irregularity (chaos, hyperchaos)and the motion states alternate between chaos and hyperchaos for large values of load amplitude.l) The project supported by the National Natural Science FOundation of China and Shanghai Municipal DoctoralProgram FOundation of institutions of Higher Education.l) The project supported by the National Natural Science FOundation of China and Shanghai Municipal DoctoralProgram FOundation of institutions of Higher Education.l) The project supported by the National Natural Science FOundation of China and Shanghai Municipal DoctoralProgram FOundation of institutions of Higher Education.l) The project supported by the National Natural Science FOundation of China and Shanghai Municipal DoctoralProgram FOundation of institutions of Higher Education.
出处
《力学学报》
EI
CSCD
北大核心
1998年第6期692-699,共8页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金
上海市高校博士点建设基金
关键词
粘弹性矩形板
本构定律
混沌
超混沌
耗散结构
viscoelastic rectangular plate, Karman theoryt Boltzmann constitutive law, nonlineardynamical system, classical dynamical method, limit cycle, chaos and hyperchaos
