热、力、磁耦合作用下大挠度矩形薄板的分岔与混沌特性  

The Bifurcation and Chaotic Characters of a Thin Rectangular Simply Supported Plate with Large Deflection in an Environment of Thermo-mechanical and Magnetic Field Coupling

作　　者：王平[1] 陈蜀梅[2] 

机构地区：[1]燕山大学河北省重型装备与大型结构力学可靠性重点实验室,秦皇岛066004 [2]燕山大学理学院,秦皇岛066004

出　　处：《机械工程学报》2013年第15期82-87,共6页Journal of Mechanical Engineering

基　　金：国家自然科学基金(51174175);河北省自然科学基金(A2012203140)资助项目

摘　　要：针对大挠度三边简支一边自由矩形薄板,研究其在热、力、磁耦合作用下的分岔与混沌运动特性。在板壳与磁弹性力学理论的基础上,导出薄板在耦合场共同作用下的非线性控制方程,利用伽辽金原理得到薄板的非线性热磁弹性耦合振动方程。由次谐轨道Melnikov函数法,求出该动力系统Smale马蹄变换意义下出现混沌运动的阈值条件,并对该系统振动方程进行数值模拟,得到系统随机械载荷、电磁场以及温度场的参数变化的分岔图及相应的位移波形图、相平面轨迹图及庞加莱截面图。由仿真结果可知,在热、力、磁耦合作用下的大挠度矩形薄板系统的振动方程具有明显的非线性,运动特性比较复杂,呈现出非常丰富的混沌与分岔现象。通过变化机械载荷、电磁场和温度场参数,可以控制系统的振动特性。The chaotic motions of a large deflection thin rectangular plate simply supported at three sides in a coupling environment of mechanical load, magnetic field and temperature field is investigated. Based on the theory of plates and shells and the magnetic elasticity, and considering the effect of temperature field, the nonlinear governing equations of the plate undergoing the coupled fields is derived first. And then the coupled nonlinear vibration equation is obtained by using Galerkin＇s method. The chaotic motion conditions of the dynamic system under the meaning of Smale horseshoe transformation is obtained using Melnikov function method. The numerical simulations about the vibration equation of the system are also presented. The bifurcation diagram, the displacement wave diagram, the phase diagram and the Poincare section diagram of this system are shown here. The influences of the parameters variation of mechanical load, magnetic field and temperature field to the chaotic motion of this system are discussed. From the simulation, the vibration characters of this system can be controlled by changing the parameters of mechanical load, magnetic field and temperature field.

关 键 词：大挠度 热磁弹性 分岔 混沌 Melnikov函数法 

分 类 号：O343[理学—固体力学]