磁-热-流体耦合场中矩形薄板的非线性振动

摘要

Dynamic behaviors of thin plate under mechanical loads,magnetic field,and fluid influence were studied.Initially,governing equations of the plate in thermal and magnetic field were derived based on physical equation,non-linear geometric equation,and equilibrium equation.Differential dynamic system was established by applying Galerkin method.The numerical solution was obtained by using Runge-Kutta method and results induding time-history,phase trajectory,and Poincare map of the plate were given.The simulation revealed that magnetic field would inhibit the effect of nonlinear force in the dynamics system.The thermal field would influence on not only thermal deformation and stress of the thin plate,but also the dynamical behaviour characteristics of the system.The coupling effects of magnetic field and fluid play important roles on dynamics behaviours of the plate.%研究薄板结构在机械载荷、磁场和温度场共同作用下的动力学行为.考虑到板受Lorentz力的作用,根据物理方程、非线性几何方程和平衡方程建立了耦合场中薄板的运动控制方程,应用Galerkin原理推导出微分动力系统,采用Runge-Kutta方法进行数值求解,绘制了薄板运动的时程图、相轨迹图和Poincare映射图,分析温度场、磁感应强度以及机械载荷形式对系统运动规律的影响.结果表明,磁场在薄板非线性运动系统中消耗能量,可以抑制非线性作用;温度场不仅改变板内热变形和热应力,而且影响薄板的运动特征;磁场和流体压力对系统动态响应的影响是相互耦合的,静压力或脉动压力的增大不仅导致振幅的增加,而且改变系统的运动特征.