磁流变弹性体环形板的应力应变分析

摘要

通过运动方程、物理方程、几何方程及电动力学方程给出了磁流变弹性体薄板在机械场、磁场作用下的基本方程，以磁流变弹性体环形薄板问题为例，建立了含有8个基本未知量的偏微分方程组，再利用Newmark有限等差式，得到了可以应用离散正交法求解的标准型。对于变化磁场下的磁流变弹性体薄板，得到了磁场力的表达式。讨论了磁流变弹性体薄板应力、变形随外加磁场参量的变化规律，并通过实例证实了可以通过改变磁场、机械场的参数来实现对薄板的应力、应变的控制。%Based on the motion equations, physical equations, geometric equations and electrodynamics equations, the ma-gnetorheological elastomer plate basic equations in the mechanical field and the magnetic field are obtained.The magnetorheological elastomer annular plate problem is developed that contains eight basic unknowns. Newmark algorithm and discrete orthogonal me-thods are employed to get the standard types. As numerical examples for the magnetorheological elastomers plate in the changing magnetic field, the expression of the magnetic field force is derived. The formulation for the stress and deformation of the ma-gnetorheological elastomer plate in different magnetic field parameters are analyzed. It is shown that the sress and strain can be con-trolled by changing the magnetic field and the mechanical field.