功能梯度磁电弹性圆板的三维动力特性分析

Three dimensional Dynamical Analysis of Functionally Graded Magnetoelectroelastic Circular Plates

摘要:

根据正交各向异性磁电弹性材料空间问题的基本方程,假定功能梯度材料的电学、磁学和力学参数沿圆板厚度方向按同一指数函数变化,导出以位移、电势、磁势以及它们的一阶导数为状态变量的圆板动力问题的状态方程,采用微分求积法和状态空间法相结合的半解析数值方法进行求解.通过数值算例说明了本文方法的正确性和优越性.研究了功能梯度磁电弹性圆板的三维动力特性以及材料性质的不同梯度变化对该种新型智能复合材料结构动力性能的影响.研究成果可为该种智能材料结构的设计提供一定的参考.

Abstract:

Based on the three dimensional elastic theory of orthotropic magnetoelectroelastic materials and assumption that the mechanical,electric and magnetic properties of the materials vary continuously along the thickness direction and have the same exponential distribution,the state equations of dynamic analysis are derived in terms of displacement components,electric potential,magnetic potential and their first derivatives.A semi analytical numerical method that combines the one dimensional differential quadrature method with the state space method is employed to solve the governing equations.Numerical results are given to demonstrate the accuracy and superiority of the present method.Three dimensional dynamical behavior of functionally graded magnetoelectroelastic circular plates is investigated through examples and the influences of the different functionally graded material properties are analyzed.The results can be a good reference to the design of the magnetoelectroelastic structures.