用状态空间法求功能梯度电磁弹性多层板的场变量

利用状态空间法对功能梯度电磁弹性多层板场变量的精确解进行了分析.该分析基于3个假设:(1)板的四边简支;(2)在板的上、下表面存在力、电边界条件;(3)功能梯度系数在厚度方向呈指数分布.根据上述假设和电磁弹性介质控制方程,获得了层间变量的状态方程,并由此推导出了厚度方向上任意两表面间场变量的传递矩阵关系,通过这种关系求出了多层板场变量的精确解.最后用该方法解算了一个具有不同叠层顺序的三层矩形板,计算结果表明了功能梯度系数和载荷类型对场变量的影响.

Exact Solution for Field Variables of Functionally Graded Magneto-electro-elastic Laminated Plate Using State Space Method

State space method is employed to analyze a kind of multilayered rectangular plate made of functionally graded magneto-electro-elastic materials.At starting three assumptions are defined.Firstly,the edges of the plate are simply supported.Secondly,general mechanical,electric boundary conditions are applied on both the top and bottom surfaces of the plate.Thirdly,the functionally graded material is exponential in the thickness direction.Based on a structural governing equation and above assumptions,the propagation matrix for each layer is obtained,which can be used to calculate the exact solution for field variables of the multilayered plate.The method is then applied to two functionally graded(exponential) sandwich plates with different stack sequences.The numerical results clearly show the influence of the exponential factor,magneto-electro-elastic properties,and loading types on induced magneto-electric-elastic fields.