热机电耦合智能板结构的随机性分析

Randomicity Analysis of Piezothermoelasticity Intelligent Plate

对具有随机参数的热机电耦合智能薄板结构提出一种包含4个位移节点、2个电势节点和8个温度节点的有限元模型,用平板型壳体单元模型描述其位移场,用线性插值方法描述其电势场和温度场。基于虚功原理导出了智能薄板的热机电有限元方程,通过各响应量对诸随机参数灵敏度的解析求解和一次二阶矩法,依次求得结构固有频率、固有振型、温变、位移以及输出电压等随机响应的数字特征。以悬臂智能板为例,将所得计算结果与Monte Carlo数值模拟法的结果进行比较,证明了所提出的处理方法可行且有相当高的精度。

An element model including 4 displacement nodes,2 electric potential nodes and 8 temperature nodes is presented.Its displacement field is defined by means of plane shell element model,and its electric potential field and temperature field are both defined by means of linear interpolation,the detailed element equations are deduced by using virtual work principle.Through the analytic solutions of sensitivities with respect to random parameters and first order second moment method,the numerical characteristics of natural frequencies,mode shapes,temperature field,displacement field and output voltages are solved in turn. Finally,an intelligent cantilever plate is taken as an example.The numerical results are compared with those of Monte Carlo method, the results show that the computing process presented is feasible and has very good precision.