【作者】 于天崇； 聂国隽； 仲政；

【Author】 Tian-chong YU,Guo-jun NIE,Zheng ZHONG School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China

【机构】 上海四平路1239号同济大学航空航天与力学学院；

【摘要】 对于沿厚度方向材料性能梯度变化的磁电材料圆板的静动力性能,本文采用了一种半解析数值法进行求解。这种半解析数值法是沿圆板径向采用微分求积法进行求解,沿板厚方向(也就是材料性能梯度变化方向)采用状态空间法求解。根据横观各向同性磁电材料轴对称问题的基本方程,假定材料的电学、磁学和力学参数沿厚度方向按相同的指数函数变化,导出以位移、电势、磁势为基本未知量的平衡微分方程,并采用半解析数值方法进行求解。分别研究了功能梯度磁电材料圆板的静载和自由振动问题。通过数值算例将本文的计算结果与已有的理论解进行了比较,验证了本文模型和方法的正确性,另一方面,我们可以发现本文采用的半解析数值方法沿厚度方向可得出解析解,而沿径向选用少量的离散点即可得到具有相当精度的结果,与有限元方法相比,在计算效率和计算精度方面均具有一定的优越性。通过静载分析还发现功能梯度磁电材料圆板最大挠度随着梯度变化幅度的增大而减小。通过自由振动分析发现功能梯度磁电材料圆板自由振动基频随着梯度变化幅度的增大而减小。获得的这些关于磁电圆板结构响应的规律性特征,为磁电圆板的设计提供一定的参考。更多还原

【Abstract】 A semi-analytical method,which makes use of the state space method and the one-dimensional differential quadrature method,is used to obtain the static and dynamic responses of a Functionally Graded Magnetoelectroelastic Circular Plate with the material property varying only in the thickness direction.The analytical solution in the thickness direction can be obtained by using the state space method and the approximate solution in the radial direction can be derived through using the one-dimensional differential quadrature method.Based on the elastic theory of magnetoelectroelastic materials and the assumption that the mechanical,electric and magnetic properties of the materials vary continuously along the thickness direction and have the same exponential distribution,differential equations of equilibrium in terms of displacements,electric potential and magnetic potential can be presented.Numerical results are given to demonstrate the accuracy and superiority of the presented method.Some regular characteristics about the reactions of the circular plate in piezoelectric and piezomagnetic materials can be obtained by examples and the results can be used in the design of the corresponding structures.更多还原