A modified Pagano method for the 3D dynamic responses of functionally graded magneto-electro-elastic plates
A modified Pagano method for the 3D dynamic responses of functionally graded magneto-electro-elastic plates
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DOI：
10.1016/j.compstruct.2009.03.022
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发表时间：
2009-10
影响因子：
6.3
通讯作者：
Chih‐Ping Wu;Yixin Lu
中科院分区：
文献类型：
--
作者：
Chih‐Ping Wu;Yixin Lu
提出了一种改进的Pagano方法，用于计算三种不同侧向表面条件下简支、多层和功能梯度（FG）磁电弹性板的三维动力响应。在每个侧表面上规定了自由电/磁势或自由电/磁通条件。通过厚度坐标认为FG板的材料性能是不均匀的，然后指定为服从成分体积分数的幂律分布。对Pagano方法进行了改进，将基于位移的公式改为混合公式，将系统方程的复值解转化为实值解，提出了传播子矩阵法，并采用逐次逼近法使该方法适用于FG板的耦合分析。在举例中，研究了幂律指数对FG磁电弹性板的固有频率及其在磁场、电场和弹性场中对应的模态变量随板厚度的影响。本文改进的Pagano方法与SA方法相结合，能够有效地逼近FG板的可用三维解，达到所需的精度。
A modified Pagano method is developed for the three-dimensional (3D) dynamic responses of simply supported, multilayered and functionally graded (FG) magneto-electro-elastic plates with three different lateral surface conditions. Either the free electric/magnetic potential or the free electric/magnetic flux conditions is prescribed on each lateral surface. The material properties of FG plates are regarded as heterogeneous through the thickness coordinate and then specified to obey a power-law distribution of the volume fractions of the constituents. The Pagano method is modified for the present analysis in that a displacement-based formulation is replaced by a mixed formulation, the complex-valued solutions of the system equations are transferred to the real-valued solutions, a method of propagator matrix is developed for the present method, and a successive approximation (SA) method is used to make the present method feasible for the coupled analysis of FG plates. In the illustrative examples, the influence of the power-law exponent on the natural frequencies of the FG magneto-electro-elastic plates and their corresponding modal variables in the magnetic, electric and elastic fields through the thickness of the plates is studied. The present modified Pagano method combined with the SA method is capable of efficiently approximating the available 3D solutions of FG plates to any desired accuracy.