FREE VIBRATIONS OF SIMPLY SUPPORTED AND MULTILAYERED MAGNETO-ELECTRO-ELASTIC PLATES
FREE VIBRATIONS OF SIMPLY SUPPORTED AND MULTILAYERED MAGNETO-ELECTRO-ELASTIC PLATES
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DOI：
10.1006/jsvi.2001.3693
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发表时间：
2002-05
影响因子：
4.7
通讯作者：
E. Pan;P. Heyliger
中科院分区：
文献类型：
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作者：
E. Pan;P. Heyliger
导出了三维、线性各向异性、磁电弹性和多层矩形板在简支边缘条件下的自由振动的解析解。对于任何齐次层，我们用一种类似于Stroh形式的简单形式构造了通解，在给定的边界条件下，任何物理量都可以从这种形式解出来。特别是，表征固有频率和波数之间关系的色散方程可以用一种简单的形式得到。对于多层板，我们导出了用传播矩阵表示的色散关系。目前的解决方案包括所有以前的解决方案，如压电，压磁和纯弹性解决方案作为特殊情况，可以作为各种厚板理论和数值方法的基准，用于层状复合材料结构的建模。给出了压电/压磁夹层板的典型固有频率和模态振型。结果清楚地表明，有些模态是纯弹性的，而另一些模态则与压电/压磁量完全耦合，后者在很大程度上取决于材料性质和堆叠顺序。这些频率和模态振型特征对于分析和设计由磁-电弹性复合材料层压板构成的各种“智能”传感器/致动器特别感兴趣。
Abstract Analytical solutions are derived for free vibrations of three-dimensional, linear anisotropic, magneto-electro-elastic, and multilayered rectangular plates under simply supported edge conditions. For any homogeneous layer, we construct the general solution in terms of a simple formalism that resembles the Stroh formalism, from which any physical quantities can be solved for given boundary conditions. In particular, the dispersion equation that characterizes the relationship between the natural frequency and wavenumber can be obtained in a simple form. For multilayered plates, we derive the dispersion relation in terms of the propagator matrices. The present solution includes all previous solutions, such as piezoelectric, piezomagnetic, and purely elastic solutions as special cases, and can serve as benchmarks to various thick plate theories and numerical methods used for the modelling of layered composite structures. Typical natural frequencies and mode shapes are presented for sandwich piezoelectric/piezomagnetic plates. It is shown clearly that some of the modes are purely elastic while others are fully coupled with piezoelectric/piezomagnetic quantities, with the latter depending strongly upon the material property and stacking sequence. These frequency and mode shape features could be of particular interest to the analysis and design of various “smart” sensors/actuators constructed from magneto-electro-elastic composite laminates.