Hamiltonian Parametric Element and Semi-Analytical Solution for Smart Laminated Plates
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摘要: 根据压电材料修正后的Hellinger-Reissner(H-R)变分原理，建立了各向异性压电材料4节点Hamilton等参元的一般形式．为智能叠层板自由振动问题和带有压电块的叠层悬臂梁的瞬态响应等问题提出了一种新的半解析法．数学模型的基本步骤：将压电层和主体层看成独立的三维体，在平面内离散各层，分别建立各层的方程；根据主体层和压电层在连接界面上广义应力和广义位移的连续条件，联立主体层和压电层的方程得到全结构的控制方程．等参元不限制智能板侧面的几何边界形状、板的厚度和层数，有广泛的应用领域．
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关键词:
- 压电材料 /
- 智能叠层板 /
- 振动分析 /
- Hamilton等参元 /
- 半解析法
Abstract: Based on the Hellinger-Reissner (H-R) mixed variational principle for piezoelectric material, a unified 4-node Hamiltonian isoparametric element of anisotropy piezoelectric material was established. A new semi-analytical solution for the natural vibration of smart laminated plates and the transient response of the laminated cantilever with piezoelectric patch was presented. The major steps of mathematical model are as follows: the piezoelectric layer and host layer of laminated plate were considered as unattached three-dimensional bodies and discretized by the Hamiltonian isoparametric elements. The control equation of whole structure was derived by considering the compatibility of generalized displacements and generalized stresses on the interface between layers. There is no restriction for the side-face geometrical boundaries, the thickness and the number of layers of plate by the use of the present isoparametric element. The present method has a wide application a. -
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