A new efficient numerical method and the dynamic analysis of composite laminates with piezoelectric layers
A new efficient numerical method and the dynamic analysis of composite laminates with piezoelectric layers
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DOI：
10.1016/j.compstruct.2005.11.002
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发表时间：
2007-06
影响因子：
6.3
通讯作者：
G. Qing;Jian-xin Xu;Pei Li;J. Qiu
中科院分区：
文献类型：
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作者：
G. Qing;Jian-xin Xu;Pei Li;J. Qiu
首先，提出了一种拉普拉斯变换求逆的数值方法，并通过算例说明了该方法的精度。然后，由压电体的修正混合变分原理直接推导出压电板动力问题的状态向量方程，并简单地给出了简支矩形压电板动力问题的精确解。对于多层杂交板，我们用传播矩阵的形式给出了解。该方法考虑了弹性层和压电层界面上的广义位移和广义应力的协调，并在结构的整体代数方程中考虑了层合板的横向剪切变形和转动惯量。同时，对厚度和层数没有限制。作为拉普拉斯变换数值逆方法的应用，给出了简谐振动和暂态响应的典型数值算例。由于数值结果具有很高的精度，因此可以作为检验各种厚板理论和各种数值方法的基准，例如求解瞬态响应问题的有限元和边界元方法。
Firstly, a numerical method for the inversion of Laplace transform is developed and its accuracy is shown through examples. Then, a state-vector equation for the dynamic problems of piezoelectric plates is deduced directly from a modified mixed variational principle for piezoelectric bodies and its exact solution for the dynamic problems of simply supported rectangle piezoelectric plate is simply given. For multilayered hybrid plates, we derive the solution in terms of the propagator matrices. The techniques accounts for the compatibility of generalized displacements and generalized stresses on the interface both the elastic layers and piezoelectric layers, and the transverse shear deformation and the rotary inertia of laminate are also considered in the global algebraic equation of structure. Meanwhile, there is no restriction on the thickness and the number of layers. As an application of the numerical inversion of Laplace transform presented in this paper, typical numerical examples of the harmonic vibration and transient response are proposed and discussed. Since the highly accurate numerical results, they can serve as benchmarks to test various thick plate theories and various numerical methods, such as the finite and boundary element methods for transient response problems.