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Free vibration analysis of thick viscoelastic composite plates on visco-Pasternak foundation using higher-order theory

机译：基于高阶理论的粘-帕斯特纳克地基上厚粘弹性复合材料板的自由振动分析

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摘要

Free vibration of laminated viscoelastic composite plates on Pasternak viscoelastic medium with simply supported edge conditions is investigated. The composite plate consists of linear viscoelastic polymeric matrix reinforced by transversely isotropic elastic fibers. Multi-cell micromechanical approach together with relaxation functions of bulk/shear moduli and Boltzmann superposition principle are adopted to establish time-dependent stiffness coefficients of laminates. The coupled integro-PDEs of motions are derived based on third-order shear deformation theory by Laplace transformation and Hamilton principle. Complex frequencies and closed form solutions for transient response are achieved by weighted residual method, iterative numerical algorithm and Fourier transform. To verify, the results are compared for thick elastic composite plates on Pasternak elastic foundation and thick viscoelastic composite sandwich plates without foundation that represent acceptable accuracy. By parametric study, effects of materials, lamination scheme, geometry and medium on dynamic characteristics are scrutinized. (C) 2017 Elsevier Ltd. All rights reserved.
机译：研究了具有简单支撑边缘条件的Pasternak粘弹性介质上层状粘弹性复合材料板的自由振动。该复合板由线性各向同性弹性纤维增强的粘弹性聚合物基体组成。采用多单元微机械方法，结合体/剪切模量的松弛函数和玻尔兹曼叠加原理，建立了层板随时间变化的刚度系数。基于拉普拉斯变换和汉密尔顿原理，基于三阶剪切变形理论，导出了运动的积分PDE。通过加权残差法，迭代数值算法和傅里叶变换获得了复杂的频率和瞬态响应的闭式解。为了进行验证，将在Pasternak弹性地基上的厚弹性复合材料板与没有基础的厚粘弹性复合材料夹心板的结果进行了比较，这些精度都可以接受。通过参数研究，研究了材料，层压方案，几何形状和介质对动力特性的影响。 （C）2017 Elsevier Ltd.保留所有权利。

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