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An analytical solution for dynamic behavior of thick doubly curved functionally graded smart panels

机译：一种双曲线功能梯度厚智能面板动态行为的解析解决方案

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In this paper, an analytical solution is presented for free vibration and dynamic behavior of doubly curved laminated shell consisting of a functionally graded core layer and surface attached functionally graded piezoelectric layers. Shell through-thickness kinematics is based on higher order shear deformation theory of shells, whereas a quadratic variation is assumed for electric potential. Using Hamilton's principle and Maxwell's equation, the governing equations of motion under mechanical loads are derived as seven highly coupled partial differential equations. Implementing Laplace transformation, doing few mathematical operations and using Laplace inverse method, time dependencies of displacement components are expressed in explicit phrases. Besides numerical results for shell natural frequencies, effects of different material properties and shell geometries on the transient response are discussed in details. In particular the influence of shell curvature on the spectra of maximax response has been studied. It is found that, these parameters play major roles on determining the time-histories of the electric potential and displacement components.
机译：在本文中，提出了一种双曲线叠层壳的自由振动和动态行为的解析解决方案，该叠层壳由功能渐变的芯层和表面附着的功能渐变的压电层组成。壳厚度运动学基于壳的高阶剪切变形理论，而电势被认为是二次方变化。利用汉密尔顿原理和麦克斯韦方程，将机械载荷下的运动控制方程导出为七个高度耦合的偏微分方程。实现拉普拉斯变换，进行少量数学运算并使用拉普拉斯逆方法，位移分量的时间相关性用显式短语表示。除了壳固有频率的数值结果外，还详细讨论了不同材料特性和壳几何形状对瞬态响应的影响。特别是，研究了壳曲率对最大响应光谱的影响。已经发现，这些参数在确定电势和位移分量的时间历史方面起主要作用。

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