Abstract

The three-dimensional bending behavior of a viscoelastic functionally graded material (FGM) layer embedded between piezoelectric layers and subjected to an electric field as well as a uniform transverse pressure is studied. An analytical solution is computed for a simply supported viscoelastic smart FGM plate using the state space technique along the thickness direction and a Fourier expansion along the in-plane coordinates. The governing differential equations in the time domain are transformed to the Laplace domain, solved in the Laplace domain, and transformed back to the time domain using the inverse Laplace transform. In the present study, the relaxation modulus of the FGM layer is assumed in the form of a Prony series, and it varies according to the power law in the thickness direction. The validity of the proposed approach is assessed by comparison of the numerical results of the approach with those of published works in the literature. The effects of geometric dimensions, electromechanical loads, and relaxation time constant on the behavior of the smart plate are investigated.

摘要

研究了嵌入压电层之间并受到电场和均匀横向压力的粘弹性功能梯度材料 ( FGM ) 层的三维弯曲行为。使用沿厚度方向的状态空间技术和沿面内坐标的傅里叶展开计算简支粘弹性智能FGM板的解析解。时域中的控制微分方程被转换到拉普拉斯域，在拉普拉斯域中求解，然后使用拉普拉斯逆变换转换回时域。在本研究中，FGM的松弛模量层假设为 Prony 级数形式，在厚度方向上按幂律变化。通过比较该方法的数值结果与文献中已发表作品的数值结果来评估所提出方法的有效性。研究了几何尺寸、机电负载和弛豫时间常数对智能板行为的影响。