In this paper, an analytical solution for functionally graded sandwich plate adhesively bonded by viscoelastic interlayer is proposed to research its time-dependent behavior. The Kirchhoff plate theory is employed to describe the mechanical property of each gradient layer with elastic modulus defined as the arbitrary function through the thickness direction. The standard linear solid model is applied to simulate the viscoelasticity of the interlayer with considering the strain memory effect. By the use of the vibrational method and the Laplace transformation, the solutions of stresses and displacements are solved analytically. The validation study indicates that the present solution is correct and more effective than the finite element solution because of the fine mesh both in the geometric shape and the time step. In addition, the influences of the geometry and material parameters on the time-dependent behavior of the sandwich plate are investigated in detail.

中文翻译：

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基于基尔霍夫板理论的粘弹性夹层粘合的功能梯度夹心板解析解

本文提出了一种粘弹性夹层粘合的功能梯度夹层板的解析解，以研究其随时间变化的行为。基尔霍夫板理论用于描述梯度层的力学性能，弹性模量定义为沿厚度方向的任意函数。考虑应变记忆效应，采用标准线性实体模型模拟夹层的粘弹性。通过使用振动方法和拉普拉斯变换，解析求解应力和位移的解。验证研究表明，由于几何形状和时间步长上的网格精细，本解法比有限元解法正确且更有效。此外，