This paper studies the dynamic viscoelastic response of functionally graded (FG) thick 2D cantilever and simply supported beams under dynamic pulse load, for the first time. A point load applied at a specific spatial point is described as a time-pulse sinusoidal load. Two-dimensional plane-stress constitutive equation is exploited to describe the local stress–strain relation through the beam. The gradation of material is depicted by generalized power law function through the layer thickness across beam thickness. The Kelvin–Voigt viscoelastic model is proposed to describe material damping of structure. Lagrange’s equation is employed to derive governing motion equation. A finite element method (FEM) is exploited to discretize the spatial domain of 2D beam structure by using 12-node 2D plane element. Numerical Newmark implicit time integration method is proposed to solve the equation of motion incrementally and get the response of beam structure. Two types of boundary conditions are considered in the numerical examples. In numerical results, effects of stacking sequence, geometry parameters and material gradation index and viscoelasticity coefficients on the displacement-time response of layered functionally graded viscoelastic deep beams for different boundary conditions.

中文翻译：

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脉冲载荷作用下不同边界条件的层状功能梯度粘弹性深梁动态分析

本文首次研究了功能梯度（FG）厚二维悬臂梁和简支梁在动态脉冲载荷下的动态粘弹性响应。施加在特定空间点的点载荷被描述为时间脉冲正弦载荷。利用二维平面应力本构方程来描述通过梁的局部应力-应变关系。材料的渐变通过跨梁厚度的层厚度通过广义幂律函数来描述。提出了 Kelvin-Voigt 粘弹性模型来描述结构的材料阻尼。拉格朗日方程用于推导控制运动方程。采用有限元法（FEM），利用12节点二维平面单元对二维梁结构的空间域进行离散化。提出了数值Newmark隐式时间积分方法对运动方程进行增量求解，得到梁结构的响应。在数值例子中考虑了两种类型的边界条件。在数值结果中，堆叠顺序、几何参数和材料级配指数和粘弹性系数对不同边界条件下分层功能梯度粘弹性深梁位移-时间响应的影响。