In this study, an analytical procedure for the bending problem of a viscoelastic sandwich plate with a corrugated core is presented. Reissner–Mindlin plate theory and N-termed Prony series are employed to define the elastic and time-dependent contributions of the governing equations, respectively. Three different corrugation patterns, i.e., rectangular, trapezoidal, and triangular, are examined. Moreover, the structure is analyzed under both simply support and clamp boundary conditions. The calibrated material parameters of polymethyl methacrylate (PMMA) for the Generalized Maxwell rheological model are employed to show the viscoelastic response of the structure. A 3D finite element simulation of the problem is also conducted to confirm the accuracy of the analytical formulation. The two well-known creep and stress relaxation phenomena of the viscoelastic materials are examined for the mentioned corrugation cores and both boundary conditions analytically and numerically. The time-dependent dimensionless deflection and resultant von Mises stress distributions are provided. Besides, the variation of the results with various rise-times and applied load are studied in detail. The von Mises stress contours of the upper surface of the structure at the end of the creep test are also presented. The finite element method outcomes verify the analytical results with excellent compatibility. The proposed analytical procedure can be used as an efficient tool to study the effects of various parameters such as material, geometrical constants, and corrugation pattern on bending of viscoelastic sandwich plates with corrugated core problems for design and optimization, which involves a high number of simulations.

在这项研究中，提出了一种对具有波纹芯的粘弹性夹心板弯曲问题的分析程序。使用Reissner-Mindlin板理论和N项Prony级数分别定义控制方程的弹性和时间相关贡献。检查了三种不同的波纹图案，即矩形，梯形和三角形。此外，在简单的支撑和夹紧边界条件下对结构进行了分析。使用针对通用麦克斯韦流变模型校准的聚甲基丙烯酸甲酯（PMMA）的材料参数来显示结构的粘弹性响应。还对该问题进行了3D有限元模拟，以确认分析配方的准确性。分析和数值分析了上述波纹芯的粘弹性材料的两种众所周知的蠕变和应力松弛现象。提供了随时间变化的无量纲挠度和合成的冯·米塞斯应力分布。此外，还详细研究了结果在不同的上升时间和施加的载荷下的变化。还显示了蠕变测试结束时结构上表面的von Mises应力轮廓。有限元方法的结果证明了分析结果具有出色的兼容性。拟议的分析程序可以用作研究各种参数（例如材料，几何常数，