The paper addresses the free vibration problem of a laminated composite sandwich plate with compressible core, placed at the bottom of a tank filled in with fluid. The analysis is performed based on the extended higher order sandwich plate theory (EHSAPT). First-order shear deformation theory (FSDT) is used for the face sheets. Cubic and quadratic polynomials are used to describe the in-plane and transverse displacements of the core, respectively. The fluid is assumed inviscid, incompressible, and irrotational. To obtain the kinetic energy of the fluid, its velocity potential is expressed by using the compatibility and boundary conditions. The governing differential equations and corresponding boundary conditions are derived from Hamilton’s principle. A single series expansion is considered with two-variable orthogonal polynomials as a set of admissible functions satisfying the boundary conditions. The natural frequencies of the coupled sandwich plate-fluid system are calculated by using the Rayleigh-Ritz method. Convergence of the adopted strategy is first investigated. Then, comparisons are conducted with previous results reported in the literature. Also, the effects are investigated of several parameters, such as the plate side-to-thickness ratio, the core-to-face sheets thickness ratio, the face sheet-to-core flexural modulus ratio, the height and aspect ratio of the tank.

本文解决了带有可压缩芯层的层压复合材料夹心板的自由振动问题，该夹心板置于装有液体的罐体底部。基于扩展的高阶夹心板理论（EHSAPT）进行分析。一阶剪切变形理论（FSDT）用于面板。三次多项式和二次多项式分别用于描述岩心的平面内位移和横向位移。假定流体不粘稠，不可压缩且无旋转。为了获得流体的动能，通过使用相容性和边界条件来表达其速度势。控制性微分方程和相应的边界条件是根据汉密尔顿原理得出的。具有两个变量的正交多项式的单序列展开被认为是满足边界条件的一组允许函数。耦合夹层板-流体系统的固有频率是通过使用瑞利-里兹方法来计算的。首先研究所采用策略的收敛性。然后，与文献中报道的先前结果进行比较。此外，还研究了几个参数的影响，例如板的边长与厚度之比，板芯对板的厚度比，板对芯的弯曲模量比，储罐的高度和长宽比。首先研究所采用策略的趋同性。然后，与文献中报道的先前结果进行比较。此外，还研究了几个参数的影响，例如板的边长与厚度之比，板芯对板的厚度比，板对芯的弯曲模量比，储罐的高度和长宽比。首先研究所采用策略的收敛性。然后，与文献中报道的先前结果进行比较。此外，还研究了几个参数的影响，例如板的边长与厚度之比，板芯对板的厚度比，板对芯的弯曲模量比，储罐的高度和长宽比。