Investigating dynamic free vibration response of isotropic thin rectangular plate resting on two-parameter elastic foundation is of interest in the field of geotechnics, structure, highway, railway and mechanical engineering. This study employs analytical approach to the investigation of free vibration analysis of isotropic rectangular plate submerged in fluid and resting on combined elastic foundations under different support conditions. The nonlinear partial differential equation of the system is transformed into nonlinear ordinary differential equation using the Galerkin method of separation. The resulting ordinary differential equation is solved using Adomian decomposition method (ADM). The reliability of the solutions obtained is validated with numerical and existing results as reported in the literature. Also, the bending moment and stress are analysed. The analytical solutions are used for the investigation of dynamic behaviour of plates in fluid, effect of aspect ratio, effect of elastic foundation parameters on natural frequency and effect of bending moment and stress on the mode of the vibrating plate. From the results, it is observed that the increase in elastic foundation parameter increases the natural frequency. Increasing the aspect ratio increases the natural frequency. Increasing the combined elastic foundation parameters increases the natural frequency. Natural frequency of plates reduces when submerged in fluid with the mode shapes not significantly affected. The node and antinodes of the mode shapes are affected by moment and stress. It is expected that the present study will add to the existing knowledge in the field of vibration of plates.

中文翻译：

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Adomian分解法在流体浸没的各向同性矩形薄板自由振动分析中的应用

研究基于二参数弹性基础的各向同性薄矩形板的动态自由振动响应是岩土、结构、公路、铁路和机械工程领域的研究热点。本研究采用解析方法研究浸没在流体中并搁置在不同支撑条件下的组合弹性基础上的各向同性矩形板的自由振动分析。系统的非线性偏微分方程采用伽辽金分离法转化为非线性常微分方程。使用 Adomian 分解方法 (ADM) 求解所得常微分方程。获得的解决方案的可靠性通过文献中报道的数值和现有结果进行了验证。还，分析弯矩和应力。解析解用于研究板在流体中的动态行为、纵横比的影响、弹性基础参数对固有频率的影响以及弯矩和应力对振动板模式的影响。从结果可以看出，弹性基础参数的增加会增加固有频率。增加纵横比会增加固有频率。增加组合弹性基础参数会增加固有频率。当浸入流体中时，板的固有频率会降低，而模态形状不会受到显着影响。振型的节点和波腹受力矩和应力的影响。