This paper for first time proposes an isogeometric analysis (IGA) for free vibration response of bi-directional functionally graded (BDFG) rectangular plates in the fluid medium. Material properties of the BDFG plate change in both the thickness and length directions via power-law distributions and Mori-Tanaka model. The governing equation of motion of BDFG plate in the fluid-plate system is formulated basing on Hamilton's principle and the refined quasi three-dimensional (3D) plate theory with improved function f(z). The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to determine the added mass. The discrete system of equations is derived from the Galerkin weak form and numerically analyzed by IGA. The accuracy and reliability of the proposed solutions are verified by comparing the obtained results with those published in the literature. Moreover, the effects of the various parameters such as the interaction boundary condition, geometric parameter, submerged depth of plate, fluid density, fluid level, and the material volume control coefficients on the free vibration behavior of BDFG plate in the fluid medium are investigated in detail. Some major findings regarding the numerical results are withdrawn in conclusions.

本文首次提出了双向功能梯度（BDFG）矩形板在流体介质中的自由振动响应等几何分析（IGA）。BDFG 板的材料特性通过幂律分布和 Mori-Tanaka 模型在厚度和长度方向上发生变化。基于Hamilton原理和改进函数f ( z）。流体速度势源自流体板系统的边界条件，用于确定附加质量。离散方程组源自 Galerkin 弱形式，并通过 IGA 进行数值分析。通过将获得的结果与文献中发表的结果进行比较，验证了所提出解决方案的准确性和可靠性。此外，还研究了相互作用边界条件、几何参数、板浸没深度、流体密度、液位和材料体积控制系数等各种参数对BDFG板在流体介质中的自由振动行为的影响。细节。关于数值结果的一些主要发现在结论中被撤回。