In the present work, effect of hygrothermal environment on vibration and buckling behavior of embedded functionally graded elliptical plate under uniform in plane compression is studied. The properties of elliptical plate vary in transverse direction following power law. The functionally graded elliptical plate is considered to be resting on the Winkler–Pasternak elastic foundation. The governing equations are derived using the principle of virtual work and solved by employing the Rayleigh–Ritz method. The algebraic polynomials are employed to satisfy the different boundary constraints. The advantage of the presented mathematical model over the previously reported methods is that it eliminates the constraints regarding edge conditions, and it is simple and computationally fast. The inclusive results depicting the effect of various parameters namely, material property exponents, foundation parameters, aspect ratio on mechanical and thermomechanical buckling, and natural frequency of embedded functionally graded elliptical plate in a hygrothermal environment are reported after the test of convergence and extensive comparisons. The study shows that increase in foundation moduli lead to an increase in natural frequency and buckling parameter. Furthermore, it is noticed that the temperature and moisture concentration remarkably affect the buckling and vibration behavior of functionally graded elliptical plate.

在目前的工作中，研究了湿热环境对均匀压缩面内嵌入的功能梯度椭圆板的振动和屈曲行为的影响。椭圆板的特性在横向上遵循幂律变化。功能渐变椭圆板被认为位于Winkler-Pasternak弹性地基上。控制方程是根据虚拟功原理导出的，并通过瑞利-里兹方法进行求解。代数多项式用于满足不同的边界约束。相对于先前报道的方法，所提出的数学模型的优点在于，它消除了关于边缘条件的约束，并且简单且计算速度快。包含性结果描述了各种参数的影响，包括材料特性指数，地基参数，纵横比对机械和热机械屈曲以及在湿热环境中嵌入功能梯度椭圆板的固有频率的影响。研究表明，基础模量的增加导致固有频率和屈曲参数的增加。此外，注意到温度和水分浓度显着影响功能梯度椭圆板的屈曲和振动行为。经过收敛性测试和大量比较后，报道了在湿热环境中嵌入功能梯度椭圆板的固有频率和固有频率。研究表明，基础模量的增加导致固有频率和屈曲参数的增加。此外，注意到温度和水分浓度显着影响功能梯度椭圆板的屈曲和振动行为。经过收敛性测试和大量比较后，报道了在湿热环境中嵌入功能梯度椭圆板的固有频率和固有频率。研究表明，基础模量的增加导致固有频率和屈曲参数的增加。此外，注意到温度和水分浓度显着影响功能梯度椭圆板的屈曲和振动行为。