Buckling and free vibration characteristics of embedded inhomogeneous functionally graded elliptical plate in hygrothermal environment

Abstract

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.