Nonlinear vibration analysis of functionally graded porous circular plates under hygro-thermal loading

Abstract

In this work, the nonlinear vibrations of functionally graded (FG) porous circular plates under hygro-thermal loading is studied utilizing a numerical approach. Hygroscopic stresses generated due to the nonlinear rise in moisture concentration, even and uneven porosity distributions, and temperature dependency of material properties are all taken into account. Modified Voigt’s rule of mixture is applied to obtain the hygro-thermo-mechanical properties of the FG circular plate. All material properties are assumed to be temperature-dependent using the Touloukian formula. In order to obtain the equations of motion, the first-order shear deformation theory, von-Kármán geometrical non-linearity assumption, and hygro-thermal strains are considered concurrently. After deriving the equations of motion using Hamilton’s principle, the differential quadrature method and the Newmark-beta time integration scheme are employed in conjunction with an iterative approach to solve the set of nonlinear governing differential equations of motion. The effects of various parameters including temperature distribution, plate’s thickness, porosity volume fraction, moisture concentration, and FG index are studied on plate’s maximum non-dimensional lateral deflection.