Nonlinear free vibration and transient responses of porous functionally graded magneto-electro-elastic plates

The geometrically nonlinear free vibration and transient response of porous functionally graded magneto-electro-elastic (PFG-MEE) plates are studied based on the first-order shear deformation (FSDT) theory, von Karman's nonlinear strain-displacement relations along with modified power law. With Hamilton's theory, the coupled equations of motion are obtained and analyzed by adapting finite element methods (FEM). Moreover, using Newmark's, Picard's, and Newton-Raphson methods, a porous FG-MEE plate's nonlinear and transient response is analyzed using MATLAB software. After validating the present study, the influence of porosity distribution, porosity index, boundary conditions, aspect ratios, and thickness to length ratios on the nonlinear frequency ratio and nonlinear transient response of porous FG-MEE plate is investigated. It is revealed that geometric parameters, porosity index, boundary conditions, and form of porosity distribution significantly influence the nonlinear frequency ratio and nonlinear transient deflections of porous FG-MEE plates.

Automated summary

This study investigates the geometrically nonlinear free vibration and transient response of porous functionally graded magneto-electro-elastic plates. The coupled equations of motion are obtained using finite element methods and analyzed using MATLAB software. The study reveals that various factors significantly influence the nonlinear frequency ratio and nonlinear transient deflections of the plates.