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

• Published in: Archives of Civil and Mechanical Engineering Vol. 22; no. 1; p. 38
• Main Authors: Sh, Esayas L., Kattimani, Subhaschandra, Vinyas, M.
• Format: Journal Article
• Language: English
• Published: London Springer London 04.01.2022; Springer Nature B.V
• Subjects: Aspect ratio; Boundary conditions; Civil Engineering; Composite materials; Deformation; Elastic deformation; Elastic plates; Engineering; Equations of motion; Finite element method; Free vibration; Functionally gradient materials; Graphene; Investigations; Magnetic fields; Mechanical Engineering; Newton-Raphson method; Nonlinear response; Original Article; Porosity; Porous materials; Shear deformation; Structural Materials; Temperature; Transient response; Vibration analysis; Porosity distribution; Transient deflection; Nonlinear frequency ratio; Porous functionally graded magneto-electro-elastic (PFG-MEE) plates
• ISSN: 2083-3318; 1644-9665; 2083-3318
• DOI: 10.1007/s43452-021-00357-6

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.