Effect of different geometrical non-uniformities on nonlinear vibration of porous functionally graded skew plates: A finite element study

Abstract

This article presents the investigation of nonlinear vibration analysis of tapered porous functionally graded skew (TPFGS) plate considering the effects of geometrical non-uniformities to optimize the thickness in the structural design. The TPFGS plate is analyzed considering linearly, bi-linearly, and exponentially varying thicknesses. The plate's effective material properties are tailor-made using a modified power-law distribution in which gradation varies along the thickness direction of the TPFGS plate. Incorporating the non-linear finite element formulation to develop the kinematic equation's displacement model for the TPFGS plate is based on the first-order shear deformation theory (FSDT) in conjunction with von Karman's nonlinearity. The nonlinear governing equations are established by Hamilton's principle. The direct iterative method is adopted to solve the nonlinear mathematical relations to obtain the nonlinear frequencies. The influence of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the TPFGS plate for different skew angles and variable thicknesses are studied for various geometrical parameters. The influence of taper ratio, variable thickness, skewness, porosity distributions, gradation, and boundary conditions on the plate's nonlinear vibration is demonstrated. The nonlinear frequency analysis reveals that the geometrical non-uniformities and porosities significantly influence the porous functionally graded plates with varying thickness than the uniform thickness. Besides, exponentially and linearly variable thicknesses can be considered for the thickness optimizations of TPFGS plates in the structural design.

Keywords

• Functionally graded material
• Shear deformation theory
• Porosity distributions
• Variable thickness
• Geometrical skewness
• Nonlinear free vibration