Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates

This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.

Nonlinear transient responses of rotating twisted FGM cylindrical panels

This paper develops a new structure dynamic model to investigate nonlinear transient responses of the rotating blade made of functionally graded material(FGM). The rotating blade is simplified as a rotating FGM cylindrical panel with a presetting angle and a twist angle. The geometric nonlinearity effects are taken into account in the strain-displacement relationships, which are derived by Green strain tensor. Based on the first-order piston theory and the first-order shear deformation theory, the equations of motion for the rotating twisted FGM cylindrical panel are acquired by means of Hamilton principle and Galerkin method.Backward Differentiation Formula(BDF) and Runge-Kutta Algorithm are used to solve the nonlinear equations of motion for the system. The effects of four pulse load conditions on the system subjected to the internal pulse load or the external pulse load are fully discussed. A detailed parametric analysis is performed by considering the effects of the rotating speed, volume fraction index and temperature.

Nonlinear Transient Response of Functionally Graded Material Sandwich Doubly Curved Shallow Shell Using New Displacement Field

In this paper, the nonlinear transient dynamic response of functionally graded material （FGM） sandwich doubly curved shell with homogenous isotropic material core and functionally graded face sheet is analyzed using a new displacement field on the basis of Reddy＇s third-order shear theory for the first time. The equivalent material properties for the FGM face sheet are assumed to obey the rule of simple power law function in the thickness direction. Based on Reddy＇s theory of higher shear deformation, a new displacement field is developed by introducing the secant function into transverse displacement. Four coupled nonlinear differential equations are obtained by applying Hamilton＇s principle and Galerkin method. It is assumed that the FGM sandwich doubly curved shell is subjected to step loading, air-blast loading, triangular loading, and sinusoidal loading, respectively. On the basis of double-precision variable- coefficient ordinary differential equation solver, a new program code in FORTRAN software is developed to solve the nonlinear transient dynamics of the system. The influences of core thickness, volume fraction, core-to-face sheet thickness ratio, width-to-thickness ratio and blast type on the transient response of the shell are discussed in detail through numerical simulation.