A semi-analytical state-space approach for 3D transient analysis of functionally graded material cylindrical shells

Abstract

Abstract:A good understanding of the mechanical behavior of functionally graded material (FGM) cylindrical shells is necessary for designers and researchers. However, the 3D transient response of FGM cylindrical shells under various boundary conditions has not yet been analyzed. In this paper, the problem is addressed by proposing an approach integrating the state space method, differential quadrature method, and Durbin's numerical inversion method of Laplace transform. The laminate model is used to obtain the transient solution in the radial direction. At the edges, four kinds of boundary conditions are considered: Clamped-Clamped, Clamped-Simply supported, Clamped-Free, and Simply supported-Simply supported. The results of the proposed method and finite element (FE) method agree with each other excellently. Convergence studies show that the proposed method has a fast convergence rate. The natural frequencies obtained by the proposed method, experiment, and other theoretical methods are in close agreement with each other. The effects of the load frequency and duration, length/outer radius ratio, and the (outer radius−inner radius)/outer radius ratio on the transient response of FGM shells are investigated. Two laws of variation of material properties along the radial direction are considered: the first has material properties varying according to an exponential law along the radial direction, while the second has material properties varying according to a power law. The effect of a functionally graded index on the transient response of FGM shells is investigated in both cases. The results obtained in this paper can serve as benchmark data for further research.

Three-dimensional semi-analytical solutions for the transient response of functionally graded material cylindrical panels with various boundary conditions

“…The force applying to the outer surface ( r = a ) of the cylindrical panel is given as 31 where cA=true(C33,A/ρAtrue)1/2 is the longitudinal wave velocity of aluminium. 44…”

“…At the outer and inner surfaces, the boundaries equations (31) and (32) are applied into equation (38) f…”

“…The force applying to the outer surface (r¼a) of the cylindrical panel is given as 31 at r ¼ a; r r ¼ 10 À3 C 33;A sin jp a h…”

“…Liang et al. 31t a investigated the 3D transient response of FGM rectangular plates, annular sector plates and cylindrical shells under various boundary conditions. The responses were calculated by a proposed approach combining the SSM with DQM and Durbin’s 34 numerical method.…”

Three-dimensional dynamics of functionally graded piezoelectric cylindrical panels by a semi-analytical approach

“…For the orthotropic properties, the stiffness coefficients, mass density, piezoelectric constants and dielectric constants are supposed to obey the identical exponential law with the thickness coordinates. The material properties along the radial direction are given by the following equation [41] (37)…”