Free vibration analysis of two-dimensional functionally graded axisymmetric cylindrical shell on Winkler–Pasternak elastic foundation by First-order Shear Deformation Theory and using Navier-differential quadrature solution methods

Abstract

This paper focuses on the dynamic behavior of moderately thick functionally graded cylindrical shell based on the First-order Shear Deformation Theory (FSDT). The FSDT is applied to investigate free vibration of 2D-FG cylindrical shell surrounded by Winkler–Pasternak elastic foundation. The material properties of functionally graded cylindrical shell are graded in two directional (radial and axial) and assumed to obey the power law distribution. The energy method is used to derive the potential, kinematic and virtual work energy functions. Then the Euler’s equation and Hamilton’s principle are employed to derive the stability and equations of motion, respectively. The GDQ method is examined by comparing its results with those available in the literature. The GDQ approach is used to obtain as natural frequencies and mode shapes as we want without any frequency missing. The main advantages of this method are known for its higher accuracy with small computational expensiveness in compare to Navier-type solution with twofold Fourier series. Fundamental frequencies and mode shapes are presented in this paper. The determined facets like boundary conditions, values of translational and rotational spring constants and the volume fraction indices on the natural frequencies and mode shapes are discoursed.