Effect of two-dimensional material distribution on dynamic and buckling responses of graded ceramic-metal higher order beams with stretch effect

Abstract

The contribution provided in this article is to examine free vibration and stability response of bidirectional graded material beams (BDFB) considering different boundary conditions. The stretch effect by means of a normal deformation in conjunction with the shear deformation influence are integrated for accurate results. The beam materials features are expected to depend on gradation pattern over the length and transverse directions via power law form. Lagrange’s principle is employed in order to extract the governing equations of motion. A novel approach namely differential quadrature-based Galerkin method (DQGM) is used as an effective and accurate semi-analytical tool to compute the critical stability loads and natural frequencies of (BD-FG) beam for the first time. The approach takes features from simplicity and reduced computational cost of the DQ in combination with the efficacy of the Galerkin method for its analytical aspect and easy dealing with mixed boundary conditions resulting in more accurate results. The correctness of the results obtained from the present approach for two-directional functionally graded materials (FGMs) beams have been verified. Finally, the impacts of design parameters such as material grading exponent distributions, length to thickness ratios, porosity amount, and end support types on the natural frequencies and maximum of stability loads related to the present 2D-FGM beams are examined.