Nonlinear frequency analysis of porous Bi directional functionally graded beams utilizing reddy shear deformation theory

The nonlinear frequency response of bi-directional functionally graded porous beams experienced range of various end conditions is investigated in this work. The end conditions which are simply supported, clamped-simply supported, clamped-clamped, and clamped-free are taken by using the Von Karman geometric nonlinearity, Green's tensor and Reddy third-order shear deformation theory. A generalized differential quadrature technique (GDQM) accompanied by direct numerical iterance approach is proposed to solve equations. The findings are presented to aid in future research into the effects of various gradient indices, vibration amplitude ratios, porosity coefficients, shear and elastic substrate parameters, boundary conditions, and vibration frequencies on the bi-directional functionally graded beams. The outcomes of this research have practical applications and can be utilized to enhance the design of bi-directional beams. The results are also highly useful in anticipating and identifying potential causes of failure in these beams.