Large amplitude vibration and post-buckling analysis of variable cross-section composite beams on nonlinear elastic foundation

• Large amplitude vibration and post-buckling of non-uniform laminated beam is investigated.
• Effect of the variation cross-section on vibration and buckling of laminated beam is investigated.
• Influence of foundation coefficients on natural frequencies and buckling loads is presented.
• Differential quadrature method used to solution of nonlinear partial differential equations.

In this study, large amplitude vibration and post-buckling analysis of variable cross-section laminated composite beams with symmetric and asymmetric lay-ups resting on nonlinear elastic foundation is investigated using the generalized differential quadrature (GDQ) method. Geometric nonlinearity of von-Karman type is considered. Various combinations of boundary conditions including free edges are considered. Furthermore, elastic foundation consists of shearing layer, linear and cubic nonlinearity. Natural frequencies are obtained for the nonlinear problem using the Picard iterative method. Results for linear and nonlinear analyses of uniform laminated beams are validated with the available data in the open literature, which show close agreement. Moreover, some new results are also presented for the nonlinear natural frequencies and buckling load of the non-uniform laminated composite beams to study effects of vibration amplitude, elastic coefficients of foundation, axial force, boundary conditions and variation of cross-section.