On an exact bending curvature model for nonlinear free vibration analysis shear deformable anisotropic laminated beams

Geometrically nonlinear free vibration analysis of shear deformable anisotropic laminated composite beams resting on a two-parameter elastic foundation is presented. The material of each layer of the beam is assumed to be linearly elastic and fiber-reinforced. A new nonlinear beam model involving the exact expression of bending curvature is introduced, and the nonlinear vibration analysis with exact nonlinear characteristics of the work done by axial loading is accordingly performed. The governing equations are based on higher order shear deformation beam theory with a von Kármán-type of kinematic nonlinearity and including the bending–stretching, bending–twisting, and stretching–twisting couplings. Two kinds of end conditions, namely movable and immovable, are considered, and a perturbation technique is employed to determine the linear and nonlinear frequencies of a composite beam with or without initial stresses. The frequency response of laminated beams with different geometric and material parameters, end conditions and effect on elastic foundation is numerically illustrated. The results reveal that the geometric and physical properties, end conditions, and elastic foundation effect have a significant influence on large amplitude vibration behavior of anisotropic laminated composite beams.