Imperfection sensitivity of free vibration of symmetrically/anti-symmetrically laminated FRC beams in thermally pre-and post-buckling equilibrium states

Linear/nonlinear free vibration of imperfect symmetrically/anti-symmetrically laminated fibre-reinforced composite (FRC) beams in the pre-and post-buckling equilibrium states are studied. It is assumed that the initial defect has the same shape as the first-order buckling mode and the in-plane boundaries are immovable. A modified higher-order shear deformation zig-zag beam model is applied for refined modeling of the laminated beams. The Hamilton variational principle is utilized to obtain the governing equations of motion. The two-step perturbation technique is combined with the harmonic balance method to obtain the asymptotic analytic solutions. The results based on the zig-zag model and its degenerate equivalent single-layer models are compared and verified. Further, the sensitivity of vibration characteristics to the size of imperfections at different temperature rise is investigated. Numerical results suggest that there exists a load range near the critical buckling load of the perfect beams where the linear/nonlinear frequency is sensitive to the initial imperfections.