Multi-modal geometrical non-linear free vibration of fully clamped composite laminated plates

Abstract The geometrically non-linear free vibration of thin composite laminated plates is investigated using the hierarchical finite-element (HFEM) and the harmonic-balance methods (HBM). Von Karman's non-linear strain–displacement relationships are employed and the mid-plane in-plane displacements are included in the model. The equations of motion are developed by applying the principle of virtual work and are solved by a continuation method. The convergence properties of the HFEM and of the HBM are analyzed. Internal resonances are discovered and the consequent multi-modal and multi-frequency vibration of the plates is shown. The variation of the plates' mode shape and the effect of the fibres' orientation are investigated.