Vibration of thermally post-buckled hybrid laminates with two non-uniformly distributed fibers

This study presents the first vibration analysis of thermally post-buckled hybrid laminates with non-uniformly distributed graphite and E-glass fibers in a single lamina. A 54 degree-of-freedom high order triangular plate element is developed based on the Von Karman large deflection assumption. The formulation of the location dependent linear, nonlinear stiffness and mass matrices due to non-homogeneous material properties, geometrical stiffness matrix due to thermal effects and thermal moment vector due to temperature gradient is derived. The effects of hybrid-fiber distribution on the natural frequencies and mode shapes of thermally post-buckled laminates are discussed. The numerical results reveal that the redistribution of two fibers can considerably decrease the postbuckling deflections of the hybrid laminates and significantly modify the natural frequencies. The stiffening effect of fiber redistribution is more obvious for the laminate with a higher volume fraction index and clamped edges. Special buckling and vibration mode shapes are observed, along with multiple vibration mode shifting.