Influence of initial imperfection and coupling between bending and extension on vibration, buckling and nonlinear dynamic stability of laminated plates (Q1818163)

The authors analyze the influence of initial imperfection and bending-extension coupling on buckling and nonlinear dynamic stability of plates. The derived governing equation is a nonlinear modified Mathieu equation. Numerical solutions are obtained for five typical composite materials. Results reveal that the initial imperfection and coupling effect make the plates more sensitive to parametric resonance with amplitude larger than that for perfect plates. According to linear theory of dynamic stability, in the unstable regions the vibration amplitude increases rapidly and becomes unbounded. Experiments reveal that the vibration amplitude at the first stage increases rapidly, but when it reaches a certain value in the small-deflection regime, it enters a second transitional stage, and then either passes to a steady regime with a large amplitude or enters an unstable regime with growing amplitude. Linear theory cannot explain these phenomena. Therefore, here the authors study the nonlinear dynamic stability problem, and use the solution of nonlinear modified Mathieu equation to compute large vibration amplitudes in a wide range of exciting frequency.