Post-buckling path and free vibration of a symmetric laminated plate vertically coupled with fluid under in-plane load

Abstract

In this paper, the effect of compressive in-plane load on the equilibrium paths and vibration characteristics of a vertical symmetric laminated plate coupled with fluid is studied theoretically both in the pre- and post-buckling state. The Third-order shear deformation theory and von Karman nonlinear strain displacement relationship are utilized to describe the nonlinear deformation of the plate consists of a number of fiber-reinforced layers. The Hamilton's principle is introduced to formulate the plate-fluid coupled governing equations. A two-step theoretical approach is developed. Firstly, based on the Cylindrical arc-length method, we solve the nonlinear static equations to trace the snap-back behavior and pass the limit points along the complex equilibrium paths obtaining the stable buckling deflection. Then the coupled vibration characteristics are calculated using the tangent stiffness at the stable positions. The present theoretical results are validated by the numerical results. The effects of added mass and hydrostatic load are compared and analyzed. It is noted that, in the post-buckling state, the number of limit points along the static unstable equilibrium path increases with the compressive in-plane load getting larger. The variation trends of the natural frequencies and modes under different in-plane loads in pre- and post-buckling state are investigated.