Vibration of a plate coupled with fluid considering the effects of stress and deformation under hydrostatic load

Abstract

Abstract The effects of inner stress and geometric deformation caused by hydrostatic load on the vibration of a bottom plate-fluid coupled system are studied in detail. The Von Karman nonlinear strain displacement relationship and the Hamilton's principle are utilized to formulate the two sets of governing equations: nonlinear static equations under hydrostatic load and linear vibration equations of the plate-fluid coupled system considering the hydrostatic load effect at the nonlinear static position. A two-step theoretical approach is developed based on the equations. Experimental and numerical researches are carried out to validate the theoretical approach, and the natural frequencies derived by the three approaches coincide well. The results show that with the fluid height increasing, the natural frequencies of the plate decrease sharply at the very beginning, then increase constantly except that the fundamental frequency continues to decrease slowly. That means the added mass effect is the dominating effect when the fluid height is low, and the stiffening effect of the hydrostatic load plays a more important role with the fluid getting higher. The stress and deformation effects are considered respectively and compared in detail. Models with different fluid-plate size ratios are studied. Moreover, the hydrostatic load effect on the hydroelastic vibration responses of the plate is also analyzed.