An analytical solution for nonlinear vibration of floating plate on the fluid by modified multiple scales method

The aim of the present paper is to analytically study the nonlinear forced vibration of a rectangular plate floating on the fluid by Modified Multiple Time Scales method for the first time. It is assumed that the fluid is stationary, incompressible, non-viscous, and non-rotational, and the plate is subjected to transversal excitation. The boundary condition is considered to be simply supported. Using von Karman nonlinear strain displacement relationships, the extended Hamilton principle, and FSTD plate theory, the partial differential equations of motion are derived. The fluid is mathematically modeled by Bernoulli equation and the velocity potential function. Galerkin method is then applied for converting the nonlinear partial differential equations into time-dependent nonlinear ordinary differential equations. The resulted equations are solved analytically by the Modified Multiple Scales Method, thereafter. Despite the large number of derivatives and calculations of the conventional multiple scale method, this approach is very simple and straightforward. The results reveal an excellent agreement with the traditional Multiple Scales method results and existing studies, and are more accurate than other available results. The effect of the presence of fluid near the plate on natural frequency and amplitude of vibration of plate are studied. The effects of some key parameters of the system are also examined.