Vibration of a plate with arbitrary shape in contact with a fluid

This paper is concerned with a method for solving vibration problems of arbitrarily shaped plates in contact with a fluid. Expressions of natural frequencies, displacements, and pressures for arbitrary plates in contact with a fluid are obtained with consideration of viscosity of fluid. The analysis applies the exact solution of the equations of motion and the Fourier expansion collocation method for satisfying the boundary conditions. Numerical calculations have been carried out for elliptical plates and rectangular plates with round corners in contact with a fluid.