Abstract
This paper is concerned with a method for solving the vibration of uniform columns with arbitrarily shaped cross-sections partially submerged in water considering the effects of surface wave and compressibility of water. First, the exact expression for the velocity potential of water motion is obtained by the method of separation of variables, whose coefficients are decided by utilizing the orthogonality of a group of generalized trigonometric series and the Fourier expansion collocation method. Then, the analytical solution of the differential equation of motion of the column in water is obtained, frequency equation and mode shapes are derived by the use of the boundary conditions of the column. The results may be numerically given by means of a computer.
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