| Abstract: | An eigenfunction solution is presented for the dynamic response of vertical circular cylinders to earthquake excitation in a compressible fluid of finite depth. This single eigenseries expansion eliminates the need for a double summation over both the eigenfunctions and the trial functions as required by Rayleigh-Ritz methods. Revised definitions for the added mass and hydrodynamic radiation damping coefficients per unit length are derived from the hydrodynamic fluid pressures. Based on comparisons between these newly defined coefficients, the compressibility of the fluid is found to be relatively more important at dimensionless frequencies greater than unity (ω > 1.0) when analysing both rigid and flexible cylinders having relatively large diameter to water depth ratios,r0/h > 0.25 (squatty type). This conclusion regarding the relative importance of the fluid compressibility is derived from a comparison between the relative magnitudes and the vertical distributions over depth of both the added mass and radiation damping coefficients per unit length for both rigid and flexible squatty cylinders. From additional comparisons with Rayleigh-Ritz solutions that require trial functions, the results for totally immersed flexible slender cylinders (r0/h< 0.10) are shown to be equivalent; but the results for totally immersed flexible squatty cylinders (r0/h > 0.25) are not. The reason for this difference appears to be in the truncation of the trial function series in the Rayleigh-Ritz methods, which excludes the higher mode shapes, and in the definitions of the added mass coefficients. Comparisons with laboratory data for both rigid and flexible cylinders confirm the accuracy of the solutions obtained by the eigenseries in the limited frequency interval above the highest frequency for surface gravity waves (f > 1.0 Hz) and below the first dimensionless cut-off frequency for acoustic waves (ω< 1.0). |
