Dynamic Stresses and Strains in a Buoy Cable System Subjected to Longitudinal Excitation Using a Continuum Approach

Abstract

This paper deals with the analysis of the stresses and displacements in a buoy cable system subjected to longitudinal excitation when one-dimensional wave effects are taken into account. The cable is considered as a distributed mass with external linear damping due to fluid viscosity and internal damping simulating viscoelastic behavior of the cable material. The payload mass is attached to a rigid foundation by an elastic spring and a dashpot. The results are presented in terms of parameters common to a discrete single degree of freedom (df) system so that comparisons could be made showing the effects of cable distributed mass and cable external damping. Numerical results are presented for the case of a sinusoidal displacement at the upper end of an externally damped elastic cable and payload damping at the lower end. The results show that the cable stress in the low-frequency range can be higher for a system with cable damping than the stress value obtained in the case of a system with no damping. External damping, however, does reduce the stress in the vicinity of the resonant frequencies. It is also shown that the cable stress increases significantly at the higher harmonic resonant frequencies. Comparisons of the analysis of a distributed mass system with the one corresponding to a lumped parameter system using an effective cable mass of one-third its actual mass in a single (df) discrete system indicates fairly good agreement below the first fundamental frequency. The largest difference occurs in the vicinity of resonance where the continuum approach yields higher amplification factors. Better agreement over the fundamental-frequency range is obtained using a two-parameter lumped system. The case of a two-material cable system is also analyzed and experimental verification of the linear mathematical model is presented. Future research will consider improvement of some of the simplifications introduced in the analysis: nonlinear versus linear external damping, finite versus infinitesimal deformations, etc.