Efficient calculation of the hydrodynamic coefficients and dynamic stiffness of an air-spring type vibration absorber

Abstract

Integration of an air-spring device into an offshore platform can be an effective solution to modify the system properties, such as the restoring stiffness. In this study, the dynamic stiffness due to the linear vibration of the air and fluid entrapped inside an air-spring type vibration absorber is investigated. The device is modelled as a hollow column with a closed top and floats vertically in a water of constant depth. At the initial time, the free surfaces inside and outside the device are at the same level and there is an amount of air entrapped above the inner water surface. Within the device, the variation to the air pressure is assumed to occur adiabatically and the free-surface boundary condition is derived based on the ideal gas state equation. Energy dissipation is introduced into the region within the device by adding a resistance force on the inner free surface. The wave radiation due to the heave motion of the device is then concerned and an analytical model is developed to evaluate the associated hydrodynamic coefficients and the induced dynamic stiffness by using the method of separation of variables in conjunction with the matching technology. An alternative solution of the dynamic stiffness has also been developed based on a decomposition of the total velocity potential into two parts which depend purely on the oscillation of the device and the dynamic air pressure applied on the inner free surface, respectively. Based on the developed model, detailed numerical analysis is performed. The relative phases between the body motion and the dynamic stiffness are discussed for different wave conditions and geometric parameters.