The added mass of a closed-type cushion in uniform flow

Abstract

Ethylene-Tetra-Fluoro-Ethylene (ETFE) cushions are popularly used in modern civil engineering structures. When a cushion vibrates in uniform flow, the surrounding fluid will be driven to move along with it. The inertia of fluid then produces an action on the cushion, which is known as the effect of added mass. This effect is usually very significant due to the light weight of these cushions. This paper proposes a new method to estimate the added mass on a close-type ETFE cushion vibrating in uniform flow with an improved accuracy compared with methods in the literature. The aerodynamic force is assumed to consist of pressures from uniform flow and potential flow induced by perturbation of the vibrating cushion. An analytical expression for the added mass on the cushion is then proposed based on the Laplace equation and Bernoulli equation, in which the velocity of the potential fluid above the vibrating cushion is assumed to vary along the z-direction in the form of a quartic function, and the non-uniform distribution of the added mass over the enveloping membrane is also considered. The proposed method is verified by comparing the dynamic responses of the cushion considering the added mass from the Computational Structural Dynamics (CSD) module of ADINA with those in the literature and those obtained from the fluid–structure interaction (FSI) analysis. The effects of different influencing factors on the accuracy of the method, e.g., side length of the cushion, initial inner pressure, wind velocity and wind direction angle, are further studied. Results show that: (a) the proposed method to estimate the added mass is more accurate than those in the literature with results closer to those from the FSI analysis; (b) an increase in the side length of the cushion will lead to a more non-uniform distribution of the added mass; (c) the side length of the cushion and wind velocity have a slight effect on the accuracy of the proposed method with the maximum error within 5%; and (d) an increase in the initial inner pressure can improve the accuracy of the proposed method while the wind direction angle seems to have little influence.