The added mass of a biaxial tensioned membrane in still air

Abstract

It is well known that added mass significantly impacts the vibration of membrane structures in still air. Numerous theoretical, numerical, and experimental studies have been conducted on the added mass of axial tensioned membranes. However, the added mass of biaxial tensioned membranes subjected to different tensile forces in two directions in still air remains unclear. Therefore, this study focuses on investigating the added mass of biaxial tensioned membranes in still air. Firstly, this paper proposes a simplified theoretical model for the added mass of biaxial tensioned membranes in still air based on the energy conservation law. To validate the accuracy of the proposed model, a modal testing system for a rectangular membrane is designed to identify the frequencies of biaxial tensioned membranes in still air. In the experimental system, the utilization of a laser displacement sensor array is to obtain the time-displacement information of observation points. Then, a combination of Fast Fourier Transform (FFT) and Stochastic Subspace Identification (SSI) methods is employed for modal identification. Comparative analysis between the experimental and theoretical model results demonstrates an excellent agreement in frequencies. Additionally, the proposed added mass model is closer to the experimental added mass than other models, with a maximum deviation of only 4.77 %. This research provides a reference for the study of the impact of air on the ground vibration of membranes.