Study on the added mass of inflated beams in still air

Inflated beam structures are widely deployed in aerospace, civil, and marine engineering due to their outstanding performance. However, for structures with thin membranes, the added mass effect can significantly alter the structural vibrations and influence the natural frequencies of the beams. In this study, the governing equations for both internal and external fluids of an inflated beam are established based on potential flow theory. Analytical solutions for the gas added mass are derived through numerical computations and subsequently validated against experimental and simulation results. Comparison with test results reveals that the deviations in the added mass are 1.46% for the first-order bending mode and 4.58% for the second-order bending mode, thereby demonstrating the accuracy of the proposed model. Furthermore, the parametric influences on the gas added mass are investigated using the established model, indicating that the added mass is governed by the geometry, dimensions, mode shapes, and inflation pressure of the inflated beam. For a specified beam configuration and inflation pressure, the added mass remains constant, and its effect on each bending mode depends solely on the membrane thickness. Specifically, at a membrane thickness of 105 μm, the added mass effect alters the bending modes by 0.76% in vacuum and by 5.46% in air. These numerical findings provide valuable insights into the evaluation of aerodynamic added mass for thin-membrane structures.