Numerical analysis of added mass for open flat membrane vibrating in still air using the boundary element method

Abstract

Added mass has significant effect on the vibration of membrane structures, which cannot be ignored during vibration analysis. Actually, the added mass of typical objects, such as cylinders and spheres, moving in fluid with acceleration have been widely investigated. However, research on the added mass of flexible structures is still limited. Although several numerical methods had been developed to investigate the added mass of flexible structures, the efficiency of the numerical methods is not verified by experiment tests. In this study, a framework to numerically analysis the added mass of open flat membranes has been established by using the Boundary Element Method (BEM). In order to evaluate hypersingular integral, the Stokes formula converting the surface integral to the curvilinear integral is used. Two added mass models are discussed, one only considering the effect of the membrane geometric shape, and another considering the effect of the geometric shape and the mode shape of membranes. Based on comparative analysis between numerical results and experimental results, it is shown that the added mass only considering the effect of geometric shape can agree well with the test results in low-order modes, however, the error will be increased as the order of vibration modes increasing. The added mass considering the effect of the geometric shape and the mode shape can have much better conformity with the test results both in low-order modes and high-order modes. The Modal Assurance Criterion (MAC) is used to compare the mode shapes of membranes vibrating in vacuum and in air. MAC values indicate that for uniform mass distribution of the membrane, there is little difference between the mode shapes of the membrane vibrating in vacuum and in air, while for nonuniform mass distribution of the membrane, the difference between the mode shapes of the membrane vibrating in vacuum and in air is little in low modes and is large in high modes.