Numerical and experimental studies on the dynamic equivalence of a large rectangular membrane and a grid membrane

Abstract

While the dynamic equivalent methodology of substituting grid membranes for rectangular membranes in air vibration testing has been validated at small scales, scaling up to large rectangular membranes presents challenges such as gravity, uneven stress, and low-frequency identification. This paper uses numerical and experimental methods to explore the dynamic equivalence of a large rectangular membrane and a grid membrane. An experimental system is designed to conduct vibration tests of grid membranes in air, with the vertically arranged, bi-directionally tensioned grid membranes reducing the influence of gravity and flexible tensioning devices, eliminating shear stresses, and facilitating the realization of a uniform stress field. Additionally, the grid membrane is excited using rapid sinusoidal sweep excitation with an exciter, which effectively excites the low-order modes. At the same time, a laser vibrometer is utilized to accurately measure the velocity time history data at the observation points. Combining the observation points’ velocity time history data with the exciter’s force time history data, signal processing, and modal analysis techniques effectively identify the low-order modes. A series of grid membranes with various added masses are compared with the numerical results of rectangular membranes with respect to frequency and mode shape. The first three modes show a consistent frequency and mode shape between the large rectangular and grid membranes, while the mode correlation decreases with higher modes. Increasing the additional mass at the intersection of the grid membrane enhances frequency consistency without altering mode correlation.