Dynamic equivalent methodology of a rectangular membrane and a grid membrane: Formulation, simulation and experiment

Abstract

Abstract The pretensioned rectangular membrane is a basic structural component that is widely used in various spacecraft, and requires experimental ground verification before being launched into orbit. However, the dynamic calibration of the membrane is a considerable challenge, because the dynamic response is sensitive to the air resistance effect. A grid membrane can be intuitively thought of as being insensitive to a great extent and proposed as a dynamic equivalent structure. The dynamic equations of the two structures are respectively formulated, and the dynamic equivalent methodology of the two structures is formulated by making the corresponding coefficients of the two equations equal to one another. In the simulations, the frequencies of the two structures under the same vibration amplitude are essentially identical. A low vacuum chamber and biaxial extension frame are developed for experimental validation. In the experiment, the dynamic response of the grid membrane in air shows a fine consistency with the rectangular membrane in low vacuum. Therefore, the proposed dynamic equivalent methodology is demonstrated to be valid, and the grid membrane can be used as a substitute structure for the rectangular membrane in order to reduce the air resistance effect.