Nonlinear vibration control of a membrane antenna structure

In this paper, the active control of nonlinear vibration of a membrane antenna structure is investigated. Considering the geometric nonlinearity of large amplitude vibration of the membrane, the von Karman type geometrical nonlinear strain–displacement relationship is employed in this paper. Then, a nonlinear dynamic model of the membrane antenna structure is established by using the finite element method. It is assumed that the amplitude of vibration of the structure is relatively small when the controller in on, and then a $H_{\infty }$ robust controller is developed to control the undesired nonlinear vibration of the membrane antenna structure based on the linearized model of the structure. Active control of both the free vibration and forced vibration of the structure are investigated. Numerical simulations are presented to study the nonlinearity of the large amplitude vibration of the structure and the effectiveness of the presented controller.