Nonlinear model order reduction and vibration control of a membrane antenna structure

Abstract

In this paper, model order reduction (MOR) of the nonlinear dynamic model of a membrane antenna structure is studied. Nonlinear vibration control of the membrane antenna structure by using cable actuators has also been investigated. First, the nonlinear dynamic model of the membrane antenna structure is established by using the nonlinear finite element method. Then, MOR of this nonlinear model is carried out. The vibration modes obtained by the linearized model are used as transformation bases, and the method of polynomial fitting is applied to approximate the nonlinear terms. Based on the reduced nonlinear dynamic model, by using the tension cables as actuators, a vibration controller is proposed to suppress the nonlinear vibration of the structure. The nonlinear vibration of the membrane antenna structure is suppressed by adjusting the tension force in the cable actuators. Numerical simulations show that the reduced dynamic model obtained by the presented MOR method can approximate the original nonlinear model very well meanwhile reduce the calculation cost significantly, and the nonlinear vibration of the structure can be suppressed effectively by the cable actuators with the proposed control law.