Nonlinear vibration control effects of membrane structures with in-plane PVDF actuators: A parametric study

In recent years, with the increasing use of membrane structures in space applications, the problems of large-amplitude (compared to the thickness) vibrations arise; leading to the degradation of their working performance. It is challenging to control the large-amplitude vibrations of membranes due to the high flexibility, low damping, and strong geometrical nonlinearity. In this study, polyvinylidene fluoride (PVDF) actuators are considered to develop the active vibration control of a pre-tensioned Kapton membrane. The governing equations are established based on the geometrically nonlinear theory of plates, taking into account the modal control force induced by the actuators. To analyze the nonlinear dynamic characteristics of the membrane, the theoretical and approximate solutions of nonlinear frequencies of the membrane are obtained, and the discrepancies between the two solutions under different vibration amplitudes are discussed. Control performance for both free vibration and harmonic forced vibration of the membrane is numerically studied. A comprehensive parametric study is carried out to investigate the influences of different system parameters, including the pretension and the size of the membrane, and the position and number of the actuators, on the control performance. Analytical results indicate that the vibration of the membrane can be effectively suppressed with the appropriately laminated PVDF actuators. The results of this research can be extended to the active control of different gossamer space structures.