Analysis of nonlinear vibration control for a functionally graded material plate by NiTiNOL-steel wire ropes

Traditional nonlinear passive control for continuous structures often requires a non-negligible volume for installation and motion that indirectly changes the design of the original structure and degrades vibration attenuation. Functionally graded materials (FGMs) are typically used in aeronautics and astronautics and are constantly subjected to external excitations that cause significant undesirable vibration. To address this problem, the present work proposes a dynamic model of nonlinear forced vibration of a FGM rectangular plate coupled with NiTiNOL-steel wire ropes (NiTi-ST). NiTi-ST exerts on the FGM complex generalized recovery forces, which are investigated by using two methods: the Galerkin truncation method and the harmonic balanced method (HBM). The HBM coupled with arc-length continuation is used to predict the frequency response and closed detached response (CDR) of the coupling system. The results show that the NiTi-ST reduces the resonance frequency of the FGM plate. The linear damper term introduced by the NiTi-ST determines the level of vibration control. However, the appearance of a CDR could make the dynamic phenomenon more complicated. Furthermore, elimination of the CDR may improve the vibration suppression in the nonlinear system, making it more challenging and urgent to investigate the coupling system above.