Chaotic snap-through vibrations of bistable asymmetric deployable composite laminated cantilever shell under foundation excitation and application to morphing wing

Abstract

The realization of the dynamic snap-through behaviors provides the new design ideas in the fields of the morphing aircraft and piezoelectric energy harvesting. This paper studies 1:2 internal resonance, nonlinear vibrations and chaotic snap-through phenomena of the bistable asymmetric composite laminated (BSCL) cantilever shell with the lower-frequency and higher-frequency primary resonances for the first time. The transverse foundation excitation subjects to the fixed end of the bistable cantilever shell. The perturbation analysis of two-degrees-of-freedom nonlinear ordinary differential equations is carried out by using the first-order approximate multiple scale method. The analytical results of the frequency-amplitude and force-amplitude response curves are obtained under the small foundation excitation. The obtained results reveal that the BSCL cantilever shell exhibits the double-jumping characteristics when 1:2 internal and primary resonances occur. There is a continuous energy exchange back and forth between two modes of the bistable laminated cantilever shell. As the foundation excitation increases, the BSCL cantilever shell exhibits saturation phenomenon. Numerical simulations are finished to further investigate the effects of the large excitation on the chaotic, quasi-periodic and snap-through vibrations for the BSCL cantilever shell. The vibration experiment is carried out to investigate the internal resonance and dynamic snap-though motions of the BSCL cantilever shell. Using the snap-though behaviors of the BSCL cantilever shell, we obtain the morphing structure of the aircraft wing.