Metastable nonlinear vibrations: Third chaos of bistable asymmetric composite laminated square shallow shell under foundation excitation. (1st January 2021)

• Record Type: Journal Article
• Authors: Liu, T.; Zhang, W.; Wu, M.Q.; Zheng, Y.; Zhang, Y.F.
• Is Part Of: Composite structures. Volume 255(2021)
• Publication Date: 2021-01-01
• Subjects: Bistable asymmetric composite laminated square shallow shell -- Metastable chaos -- Zero equilibrium point -- Parametric excitation; Composite construction -- Periodicals; Composites -- Périodiques; 624.18
• DOI: 10.1016/j.compstruct.2020.112966
• Languages: English
• ISSNs: 0263-8223

Abstract

Highlights: Occurrence condition of the metastable chaotic vibrations is studied in bistable square shallow shell. Metastable chaos is observed in the vibration experiments. Critical instability condition of zero equilibrium point is analyzed. Numerical results verify the theoretical analyses. Increase of parametric excitation leads to metastable chaos easier. Abstract: The occurrence conditions of the metastable chaotic vibrations are firstly studied in the bistable asymmetric composite laminated square shallow shell under the foundation excitation. The metastable chaos is observed in the vibration experiments of the bistable asymmetric composite laminated square shallow shell. Based on the dynamic model of the bistable asymmetric composite laminated square shallow shell, the critical instability condition of the zero equilibrium point is analyzed in the bistable asymmetric composite laminated square shallow shell by using Jacobian matrix and Routh-Hurwitz criterion. We perform numerical simulations based on Runge-Kutta algorithm and the vibration experiments. A sufficient condition is found for the existence of the metastable chaos in the bistable asymmetric composite laminated square shallow shell. It is found that the zero equilibrium point of the bistable asymmetric composite laminated square shallow shell is unstable when the parametric excitation exceeds a specific critical value. The numerical results verify the theoretical analyses of the metastable chaos. It is demonstrated that the increase of the parametric excitation leads to the easier occurrence of the metastable chaos through observing the characteristics of the nonlinear dynamic behaviors of the system. Moreover, the existence of the metastable chaotic vibrations is confirmed in the bistable asymmetric composite laminated square shallow shell under the foundation excitation by using the vibration experiments. The large parametric excitation subjecting to the bistable asymmetric composite laminated square shallow shell is a key factor for the existence of the metastable chaos in the bistable asymmetric composite laminated square shallow shell under the foundation excitation.