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Fig. 1. The dynamic model is given for the bistable asymmetric composite laminated square shallow shell under the foundation excitation.
This and the next 3 images are from:
T. Liu (1), W. Zhang (1), M.Q. Wu (1), Y. Zheng (1) and Y.F. Zhang (2)
(1) Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, PR China
(2) School of Aerospace Engineering, Shenyang Aerospace University, Liaoning 110136, PR China
“Metastable nonlinear vibrations: Third chaos of bistable asymmetric composite laminated square shallow shell under foundation excitation”, Composite Structures, Vol. 255 Article 112966, 1 January 2021, https://doi.org/10.1016/j.compstruct.2020.112966
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.
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