Potential well evolution and metastable dynamics of bistable asymmetric laminated composite square shallow shell under external and parametric excitations

Abstract

This paper studies the occurrence conditions of the metastable chaos by analyzing the potential well evolution from the double potential wells to triple potential wells in the bistable asymmetric laminated composite square shallow shell under the foundation excitation. Based on the dependence of the potential well types on the parameters of the potential function, the critical condition is derived for the metastable chaos in the bistable asymmetric laminated composite square shallow shell. In the theoretical researches, when the parametric excitation is large enough to exceed the critical value, it is found that the shapes of the potential curves change from the double potential wells to triple potential wells. By contrast, the external excitation only affects the depth variation of the potential well, but not the type of the potential well. It is verified that the larger parametric excitation leads to the metastable chaos of the bistable asymmetric laminated composite square shallow shell. The results of numerical simulation are consistent with the theoretical analysis. The parametric excitation is the key factor leading to the metastable phenomena in the bistable asymmetric laminated composite square shallow shell. The influences of the external and parametric excitations on the metastable dynamics of the bistable asymmetric laminated composite square shallow shell are studied based on the results of numerical simulations. It is also found that there is no the direct jumping path between the upper-mode and lower-mode oscillations once the metastable chaos occurs.