The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.
The chaotic dynamic snap-through and complex nonlinear vibrations are investigated in a rectangular asymmetric cross-ply bistable composite laminated cantilever shell,in cases of 1:2 inter-well internal resonance and primary resonance.The transverse foundation excitation is applied to the fixed end of the structure,and the other end is in a free state.The first-order approximate multiple scales method is employed to perform the perturbation analysis on the dimensionless two-degree-of-freedom ordinary differential motion control equation.The four-dimensional averaged equations are derived in both polar and rectangular coordinate forms.Deriving from the obtained frequency-amplitude and force-amplitude response curves,a detailed analysis is conducted to examine the impacts of excitation amplitude,damping coefficient,and tuning parameter on the nonlinear internal resonance characteristics of the system.The nonlinear softening characteristic is exhibited in the upper stable-state,while the lower stable-state demonstrates the softening and linearity characteristics.Numerical simulation is carried out using the fourth-order Runge-Kutta method,and a series of nonlinear response curves are plotted.Increasing the excitation amplitude further elucidates the global bifurcation and chaotic dynamic snap-through characteristics of the bistable cantilever shell.