The nonlinear behaviors and energy harvesting of an unsymmetric cross-ply square composite laminated plate with a piezoelectric patch is presented. The unsymmetric cross-ply square composite laminated plate has two stable equilibrium positions by applying thermal stress, thus having snap-through with larger amplitude between the two stable equilibrium positions relative to the general laminated plate. Based on the von-Karman large deformation theory, the nonlinear electromechanical coupling equations of motion of the unsymmetric composite laminated plate with a piezoelectric patch are derived by using Hamilton’s principle. The influence of the base excitation amplitude on nonlinear behaviors and energy harvesting are investigated. For different base excitation amplitudes, the motions of the system demonstrate periodic motion, quasi-periodic motion, chaotic motion and snap-through, and two single-well chaotic attractors and a two-well chaos attractor coexist. Moreover, the power generation efficiency is optimal when the excitation amplitude is in a certain range due to its own unique nonlinear characteristics. The unsymmetric cross-ply square composite laminated plate subjected to thermal stress can actually be called a kind of bistable composite shell structure that has a broad application prospect in combination with morphing aircraft, large deployable antenna and solar panel, which are very likely to have nonlinear vibration.

Bistable energy harvesters have been extensively studied. However, theoretical research on the dynamics of bistable energy harvesters based on asymmetric bistable composite laminated plate and shell structures has not been conducted. In this paper, a theoretical model on the dynamics of an energy harvester based on an asymmetric bistable composite laminated shell is established. The dynamic snap-through, the nonlinear vibrations and the voltage output with two potential wells of the bistable energy harvester are studied. The influence of the amplitude and the frequency for the base excitation on the bistable energy harvester is studied. When the frequency for the base excitation with a suitable amplitude in the frequency sweeping is located in a specific range or the amplitude for the base excitation with a suitable frequency in the amplitude sweeping is located in a specific range, the large-amplitude dynamic snap-through, nonlinear vibrations and voltage output with two potential wells can be found to occur. The amplitude and the frequency for the base excitation interact on each other for the specific amplitude or frequency range which migrates due to the softening nonlinearity. The vibration in the process of the dynamic snap-through behaves as the chaotic vibration. The nonlinear vibrations of the bistable system behave as the periodic vibration, the quasi-periodic vibration and the chaotic vibration. This study provides a theoretical reference for the design of energy harvesters based on asymmetric bistable composite laminated plate and shell structures.

As bistable composite laminated plate and shell structures are often exposed to dynamic environments in practical applications, the global and local dynamics of a bistable asymmetric composite laminated shell subjected to the base excitation is presented in this paper. Temperature difference, base excitation amplitude, and detuning parameters are discussed. With the change of temperature difference, the super-critical pitchfork bifurcation occurs. Three equilibrium solutions corresponding to three equilibrium configurations (two stable configurations and one unstable configuration) can be obtained. With the increase of excitation amplitude, local and global dynamics play a leading role successively. The global dynamics between the two stable configurations behave as the periodic vibration, the quasi-periodic vibration, the chaotic vibration and dynamic snap-through when the excitation amplitude is large enough. The local dynamics that are confined to a single stable configuration behave as 1:2 internal resonance, saturation and permeation when the excitation amplitude is small. Dynamic snap-through and large-amplitude vibrations with two potential wells for the global dynamics will lead to a broad application prospect of the bistable asymmetric composite laminated shell in energy harvesting devices.