Chaotic Dynamics of the Laminated Composite Piezoelectric Shell

The laminated composite piezoelectric structure is widely used to the astronautic engineering because of its excellent performance in the area of controlling vibration. Multi-pulse chaotic dynamics of the laminated composite piezoelectric shell subjected to the in-plane and transversal excitations is investigated in this paper. The higher-order transverse shear deformation and damping are considered based upon the Sanders shell theories. Based on the Reddy's third order shear deformation theory and the von Karman type equations, the nonlinear governing equations of motion for the laminated composite piezoelectric shell are derived by using the Hamilton's principle. The four-dimensional averaged equation under the case of 1:2 internal resonance, primary parametric resonance and 1/2-subharmonic resonance is obtained by directly using the multiple scales method and Galerkin approach. From the averaged equation, the theory of normal form is used to find the explicit formulas of normal form. Based on normal form obtained, the energy phase method is utilized to analyze the multi pulse global bifurcations and chaotic dynamics. The analysis of global dynamics indicates that there exist the multi-pulse jumping orbits in the perturbed phase space of the averaged equation. From the averaged equations obtained, the chaotic motions and the multi pulse orbits are found by using numerical simulation. The results obtained above mean the existence of the chaos for the Smale horseshoe sense for the laminated composite piezoelectric shell subjected to the in-plane and transversal excitations.