Nonlinear Dynamics Of Composite Laminated Piezoelectricity Shell

The intelligent structure is perceptional which could feel the changes of environment and make suitable responses towards these changes. Intelligent structure is greatly fit for the astronautic engineering because of its excellent performance, for instance, in the area of restraining vibration. As a kind of intelligent structure, composite piezoelectricity material has also been widely used in the astronautic engineering for the following advantages, easier controlling ability, high strength and great stiffness, better anti-fatigue ability. Also as a kind of intelligent structure, the equipment which is made by the piezoelectricity shell or plate could control the vibration of itself effectively in accordance with the advantages of piezoelectricity material. Hence, as is shown before, the piezoelectricity shell and plate is very important for protecting the astronautic equipment and the future development of our astronautic business. Also the research towards the nonlinear dynamics of the composite laminated piezoelectricity structure has the critical theory or engineering applied value.This paper mainly adopts a combined method including the theory and numerical simulation to do the relevant nonlinear dynamics research towards the composite laminated piezoelectricity shell. In the above analysis process, we fully take into account the high-order transverse shear deformation and the transversal damping effect, and the Galerkin method and Asymptotic Perturbation method, multiple scales method also have been utilized. The main contents and contributions of this thesis are as follows.(1) Based on the Reddy's third-order shear deformation theory and the von Karman type equations, the governing equations of motion are established for the composite laminated piezoelectricity shell subjected to the in-plane and transversal excitations by using the Hamilton's principle. The higher-order transverse shear deformation and damping are considered based upon the Sanders shell theories.(2) Based on the nonlinear governing equations of motion for the composite laminated piezoelectricity shell, derived by using the Hamilton's principle, choosing the suitable mode function to satisfy the boundary condition of the composite laminated piezoelectricity shell, the Galerkin's approach is employed to acquire the partial differential governing equations to two-degree-of-freedom nonlinear system under combined the parametric and external excitations. Considering the resonant cases of 1:1 internal resonance and principal parametric resonance-1/2 subharmonic resonance, the method of Asymptotic Perturbation method is utilized to obtain the averaged equation of composite laminated piezoelectricity shell. Numerical method is used to study nonlinear dynamics of the composite laminated piezoelectricity shell and gets the two-dimensional phase portraits, waveforms phase, three-dimensional phase and frequency spectrum phase. The influence of the transverse excitations on the nonlinear dynamics behaviors of the composite laminated piezoelectricity shell is investigated numerically.(3) Rooted on the nonlinear governing equations of motion for the composite laminated piezoelectricity shell, derived by using the Hamilton's principle, choosing the suitable mode function to satisfy the boundary condition of the composite laminated piezoelectricity shell, the Galerkin's approach is employed to acquire the partial differential governing equations to two-degree-of-freedom nonlinear system under combined the parametric and external excitations. Considering the resonant cases of 1:2 internal resonance and principal parametric resonance-1/2 subharmonic resonance, the method of multiple scales method is utilized to obtain the averaged equation of composite laminated piezoelectricity shell. Numerical method is used to study nonlinear dynamics of the composite laminated piezoelectricity shell and gets the two-dimensional phase portraits, waveforms phase, three-dimensional phase and frequency spectrum phase. The influence of the transverse excitations and the piezoelectricity excitations on the nonlinear dynamics behaviors of the composite laminated piezoelectricity shell is investigated numerically.(4) Through the analysis to the nonlinear behaviors of systems under different modes, we find that the nonlinear behaviors of composite laminated piezoelectricity shell generally change from single or multiple period motion to quasi-period motion, and finally to the chaotic motion. Comparing to another vibration direction, the changes coming from excitation tends to lead to an obvious changes in one vibration direction, that means different modes will have different response to the changes of excitation, so this also illustrates there have enough necessities for us to consider the two-order vibration modes.