| Piezoelectric materials, which include piezoelectric lead-zirconate-titanate (PZT) and piezoelectric polyvinylidene fluoride (PVDF), are new functional materials in engineering applications. Because of its properties of high strength, stiffness and durability, such materials can be used as the actuators and sensors in various engineering structures. For instance, composite laminated piezoelectric plates have been widely adopted in aerospace engineering over the last two decades, including the structural elements of the aircraft, large space station and shuttle. Besides, the morphing structures or morphing wings may be composed of laminated piezoelectric materials, which can undergo large oscillations of motion under the external excitations. These oscillating systems are thus nonlinear in nature. Research on the nonlinear dynamics of composite laminated piezoelectric plates plays a vital role in engineering applications. Heretofore, a few studies on the bifurcation and chaotic motions of composite laminated piezoelectric plates have been conducted. To the author's best knowledge, it is the first-known solutions to reveal the bifurcation and chaotic motions of a simply supported symmetric cross-ply composite laminated piezoelectric beam and rectangular plate having the transverse and in-plane excitations. The global perturbation method is used to investigate the periodic and chaotic motions of composite laminated piezoelectric plates.The major research scope and the innovative outcome of this dissertation are briefly summarized as follows:(1) The nonlinear oscillation, bifurcation and chaotic dynamics of a simply supported laminated composite piezoelectric beam are analyzed. The beam with piezoelectric materials is forced by the axial and transverse loads. In accordance with the von Karman-type equations and Reddy's third-order shear deformation plate theory, the nonlinear equations of motion for the laminated composite piezoelectric beam are derived. The Galerkin approach is employed to transform the governing partial differential equations to two-degree-of-freedom ordinary differential equations. Consider the resonant cases of 1:9 internal resonance and principal parametric resonance-1/2 subharmonic resonance, the method of multiple scales is applied to yield the four-dimensional averaged equations. Making use of the averaged equations herein, the bifurcation and chaotic motions of the laminated composite piezoelectric beam are studied. The periodic and chaotic motions of beams are found by using the numerical simulation. It is concluded that the chaotic responses are sensitive to the piezoelectric excitations. By changing the piezoelectric excitations, we can control the nonlinear oscillation of laminated composite piezoelectric beams.(2) The nonlinear dynamics of a simply supported symmetric cross-ply composite laminated piezoelectric rectangular plate having the transverse and in-plane excitations are studied. Based on Reddy's third-order shear deformation plate theory, the nonlinear governing equations of motion for the composite laminated piezoelectric rectangular plate are derived by Hamilton's principle. The excitation loaded by piezoelectric layers is considered. The Galerkin approach is employed to deduce a two-degree-of-freedom nonlinear system under the combination of the parametric and external excitations from the governing partial differential equations. Consider the resonant cases of 1:1, 1:2 and 1:3 internal resonance and principal parametric resonance-1/2 subharmonic resonance, the method of multiple scales is utilized to form the four-dimensional averaged equation of composite laminated piezoelectric rectangular plates. Numerical method is implemented to study the bifurcation and chaotic dynamics of composite laminated piezoelectric rectangular plates. The numerical results show the existence of the periodic and chaotic motions in the averaged equation. It is observed that the chaotic responses are especially sensitive to the forcing and parametric excitations. The influence of the transverse, in-plane and piezoelectric excitations on the bifurcation and chaotic behavior of composite laminated piezoelectric rectangular plates is investigated numerically.(3) Based on Hamilton's principle, the governing nonlinear equations of motion for composite laminated piezoelectric rectangular plates are derived, Selecting the appropriate mode functions satisfies the boundary conditions of composite laminated piezoelectric rectangular plates, the Galerkin approach is employed to reduce the partial differential governing equations to a three-degree-of-freedom nonlinear system under the combination of the parametric and external excitations. Consider the resonant cases of 1:2:3 and 1:2:4 internal resonance and principal parametric resonance-1/2 subharmonic resonance, the method of multiple scales is utilized to obtain the six-dimensional averaged equation of composite laminated piezoelectric rectangular plates. Numerical method is implemented to study the bifurcation and chaotic dynamics of composite laminated piezoelectric rectangular plates. The influence of the transverse, in-plane and piezoelectric excitations on the bifurcation and chaotic behavior of composite laminated piezoelectric rectangular plates is investigated numerically.(4) By virtue of Hamilton's principle, the governing nonlinear equations of motion for the composite laminated piezoelectric rectangular plate are derived, Selecting the appropriate mode functions satisfies the boundary conditions of composite laminated piezoelectric rectangular plates, the Galerkin approach is employed to turn the partial differential governing equations into a four-degree-of-freedom nonlinear system under the combination of the parametric and external excitations. Consider the resonant cases of 1:2:9:9 internal resonance and principal parametric resonance-1/2 subharmonic resonance, the method of multiple scales is utilized to achieve the eight-dimensional averaged equation of composite laminated piezoelectric rectangular plates. Numerical method is implemented to study the bifurcation and chaotic dynamics of composite laminated piezoelectric rectangular plates. The influence of the transverse, in-plane and piezoelectric excitations on the bifurcation and chaotic behavior of composite laminated piezoelectric rectangular plates is investigated numerically.(5) Global bifurcation and Shilnikov type chaotic dynamics of composite laminated piezoelectric rectangular plates are primitively probed by means of the global perturbation method. According to the four dimensional averaged equations of composite laminated piezoelectric rectangular plates, the theory of normal form is applied to further reduce the explicit formulas to the simple one. The global perturbation method proposed by Kovacic and Wiggins are generalized herein to study the Shilnikov type single-pulse homoclinic orbit and chaotic dynamics of composite laminated piezoelectric rectangular plates. Theoretical analysis is not only to demonstrate the existence of Pitchfork bifurcation and Shilnikov type single-pulse homoclinic orbit, but also reveals the chaotic motion of the Smale horseshoe in the system. The numerical simulation of the multi-pulse orbits is presented to verify the analytical solutions.
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