Nonlinear Vibrations and Chaotic Dynamics of the Laminated Composite Piezoelectric Beam

Abstract

This paper investigates the complicated dynamics behavior and the evolution law of the nonlinear vibrations of the simply supported laminated composite piezoelectric beam subjected to the axial load and the transverse load. Using the third-order shear deformation theory and the Hamilton's principle, the nonlinear governing equations of motion for the laminated composite piezoelectric beam are derived. Applying the method of multiple scales and Galerkin's approach to the partial differential governing equation, the four-dimensional averaged equation is obtained for the case of principal parametric resonance and 1:9 internal resonance. From the averaged equations obtained, numerical simulation is performed to study nonlinear vibrations of the laminated composite piezoelectric beam. The axial load, the transverse load, and the piezoelectric parameter are selected as the controlling parameters to analyze the law of complicated nonlinear dynamics of the laminated composite piezoelectric beam. Based on the results of numerical simulation, it is found that there exists the complex nonlinear phenomenon in motions of the laminated composite piezoelectric beam. In summary, numerical studies suggest that periodic motions and chaotic motions exist in nonlinear vibrations of the laminated composite piezoelectric beam. In addition, it is observed that the axial load, the transverse load and the piezoelectric parameter have significant influence on the nonlinear dynamical behavior of the beam. We can control the response of the system from chaotic motions to periodic motions by changing these parameters.