Analysis on nonlinear vibrations near internal resonances of a composite laminated piezoelectric rectangular plate. (15th October 2018)

• Record Type: Journal Article
• Authors: Zhang, Y.F.; Zhang, W.; Yao, Z.G.
• Is Part Of: Engineering structures. Volume 173(2018)
• Page Start: 89
• Page End: 106
• Publication Date: 2018-10-15
• Subjects: Composite laminated piezoelectric plate -- Modelling -- Nonlinear vibrations -- Bifurcations -- Chaotic motions -- Internal resonance; Structural engineering -- Periodicals; Structural analysis (Engineering) -- Periodicals; Construction, Technique de la -- Périodiques; Génie parasismique -- Périodiques; Pression du vent -- Périodiques; Earthquake engineering; Structural engineering; Wind-pressure; Periodicals; 624.105
• DOI: 10.1016/j.engstruct.2018.04.100
• Languages: English
• ISSNs: 0141-0296

Abstract

Highlights: Nonlinear vibrations a simply supported piezoelectric rectangular plate are analyzed. Primary parametric resonance and 1:3 internal resonance are considered. Governing equation of motion for the composite piezoelectric rectangular plate is derived. A two-degree-of-freedom nonlinear system is obtained. Numerical results illustrate the existence of the periodic and chaotic motions. Abstract: The nonlinear vibrations and chaotic motions of a simply supported symmetric cross-ply composite laminated piezoelectric rectangular plate subjected to the transverse and in-plane excitations are analyzed in the case of primary parametric resonance and 1:3 internal resonance. It is assumed that different layers of the symmetric cross-ply composite laminated piezoelectric rectangular plate are perfectly bonded to each other and with piezoelectric actuator layers embedded in the plate. Based on the Reddy's third-order shear deformation plate theory, the nonlinear governing equation of motion for the composite laminated piezoelectric rectangular plate is derived by using the Hamilton's principle. The Galerkin's approach is employed to discretize the partial differential governing equation to a two-degree-of-freedom nonlinear system under combined the parametric and external excitations. The method of multiple scales is utilized to obtain the four-dimensional averaged equation. Numerical method is used to find the bifurcation diagram, the periodic and chaotic motions of the composite laminated piezoelectric rectangular plate. The numerical results illustrate the existence of the periodic and chaotic motions in the averaged equation. It is found that the chaotic responses are especially sensitive to the forcing and the parametric excitations. The influences of the transverse, in-plane and piezoelectric excitations on the bifurcations and chaotic behaviors of the composite laminated piezoelectric rectangular plate are investigated numerically.