Topic
Multiple-scale analysis
About: Multiple-scale analysis is a research topic. Over the lifetime, 1360 publications have been published within this topic receiving 27530 citations.
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TL;DR: In this paper, the structural response of structural elements to a simple harmonic, transverse excitation is considered, and the effects of both initial curvature and midsurface stretching are included; thus, the governing equations contain both quadratic and cubic terms.
63 citations
TL;DR: In this article, a control law based on cubic velocity feedback is proposed to suppress the vibrations of the first mode of a cantilever beam when subjected to a principal parametric resonance.
63 citations
TL;DR: In this paper, a nonlinear dynamics of fluid-conveying functionally graded material (FGM) sandwich nanoshells is investigated, where the von Karman nonlinear geometrical relations are taken into account, compressibility and viscidity of the fluid are neglected, and the velocity potential and Bernoulli's equation are used to describe the fluid pressure acting on the nano-shells.
Abstract: In the present work, nonlinear dynamics of fluid-conveying functionally graded material (FGM) sandwich nanoshells is investigated. In order to describe the large-amplitude motion, the von Karman nonlinear geometrical relations are taken into account. Compressibility and viscidity of the fluid are neglected, and the velocity potential and Bernoulli's equation are used to describe the fluid pressure acting on the nanoshells. Based on the classical shell theory and incorporating the surface stress effect, the governing equations are derived by using Hamilton's principle. After that, the Galerkin method is used to discretize the equation of motion, resulting in a set of ordinary differential equations with respect to time. The ordinary differential equations are solved analytically by utilizing the method of multiple scales. Results show that the surface stress plays important roles on the nonlinear vibration characteristics of fluid-conveying FGM sandwich thin-walled nanoshells. Furthermore, the fluid speed, the power-law index, the fluid mass density, the core thickness and the initial surface tension can also influence the vibration characteristics of fluid-conveying FGM sandwich nanoshells.
63 citations
TL;DR: In this paper, the forced vibration of a system of coupled beams is examined and it is shown that violent non-synchronous torsion and bending vibration observed in such a system may be explained by the existence of quadratic nonlinear coupling terms and internal resonance effects between three and four modes.
62 citations
TL;DR: In this article, the bifurcations and chaotic dynamics of a simply supported symmetric cross-ply composite laminated piezoelectric rectangular plate are studied for the first time.
Abstract: The bifurcations and chaotic dynamics of a simply supported symmetric cross-ply composite laminated piezoelectric rectangular plate are studied for the first time, which are simultaneously forced by the transverse, in-plane excitations and the excitation loaded by piezoelectric layers. Based on the Reddy’s third-order shear deformation plate theory, the nonlinear governing equations of motion for the composite laminated piezoelectric rectangular plate are derived by using the Hamilton’s principle. The Galerkin’s approach is used to discretize partial differential governing equations to a two-degreeof-freedom nonlinear system under combined the parametric and external excitations. The method of multiple scales is employed to obtain the four-dimensional averaged equation. Numerical method is utilized to find the periodic and chaotic responses of the composite laminated piezoelectric rectangular plate. The numerical results indicate the existence of the periodic and chaotic responses in the averaged equation. The influence of the transverse, in-plane and piezoelectric excitations on the bifurcations and chaotic behaviors of the composite laminated piezoelectric rectangular plate is investigated numerically.
62 citations