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 effect of nonlinearity on the mode coupling between two co-directional quasiharmonic surface waves propagating on a piezoelectric solid of arbitrary symmetry is examined.
6 citations
TL;DR: In this paper, an effective non-linear mathematical model for dynamic analysis of Ionic polymer-metal composites (IPMCs) cantilever actuators undergoing large bending deformations under AC excitation voltages is presented.
Abstract: This work presents development of an effective non-linear mathematical model for dynamic analysis of Ionic polymer-metal composites (IPMCs) cantilever actuators undergoing large bending deformations under AC excitation voltages. As the IPMC actuator experiences dehydration (solvent loss) in open environment, a model has been proposed to calculate the solvent loss due to applied electric potential following Cobb-Douglas production method. D’Alembert’s principle has been used for the derivation of the governing equation of motion of the system. Generalized Galerkin’s method has been followed to reduce the governing equation to the second-order temporal differential equation of motion. Method of multiple scales has been used to solve the non-linear equation of motion of the system and dehydration effect on the vibration response has been demonstrated numerically.
6 citations
TL;DR: In this article, the authors studied the dynamic behaviors of a magnetically coupled oscillator with two-degrees-of-freedom and derived the governing equations of motion using a magnetic dipole model and solved with the method of multiple scales.
6 citations
01 Aug 2009
TL;DR: In this article, a nonlinear parametric vibration is investigated in principal parametric resonance of an axially accelerating viscoelastic beam and the axial speed is characterized as a simple harmonic variation about the constant mean speed.
Abstract: Nonlinear parametric vibration is investigated in principal parametric resonance of an axially accelerating viscoelastic beam. The axial speed is characterized as a simple harmonic variation about the constant mean speed. The material time derivative is used in the viscoelastic constitutive relation. The transverse motion can be governed a nonlinear integro-partial-differential equation. The asymptotic analysis is performed to determine steady-state responses. It is proved that the mode uninvolved in the resonance has no effect on the steady-state response. The differential quadrature scheme is developed to verify results via the method of multiple scales. It is demonstrated that the straight equilibrium configuration becomes unstable and a stable steady-state emerges when the axial speed variation frequency is close to 2 times of any linear natural frequency. The numerical calculations validate the analytical results in the principal parametric resonance.
6 citations
TL;DR: Dynamical properties, feedback control performance and symmetry-breaking bifurcation are mainly considered for a PWS system with negative stiffness under nonlinear position and velocity feedback control, and interesting dynamical properties are found.
6 citations