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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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Journal ArticleDOI
TL;DR: In this article, the authors considered a two coupled Duffing-van der Pol oscillators with a nonlinear coupling and obtained a set of autonomous equations for the amplitudes and phases of the response of the system.
Abstract: We consider a two coupled Duffing–van der Pol oscillators with a nonlinear coupling. The method of multiple scales is used to obtain a set of autonomous equations for the amplitudes and phases of the response of the system. The stability boundaries of fixed points of the approximate equations are obtained using Routh–Hurwitz criterion. The stability boundaries are drawn in various parameters space. The influence of nonlinear damping, detuning, nonlinearity and the coupling strength on the response dynamics is studied. Jump phenomenon is found to occur for a range of values of the parameters of the system. The results obtained from the approximate equations are verified by numerically solving the original system and good agreement is obtained.

34 citations

Journal ArticleDOI
TL;DR: In this paper, the effect of the tip mass on the nonlinear characteristics of the frequency response is theoretically presented, taking into account the inertia and curvature nonlinearities and a quadratic damping effect of a parametrically excited cantilever beam.
Abstract: For a parametrically excited cantilever beam the effect of the tip mass on the nonlinear characteristics of the frequency-response is theoretically presented.The equation of motion governing the system is formulated by Hamilton's pronciple, taking into account the inertia and curvature nonlinearities and a quadratic damping effect of the beam.Using the method of multiple scales and center manifold theory, the bifurcation points of the frequency-response curve are analyzed.It follows that there are two transcritical bifurcations, and in addition to these bifurcations there are two saddle-node bifurcations, in the cases when the tip mass is relatively light and heavy, respectively.Experiments are also performed and the results show good qualitative agreement with the theoretical ones.

34 citations

Journal ArticleDOI
TL;DR: In this paper, the parametric instability regions of a cantilever beam with tip mass subjected to time-varying magnetic field and axial force were investigated using second-order method of multiple scales.

34 citations

Journal ArticleDOI
TL;DR: In this article, a nonlinear dynamic behavior of a parametrically excited simply supported rectangular symmetric cross-ply laminated composite thin plate for the first time has been investigated, where the geometric nonlinearity and nonlinear damping are included in the governing equations of motion.
Abstract: The present investigation deals with nonlinear dynamic behavior of a parametrically excited simply supported rectangular symmetric cross-ply laminated composite thin plate for the first time. The governing equation of motion for rectangular symmetric cross-ply laminated composite thin plate is derived by using von Karman equation. The geometric nonlinearity and nonlinear damping are included in the governing equations of motion. The Galerkin approach is used to obtain a two-degree-of-freedom nonlinear system under parametric excitation. The method of multiple scales is utilized to transform the second-order non-autonomous differential equations to the first-order averaged equations. Using numerical method, the averaged equations are analyzed to obtain the steady state bifurcation responses. The analysis of stability for steady state bifurcation responses in laminated composite thin plate is also given. Under certain conditions laminated composite thin plate may have two or multiple steady state bifurcation solutions. Jumping phenomenon occurs in the steady state bifurcation solutions. The chaotic motions of rectangular symmetric cross-ply laminated composite thin plate are also found by using numerical simulation. The results obtained here demonstrate that the periodic, quasi-periodic and chaotic motions coexist for a parametrically excited fore-edge simply supported rectangular symmetric cross-ply laminated composite thin plate under certain conditions.

34 citations

Journal ArticleDOI
TL;DR: In this paper, the Galerkin method is used to discretize the governing nonlinear integral-partial-differential equation and the method of multiple scales is applied to obtain the modulation equations in the case of primary resonance.

34 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202320
202237
202150
202042
201972
201851