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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 paper , the authors presented a new technique for nonlinear system identification that utilizes near-resonant steady-state harmonically excited vibration measurements to estimate the nonlinear normal mode backbones.

2 citations

Journal ArticleDOI
TL;DR: In this paper, the perturbation analysis method of multiple scales is applied to the problem of linear sound propagation in a rectangular waveguide with viscous and thermal dissipation effects at the boundary.
Abstract: The perturbation analysis method of multiple scales is applied to the problem of linear sound propagation in a rectangular waveguide with viscous and thermal dissipation effects at the boundary. In the past, the method of multiple scales has been applied to the corresponding problem of finite level fluctuations in a waveguide. The second‐order solution (representing the first correction due to nonlinearity) cited in these investigations would however preclude the solution of the linear problem, as it grows without bound with the axial coordinate of the waveguide. In this investigation an alternate solution at second order is proposed, which is bounded throughout the spatial domain of the duct. This property of the alternate solution allows the linear problem to be solved, including the region arbitrarily close to the cutoff frequency for higher‐order modes. In addition, the uniform solution may be directly applied to the analysis of finite level fluctuations, with consequences as yet unknown.

2 citations

01 Dec 1994
TL;DR: In this article, a mathematical model for pulse propagation in a nonlinear fiber optic communications line is presented where linear loss in the fiber is balanced by a chain of periodically spaced, Phase Sensitive Amplifiers (PSAs).
Abstract: : A mathematical model for pulse propagation in a nonlinear fiber optic communications line is presented where linear loss in the fiber is balanced by a chain of periodically spaced, Phase Sensitive Amplifiers (PSAs). A multiple scale analysis is employed to average over the strong, rapidly varying and periodic perturbations to the governing nonlinear Schroedinger equation (NLS). The analysis indicates that the averaged evolution is governed by a fourth order nonlinear diffusion equation which evolves on a length scale much greater than that of the typical soliton period. In a particular limit, stable steady state hyperbolic secant solutions of the averaged equation are analytically found to exist provided a minimum amount of over amplification is supplied. Further, arbitrary initial conditions within a wide stability region exponentially decay onto the steady state. Outside of this analytic regime, extensive numerical simulations indicate that soliton-like steady states exist and act as exponential attractors for a wide region of parameter space. These simulations also show that the averaged evolution is quite accurate in modeling the full NLS with loss and phase sensitive gain. The bifurcation structure of the fourth order equation is explored. A subcritical bifurcation from the trivial solution is found to occur for a specific over amplification value. Further, a limit point, or fold, is also found which connects the stable branch of solutions with the unstable branch from the subcritical bifurcation. The bifurcation structure can be further explored in parameter space with the use of AUTO which is capable of tracking steady state solutions for a wide range of parameters. For larger amplifier spacings, a small dispersive radiation field is generated from the periodic forcing of the loss and gain. The NLS with variably-spaced PSAs is then considered in an effort

2 citations

Proceedings ArticleDOI
20 Jun 2008
TL;DR: In this paper, a mathematical model of RLC circuit with inductance nonlinearity and harmonic excitation is established by means of Lagrange-Maxwell equation, and the first approximation solutions and corresponding to steady state solutions of the 1/3 subharmonic resonance system are obtained.
Abstract: In order to study on nonlinear vibration of RLC circuit, a mathematical model of RLC circuit with inductance nonlinearity and harmonic excitation is established by means of Lagrange-Maxwell equation. Based on the method of multiple scales for nonlinear vibration analysis, the first approximation solutions and corresponding to steady state solutions of the 1/3 subharmonic resonance system are obtained. Numerical analysis results show that the amplitude of the system increases with increasing of plate area and linear coefficient of inductance, while it decreases with increasing plate distance, voltage, and nonlinear inductance coefficient. It has also been found the nature frequency of the system increases with the increasing plate distance but it decreases when the plate area and linear inductance coefficient increase.

2 citations

Proceedings ArticleDOI
02 Aug 2015
TL;DR: In this paper, the one-to-one internal resonance occurring in a two-degree-of-freedom (2DOF) system composed by a damped nonlinear primary structure coupled with a nonlinear vibration absorber is studied via the method of multiple scales up to higher order (i.e., the first nonlinear order beyond the internal/external resonances).
Abstract: The one-to-one internal resonance occurring in a two-degree-of-freedom (2DOF) system composed by a damped non-linear primary structure coupled with a nonlinear vibration absorber is studied via the method of multiple scales up to higher order (i.e., the first nonlinear order beyond the internal/external resonances). The periodic response predicted by the asymptotic approach is in good agreement with the numerical results obtained via continuation of the periodic solution of the equations of motion. The asymptotic procedure lends itself to manageable sensitivity analyses and thus to versatile optimization by which different optimal tuning criteria for the vibration absorber can possibly be found in semi-closed form.Copyright © 2015 by ASME

2 citations


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