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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 steady state vibrations of a non-linear dynamic vibration absorber are studied using the method of multiple scales, in conjunction with digital simulations, and the main results are concerned with certain dynamic instabilities which can occur if the absorber is designed such that the desired operating frequency is approximately the mean of the two linearized natural frequencies of the system.
Abstract: The steady state vibrations of a non-linear dynamic vibration absorber are studied using the method of multiple scales, in conjunction with digital simulations. The main results are concerned with certain dynamic instabilities which can occur if the absorber is designed such that the desired operating frequency is approximately the mean of the two linearized natural frequencies of the system. A combination resonance can occur in this case, resulting in large amplitude almost-periodic vibrations. This motion destroys the effectiveness of the absorber and can coexist with the desired low-amplitude periodic response, which leads to initial condition dependent dynamics.

104 citations

Journal ArticleDOI
TL;DR: The dynamic response mechanism of multi-stable energy harvesters with high-order stiffness terms is revealed and eleven types of interesting dynamic characteristics are found with the variation of the excitation amplitude.

103 citations

Journal ArticleDOI
TL;DR: In this paper, an axially moving visco-elastic Rayleigh beam with cubic nonlinearity is considered, and the governing partial-differential equation of motion for large amplitude vibration is derived through geometrical, constitutive, and dynamical relations.

101 citations

Journal ArticleDOI
TL;DR: In this paper, a nonlinear analysis of the response of a simply-supported buckled beam to a harmonic axial load is presented, and the results are verified by integrating the governing equation using both digital and analog computers.
Abstract: A nonlinear analysis of the response of a simply-supported buckled beam to a harmonic axial load is presented. The method of multiple scales is used to determine to second order the amplitude- and phase-modulation equations. Floquet theory is used to analyze the stability of periodic responses. The perturbation results are verified by integrating the governing equation using both digital and analog computers. For small excitation amplitudes, the analytical results are in good agreement with the numerical solutions. The large-amplitude responses are investigated by using a digital computer and are compared with those obtained via an analog-computer simulation. The complicated dynamic behaviors that were found include period-multiplying and period-demultiplying bifurcations, period-three and period-six motions, jump phenomena, and chaos. In some cases, multiple periodic attractors coexist, and a chaotic attractor coexists with a periodic attractor. Phase portraits, spectra of the responses, and a bifurcation set of the many solutions are presented.

101 citations

Journal ArticleDOI
TL;DR: In this article, an Euler-Bernoulli beam is analyzed in terms of a nonlinear elastic foundation and the frequency response curves are compared using the Galerkin method.
Abstract: Approximate methods for analyzing the vibrations of an Euler--Bernoulli beam resting on a nonlinear elastic foundation are discussed. The cases of primary resonance (Ω ≈ Ω n ) and subharmonic resonance of order one-half (Ω ≈ 2 Ω n ), where Ω is the excitation frequency and Ω n is the natural frequency of the nth mode of the beam, are investigated. Approximate solutions based on discretization via the Galerkin method are contrasted with direct application of the method of multiple scales to the governing partial-differential equation and boundary conditions. The amplitude and phase modulation equations show that single-mode discretization leads to erroneous qualitative as well as quantitative predictions. Regions of softening (hardening) behavior of the system, the spatial dependence of the response drift, and frequency-response curves are numerically evaluated and compared using both approaches.

101 citations


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