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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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TL;DR: In this article, the case of strongly nonhomogeneous nonlinear system with 2 dof was analyzed and an analytical form was obtained owing to the multiple scale analysis by using the complex variables.
Abstract: Parameters optimization for energy pumping is considered. The case of strongly nonhomogeneous nonlinear system with 2 dof is analyzed. Damping in strongly nonlinear energetic sink as well as in the linear primary structure are taken into account. In particular efficiency of energy pumping is studied by using an analytical expression. This analytical form is obtained owing to the multiple scale analysis by using the complex variables. Analytical results are confirmed by numerical ones. An experimental verification based on a reduced-scale building model is also considered.

43 citations

Journal ArticleDOI
TL;DR: In this article, the nonlinear primary resonance in the vibration control of a cable-stayed beam with time delay feedback was investigated. And the effect of control gain and time delay on the amplitude and frequency response behavior were investigated.

43 citations

Journal ArticleDOI
TL;DR: In this article, two perturbation methods used in weakly nonlinear stability theory, namely, the method of multiple scales and the amplitude expansion method, are examined for their equivalence through formal analyses and numerical calculation of the Landau constants.
Abstract: Two perturbation methods used in weakly nonlinear stability theory, namely, the method of multiple scales and the amplitude expansion method, are examined for their equivalence through formal analyses and numerical calculation of the Landau constants. The method of multiple scales is shown to give results equivalent to those obtained from the amplitude expansion formulation for slightly supercritical states if a normalization condition is applied to the fundamental mode. The convergence of the expansion in the method of multiple scales is also discussed.

43 citations

Journal ArticleDOI
TL;DR: In this article, the transverse vibrations of a simply supported beam moving with constant velocity were considered and the case of transition from string to beam effects was treated, and the boundary layer problem was solved approximately using the method of multiple scales.
Abstract: The transverse vibrations of a simply supported beam moving with constant velocity is considered. The case of transition from',:string to beam effects is treated. In this model, the fourth order spatial derivative multiplies a small parameter and hence leads to a boundary layer problem. The problem is solved approximately using the method of multiple scales.

43 citations

Journal ArticleDOI
TL;DR: In this paper, the global bifurcations and chaotic dynamics of a string-beam coupled system subjected to parametric and external excitations are investigated in detail, and the theory of normal form is utilized to find the explicit formulas of normal-form associated with one double zero and a pair of pure imaginary eigenvalues.
Abstract: The global bifurcations and chaotic dynamics of a string-beam coupled system subjected to parametric and external excitations are investigated in detail in this paper. The governing equations are firstly obtained to describe the nonlinear transverse vibrations of the string-beam coupled system. The Galerkin procedure is introduced to simplify the governing equations of motion to ordinary differential equations with two-degrees-of-freedom. Using the method of multiple scales, parametrically and externally excited system is transformed to the averaged equation. The case of 1:2 internal resonance between the modes of the beam and string, principal parametric resonance for the beam and primary resonance for the string is considered. Based on the averaged equation, the theory of normal form is utilized to find the explicit formulas of normal form associated with one double zero and a pair of pure imaginary eigenvalues. The global perturbation method is employed to analyze the global bifurcations and chaotic dynamics of the string-beam coupled system. The analysis of the global bifurcations indicates that there exist the homoclinic bifurcations and the Silnikov type single-pulse homoclinic orbit in the averaged equation of the string-beam coupled system. These results obtained here mean that the chaotic motions can occur in the string-beam coupled system. Numerical simulations also verify the analytical predications.

42 citations


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