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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, a simply-supported thin laminated plate subject to in-plane excitation is established based on the classic shear theory and von Karman nonlinear theory.

20 citations

Journal ArticleDOI
TL;DR: In this article, the stability of thin viscoelastic liquid film flowing down on the inner surface of a rotating vertical cylinder by means of the long wave perturbation was investigated.
Abstract: This paper investigates the stability of thin viscoelastic liquid film flowing down on the inner surface of a rotating vertical cylinder by means of the long wave perturbation. After proving the insufficiency of the linear model in characterization of certain flow behaviors, a generalized nonlinear kinematic model is then derived to represent the physical system. This model is solved through the following procedure. In the first step, the normal mode method is used to characterize the linear behaviors. The amplitude growth rates and the threshold conditions are characterized subsequently and summarized as the by-products of the linear solutions. In the second step, a nonlinear film flow model is solved by using the method of multiple scales to characterize flow behaviors at various states of sub-critical stability, sub-critical instability, supercritical stability, and supercritical explosion. The modeling results indicate that with the increase in the rotation speed Ω and the radius of cylinder R, the film flow system will be more stable.

20 citations

Journal ArticleDOI
TL;DR: In this paper, a procedure has been developed to identify the parameters of a nonlinear structural dynamic system with a single degree of freedom, where the input of the system is treated a s an unknown.
Abstract: A procedure has been developed t o identify the parameters of a nonlinear structural dynamic system with a single degree of freedom. A cubic nonlinearity has been assumed for purposes of illustration. In comparison t o the direct identification procedures, that depend on (a) either the availability of data on all four variables, namely, velocity, acceleration, displacement and the input t o the system or (b) the formulation of a numerical algorithm that can be used a t each iterative step, the developed procedure requires the data on only one of the field variables. The input t o the system is also treated a s an unknown. The results from the perturbation identification procedure have been compared with the results from two direct identification procedures.

20 citations

Journal ArticleDOI
TL;DR: In this article, the effect of the application of an alternating magnetic field on the large transverse vibration of a cantilever beam with tip mass is investigated using D'Alembert's principle, which is reduced to its nondimensional temporal form by using the generalized Galerkin method.
Abstract: In this work the effect of the application of an alternating magnetic field on the large transverse vibration of a cantilever beam with tip mass is investigated. The governing equation of motion is derived using D'Alembert's principle, which is reduced to its nondimensional temporal form by using the generalized Galerkin method. The temporal equation of motion of the system contains nonlinearities of geometric and inertial types along with parametric excitation and nonlinear damping terms. Method of multiple scales is used to determine the instability region and frequency response curves of the system. The influences of the damping, tip mass, amplitude of magnetic field strength, permeability, and conductivity of the beam material on the frequency response curves are investigated. These perturbation results are found to be in good agreement with those obtained by numerically solving the temporal equation of motion and experimental results. This work will find extensive applications for controlling vibration inflexible structures using a magnetic field.

20 citations

Journal ArticleDOI
H. S. Bauomy1
TL;DR: It is shown that the rotor-AMB system subjected to a periodically time-varying stiffness with quadratic and cubic nonlinear under tuned, and external excitation exhibits many typical nonlinear behaviors, including multiple-valued solutions, jump phenomenon, hardening and softening nonlinear and chaos in the second mode of the system.
Abstract: A rotor-active magnetic bearing (AMB) system subjected to a periodically time-varying stiffness with quadratic and cubic nonlinear under tuned, and external excitation is studied. The method of multiple scales is applied to analyze the response of two modes of a rotor-AMB system near the simultaneous combined and sub-harmonic resonance. The stability of the steady-state solution for that resonance is determined and studied applying Rung–Kutta fourth order method. It is shown that the system exhibits many typical nonlinear behaviors, including multiple-valued solutions, jump phenomenon, hardening and softening nonlinear and chaos in the second mode of the system. The effects of the different parameters on the steady-state solutions are investigated and discussed.

20 citations


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