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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 effect of electro-magnetic and mechanical parameters for the stabilities of solutions and the bifurcation is further analyzed, and critical conditions of stability are also obtained.
Abstract: Based on the Maxwell equations, the nonlinear magneto-elastic vibration equations of a thin plate and the electrodynamic equations and expressions of electromagnetic forces are derived. In addition, the magneto-elastic combination resonances and stabilities of the thin beam-plate subjected to mechanical loadings in a constant transverse magnetic filed are studied. Using the Galerkin method, the corresponding nonlinear vibration differential equations are derived. The amplitude frequency response equation of the system in steady motion is obtained with the multiple scales method. The excitation condition of combination resonances is analyzed. Based on the Lyapunov stability theory, stabilities of steady solutions are analyzed, and critical conditions of stability are also obtained. By numerical calculation, curves of resonance-amplitudes changes with detuning parameters, excitation amplitudes and magnetic intensity in the first and the second order modality are obtained. Time history response plots, phase charts, the Poincare mapping charts and spectrum plots of vibrations are obtained. The effect of electro-magnetic and mechanical parameters for the stabilities of solutions and the bifurcation are further analyzed. Some complex dynamic performances such as period-doubling motion and quasi-period motion are discussed.

7 citations

Journal ArticleDOI
TL;DR: In this paper, an analytical study of primary resonances and bifurcation behavior of a micro-milling process, including structural nonlinearities, gyroscopic moment, rotary inertia, velocity-dependent process damping, static and dynamic chip thickness, is presented.

7 citations

Proceedings ArticleDOI
01 Jul 1978
TL;DR: In this article, an analysis of the nonparallel spatial or temporal stability of three-dimensional incompressible, isothermal boundary-layer flows taking into account the transverse velocity component as well as the axial and crossflow variations of the mean flow is presented.
Abstract: An analysis is presented of the nonparallel spatial or temporal stability of three-dimensional incompressible, isothermal boundary-layer flows taking into account the transverse velocity component as well as the axial and crossflow variations of the mean flow. The method of multiple scales is used to derive partial differential equations that describe the axial and crossflow variations of the disturbance amplitude, phase and wavenumbers. This equation is used to derive the expressions that relate the temporal and spatial instabilities. These relations are functions of the complex group velocities. Moreover, this equation is used to derive the expression that relates the spatial amplification in any direction to a calculated amplification in any other direction. These relations are verified by numerical results obtained for two- and three-dimensional disturbances in two- and three-dimensional flows.

7 citations

Journal ArticleDOI
TL;DR: In this article, the effects of the internal resonance, the exciting force and viscous damping coefficients on the nonlinear dynamic response of an axially moving thin circular cylindrical panel were investigated.
Abstract: With the 3:1 internal resonance , the primary and secondary resonances of an axially moving thin circular cylindrical panel are investigated in the present work. The governing equation and the compatibility equation are established based on the Donnell's nonlinear shell theory and solved to obtain the nonlinear steady-state responses by combining the Galerkin method and the method of multiple scales. The analytical solutions are verified by numerical solutions based on the Runge-Kutta Method. The governing equation includes both the quadratic nonlinearity and the cubic nonlinearity, so the perturbation solutions need to consider three time scales. The quadratic nonlinearity causes the softening behavior of the system. Natural frequencies and the 3:1 internal resonance condition are obtained by the linear analysis. Under the primary resonance , the internal resonance causes the coupling of the first two modes to complicate the nonlinear dynamic response. The response for the second mode possesses an extra bulge or peak due to the internal resonance. The quadratic nonlinearity results in the zero frequency drift and the second-order harmonic. Under the secondary resonance, the exciting force only arouses the second mode. Results are shown to examine the effects of the internal resonance, the exciting force and viscous damping coefficients on the nonlinear dynamic response of an axially moving thin circular cylindrical panel.

7 citations

Journal ArticleDOI
TL;DR: In this article, a simple plate model is used to represent the blade, and its angular speed is characterized as a small periodic perturbation superimposed on a constant speed, which results in parametric instability.

7 citations


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