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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 stability in transverse parametric vibration of axially accelerating viscoelastic beams is investigated and the stability conditions are obtained for combination and principal parametric resonance.

96 citations

Journal ArticleDOI
Wenjun Zhang1
TL;DR: In this article, the global bifurcations and chaotic dynamics of a parametrically excited, simply supported rectangular thin plate are analyzed using the von Karman-type equation and Galerkin's approach.

96 citations

Journal ArticleDOI
TL;DR: In this paper, an approximate solution of second-order relative motion equations is presented, where the equations of motion for a Keplerian orbit in spherical coordinates are expanded in Taylor series form using reference conditions consistent with that of a circular orbit.
Abstract: An approximate solution of second-order relative motion equations is presented. The equations of motion for a Keplerian orbit in spherical coordinates are expanded in Taylor series form using reference conditions consistent with that of a circular orbit. Only terms that are linear or quadratic in state variables are kept in the expansion. The method of multiple scales is employed to obtain an approximate solution of the resulting nonlinear differential equations, which are free of false secular terms. This new solution is compared with the previously known solution of the linear case to show improvement and with numerical integration of the quadratic differential equation to understand the error incurred by the approximation. In all cases, the comparison is made by computing the difference of the approximate state (analytical or numerical) from numerical integration of the full nonlinear Keplerian equations of motion. The results of two test cases show two orders of magnitude improvement in the second-order analytical solution compared with the previous linear solution over one period of the reference orbit.

95 citations

Journal ArticleDOI
TL;DR: In this paper, the response of a one-degree-of-freedom system with quadratic and cubic nonlinearities to a principal parametric resonance is investigated, and the results are verified by integrating the governing equation with use of a digital computer and an analogue computer.

94 citations

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the nonlinear dynamic responses of the rotating blade with varying rotating speed under high-temperature supersonic gas flow, and derived a nonlinear partial differential governing equation of motion for the pretwist, presetting, thin-walled rotating beam.
Abstract: This paper investigates the nonlinear dynamic responses of the rotating blade with varying rotating speed under high-temperature supersonic gas flow. The varying rotating speed and centrifugal force are considered during the establishment of the analytical model of the rotating blade. The aerodynamic load is determined using first-order piston theory. The rotating blade is treated as a pretwist, presetting, thin-walled rotating cantilever beam. Using the isotropic constitutive law and Hamilton’s principle, the nonlinear partial differential governing equation of motion is derived for the pretwist, presetting, thin-walled rotating beam. Based on the obtained governing equation of motion, Galerkin’s approach is applied to obtain a two-degree-of-freedom nonlinear system. From the resulting ordinary equation, the method of multiple scales is exploited to derive the four-dimensional averaged equation for the case of 1:1 internal resonance and primary resonance. Numerical simulations are performed to study the nonlinear dynamic response of the rotating blade. In summary, numerical studies suggest that periodic motions and chaotic motions exist in the nonlinear vibrations of the rotating blade with varying speed.

94 citations


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