Topic
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 paper, the dynamic response of an axially moving viscoelastic beam with simple supports is calculated analytically based on Timoshenko theory, where the beam material property is separated to shear and bulk effects.
Abstract: In this paper, the dynamic response of an axially moving viscoelastic beam with simple supports is calculated analytically based on Timoshenko theory. The beam material property is separated to shear and bulk effects. It is assumed that the beam is incompressible in bulk and viscoelastic in shear, which obeys the standard linear model with the material time derivative. The axial speed is characterized by a simple harmonic variation about a constant mean speed. The method of multiple scales with the solvability condition is applied to dimensionless form of governing equations in modal analysis and principal parametric resonance. By a parametric study, the effects of velocity, geometry and viscoelastic parameters are investigated on the response.
8 citations
TL;DR: In this article, the authors derived the modulational instability criterion from the discrete multiple scales approach, which is a criterion for the disintegration of the initial modulated waves into a train of pulses.
8 citations
8 citations
TL;DR: In this paper, a new form for describing interacting relativistic classical particles with invariant world-lines is presented, in contrast to the use of independent particle variables or of "centre of mass" and relative co-ordinates previously considered in the literature.
Abstract: A new form for describing interacting relativistic classical particles with invariant world-lines is presented. In contrast to the use of independent particle variables or of «centre of mass» and relative co-ordinates previously considered in the literature, we introduce a Lorentz matrix and an associated conjugate four-dimensional angular momentum as collective variables; these are supplemented with a suitable number of internal variables. The methods of constrained Hamiltonian dynamics are used to ensure that the number of independent degrees of freedom corresponds precisely to that for a system of a given number of particles. Independent particle variables can be defined in the formalism, and interactions included. The eleventh-generator form for relativistic Hamiltonian dynamics is essential to make relativistic invariance, invariant world-lines and interaction compatible with one another.
8 citations
TL;DR: In this article, the amplitude modulation equations for two types of excitation were analyzed in a closed analytical form and a dependence of the amplitudes of directly and indirectly excited resonant waves on the amplitude of the driving force was determined.
8 citations