منابع مشابه
Non-linear Oscillations of Milling
The principal features of two mathematical models that can be used to study non-linear oscillations of a workpiece – tool system during a milling operation are presented and explained in this article. These models are non-linear, non-homogeneous, delay-differential systems with time-periodic coefficients. In the treatment presented here, the sources of non-linearities are the multiple regenerat...
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The definition of a non-linear normal mode (NNM) as an invariant manifold in phase space is used. In conservative cases, it is shown that normal form theory allows one to compute all NNMs, as well as the attendant dynamics onto the manifolds, in a single operation. Then, a single-mode motion is studied. The aim of the present work is to show that too severe trunc ature using a single linear mod...
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The paper deals with an approximate analysis of non-linear oscillation problems with slowly varying system parameters. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by using the generalized averaging method of Sinha and Srinivasan based on ultraspherical polynomial expansions. The Bogoliubov-Mitro...
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The objective of this paper is to consider the dynamic motions of second order, weakly non-linear, discrete systems. The main attention is focused on a comparison, for such systems, of the method of Krylov–Bogoliubov (KB) and an enhanced Galerkin (EG) method which produce seemingly different solutions. Despite the apparent differences, the two methods are shown to give identical first order per...
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ژورنال
عنوان ژورنال: Nature
سال: 1963
ISSN: 0028-0836,1476-4687
DOI: 10.1038/197525a0