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Behaviour of non-linear systems with respect to low-frequency vibration are essentially changeable under action of high-frequency oscillations. Particularly, the resonance frequencies of usual and parametrical excitations as well as bifurcation points can be changed with aid of additional high-frequency excitations. The studies [1, 2, 3] on the base of oscillatory strobodynamics and on the method of direct separation of motions make it possible to obtain the equations of low-frequency “slow” oscillations of the system („vibro-transformed equations“). The analysis of these equations gives the opportunity to explain a resonance character of the amplitude changing of usual and parametric excited low-frequency vibrations with amplitude increasing of some additional high-frequency excitation. The results are discussed in connection with the theory of the stochastic resonance – pick response of a system on increasing of random excitation intensity. Another application is explanation of noise-induced phase transition.
References
1 Blekhman I.I., Sorokin V.S. Effects produced by oscillations applied to nonlinear dynamic systems: a general approach and examples // Nonlinear Dynamics. 2016, Volume 83, Issue 4, pp 2125-2141.
DOI: 10.1007/s11071-015-2470-x http://link.springer.com/article/10.1007/s11071-015-2470y-x
2 E. Kremer. Slow Motions in Systems with Fast Modulated Excitation // Journal of Sound and Vibration. Vol. 383. November 2016, pp. 295–308. http://dx.doi.orgal/10.1016/j.jsv.2016.07.006
3. Blekhman I. I., Landa P. S. (2004) Conjugate Resonances and Bifurcations in Nonlinear Systems under Biharmonical Excitation. Intern. Journ. of Nonlinear Mechanics 39: 421-426