Weakly coupled oscillators in the presence of elactic support in the conditions of acoustic vacuum
Received 05 November 2014
2014, Vol. 10, No. 3, pp. 245-263
Author(s): Koroleva (Kikot) I. P., Manevitch L. I.
A weightless string without preliminary tension with two symmetric discrete masses, which are
influenced by elastic supports with cubic characteristics, is investigated both by numerical and
analytical methods. The most important limit case corresponding to domination of resonance lowenergy
transversal oscillations is considered. Since such oscillations are described by approximate
equations only with cubic terms (without linear ones), the transversal dynamics occurs n the
conditions of acoustic vakuum. If there is no elastic supports nonlinear normal modes of the
system under investigation coincide with (or are close to) those of corresponding linear oscillator
system. However within the presence of elastic supports one of NNM can be unstable, that
causes formation of two another assymmetric modes and a separatrix which divides them. Such dynamical transition which is observed under certain relation between elastic constants of the
string and of the support, relates to stationary resonance dynamics. This transition determines
also a possibility of the second dynamical transition which occurs when the supports contribution
grows. It relates already to non-stationary resonance dynamics when the modal approach turns
out to be inadequate. Effective description of both dynamical transitions can be attained in terms
of weakly interacting oscillators and limiting phase trajectories, corresponding to complete energy
echange between the oscillators.
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