Nonstationary Resonant Dynamics of Oscillatory Chains and Nanostructures

Abstract

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Forced oscillations of the string under conditions of ‘sonic vacuum’

“…The latter property which is strongly connected with providing the conditions of acoustic vacuum [5] allows one to consider such system as efficient energy sink for defence of different structural elements from intensive external excitations by means of almost irreversible targeted energy transfer (TET). The main attention in this field has focused on the case of impulse excitation [8,9] using the simplest single-particle sink. As for periodic external loading, the efficiency of such a simple energy sink is much less studied [10,11].…”

Complex Envelope Variable Approximation in Nonlinear Dynamics

“…In fact, the "slowness" depends greatly on the formulation and the requirements of the initial problem and, sometimes, 5 to 7 periods of the steady-state oscillations can turn out to be an adequate time for the accurate description of the slow nonstationary processes. In conclusion, we would like to remark that the CEVA admits a generalization to systems with an infinite number of degrees of freedom, as was discussed in [26,27,35].…”

“…One can notice an excellent agreement of these values with the data of numerical simulations. The three problems discussed above exhaust the list of the examples by which we would like to illustrate the applications of the CEVA, but many other applications of the method discussed above can be found in [35].…”

Experimental results on the vibratory energy exchanges between a linear system and a chain of nonlinear oscillators

“…Some works have considered three degree-of-freedom (dof) vibration absorbers, showing their capacity to perform a multi-modal control of impulseloaded systems (5; 6; 7). Some researches concentrated on resonance energy exchanges between particles with the concept of limiting phase trajectories (8). A detailed overview in the area of ordered granular media such as dimer and weakly coupled chains and locally resonant acoustic metamaterials can be found in (9).…”