Transient traveling breather response of strongly anharmonic array of self-sustained oscillators: Analytical study.

In the present study, we analyze the transient response of a locally excited chain of strongly anharmonic self-sustained oscillators. This discrete system under consideration models the dynamics of genuinely nonlinear, aeroelastic metamaterial. We particularly focus on the transient evolution of the traveling dissipative breathers, forming in locally excited, finite chains of self-sustained oscillators.

Emergence of non-stationary regimes in one- and two-dimensional models with internal rotators.

In the present paper, we give a selective review of some very recent works concerning the non-stationary regimes emerging in various one- and two-dimensional models incorporating internal rotators. In one-dimensional models, these regimes are characterized by the intense energy transfer from the outer element, subjected to initial or harmonic excitation, to the internal rotator. As for the two-dimensional models (incorporating internal rotators), we will mainly focus on the two special dynamical states, namely a state of the near-complete energy transfer from longitudinal to lateral vibrations of the outer element as well as the state of a permanent, unidirectional energy locking with mild, spatial energy exchanges.

Consecutive transitions from localized to delocalized transport states in the anharmonic chain of three coupled oscillators.

In the present paper, we study the mechanism of formation and bifurcations of highly nonstationary regimes manifested by different energy transport intensities, emerging in an anharmonic trimer model. The basic model under investigation comprises a chain of three coupled anharmonic oscillators subject to localized excitation, where the initial energy is imparted to the first oscillator only. We report the formation of three basic nonstationary transport states traversed by locally excited regimes.

Solitary waves in diatomic chains.

We consider the mechanism of formation of isolated localized wave structures in the diatomic Fermi-Pasta-Ulam (FPU) model. Using a singular multiscale asymptotic analysis in the limit of high mass mismatch between the alternating elements, we obtain the typical slow-fast time scale separation and formulate the Fredholm orthogonality condition approximating a sequence of mass ratios supporting the formation of solitary waves in the general type of diatomic FPU models. This condition is made explicit in the case of a diatomic Toda lattice.

Nonlinear energy channeling in the two-dimensional, locally resonant, unit-cell model. II. Low energy excitations and unidirectional energy transport.

This paper completes a series of two publications devoted to the analytical investigation of energy channeling phenomena, emerging in a locally resonant unit-cell model. The system under consideration comprises an outer mass with internal rotator and subject to the 2D nonlinear local potential. In the present study, we focus on the analysis of the regimes of two-dimensional, nonlinear energy transport forming in the special asymptotic limit of low energy excitations.