Valeri Smirnov

Targeted Energy Transfer

This chapter presents the analytical and numerical study of energy transport in a system of n linear impulsively loaded oscillators (a primary linear system), in which the nth oscillator is coupled with an essentially nonlinear attachment—the nonlinear energy sink (NES).

Nonlinear Vibrations of the Carbon Nanotubes

The previous sections concern the discrete systems, where the discreteness of the oscillation spectra is defined by the finiteness of the number of the particles forming the system under consideration.

Emergence and Bifurcations of LPTs in the Chain of Three Coupled Oscillators

The natural question is: How the LPT concept may be extended to the systems with more than two degrees of freedom? To answer this question, we consider first a simplest extension to the case of three weakly coupled identical oscillators.

Strongly Nonlinear Lattices

The majority of physical, mechanical and engineering problems dealing with nonlinear processes cannot be solved by the direct methods. The main goal of the researchers is the construction of a simplified model, which can be solved by an approximate method without loosing the physical content.

Localized Nonlinear Excitations and Inter-chain Energy Exchange

The description of the nonlinear media in the framework of the quasi-one-dimensional models assumes the existence of the essential anisotropy of the media properties, for example, the considerable difference between coupling constants along and transversely the chains in the polymeric crystals.

Nonlinear Energy Channeling in the 2D, Locally Resonant, Systems

Passive control of the acoustic wave propagation in metamaterials is a subject of broad scientific and practical interest in various aspects of applied sciences and engineering.

Two Coupled Oscillators

Let us consider first the most simple nonlinear problem of energy transfer in the system of two weakly coupled nonlinear oscillators with cubic restoring forces (Fig. 1.1). Its linearized version is a widely used example of beating phenomenon. In this limiting case, due to superposition principle, every vibrational process can be presented as a combination of two basic oscillations corresponding to in-phase and out-of-phase linear normal modes. If the coupling between the oscillators is relatively weak and only one of oscillators is initially excited, the beat with a slow periodic inter-particle energy exchange is observed.

Two-Particle Systems Under Conditions of Sonic Vacuum

In this section, we investigate resonance energy transport in a purely nonlinear system, wherein harmonic oscillations are prohibited by the properties of the system potential of degree higher than two.

Quasi-One-Dimensional Nonlinear Lattices

In this section, it is shown how the LPT concept can be extended to finite-dimensional oscillatory chains. The systems under consideration are finite-dimensional analogues of several classical infinite models which were initially used for analysis of such significant physical phenomena as recurrent energy transfer and localization.

Classical Analog of Linear and Quasi-Linear Quantum Tunneling

In this part of the report, we develop an analytical framework to investigate irreversible energy transfer in a system of two unforced weakly coupled oscillators with slowly time-varying frequencies. In the system under consideration, one of the oscillators is initially excited by an initial impulse, while the second one is initially at rest. As shown in the previous sections, these initial conditions provide motion along the LPT with a maximum possible energy transfer from the excited oscillator to the second one.