Forced System with Vibro-impact Energy Sink: Chaotic Strongly Modulated Responses

AbstractThe paper treats forced response of primary linear oscillator with vibro-impact energy sink. This system exhibits some features of dynamics, which resemble forced systems with other types of nonlinear energy sinks, such as steady-state and strongly modulated responses. However, the differences are crucial: in the system with vibro-impact sink the strongly modulated response consists of randomly distributed periods of resonant and non-resonant motion. This salient feature allows us to identify this type of dynamic behavior as chaotic strongly modulated response (CSMR). It is demonstrated, that the CSMR exists due to special structure of a slow invariant manifold (SIM), which is derived with the help of a multiple-scale analysis of the system. In the considered system, this manifold has only one stable and one unstable branch. This feature defines new class of universality for the nonlinear energy sinks. In the system with the vibro-impact sink, such responses are observed even for very low level of the external forcing. This feature makes such system viable for possible energy harvesting applications

Heat conduction in 1D lattices with on-site potential

The process of heat conduction in one-dimensional lattice with on-site potential is studied by means of numerical simulation. Using discrete Frenkel-Kontorova, $\phi$--4 and sinh-Gordon we demonstrate that contrary to previously expressed opinions the sole anharmonicity of the on-site potential is insufficient to ensure the normal heat conductivity in these systems. The character of the heat conduction is determined by the spectrum of nonlinear excitations peculiar for every given model and therefore depends on the concrete potential shape and temperature of the lattice. The reason is that the peculiarities of the nonlinear excitations and their interactions prescribe the energy scattering mechanism in each model. For models sin-Gordon and $\phi$--4 phonons are scattered at thermalized lattice of topological solitons; for sinh-Gordon and $\phi$--4 - models the phonons are scattered at localized high-frequency breathers (in the case of $\phi$--4 the scattering mechanism switches with the growth of the temperature).Comment: 26 pages, 18 figure

On the universality of anomalous one-dimensional heat conductivity

In one and two dimensions, transport coefficients may diverge in the thermodynamic limit due to long--time correlation of the corresponding currents. The effective asymptotic behaviour is addressed with reference to the problem of heat transport in 1d crystals, modeled by chains of classical nonlinear oscillators. Extensive accurate equilibrium and nonequilibrium numerical simulations confirm that the finite-size thermal conductivity diverges with the system size $L$ as $\kappa \propto L^\alpha$. However, the exponent $\alpha$ deviates systematically from the theoretical prediction $\alpha=1/3$ proposed in a recent paper [O. Narayan, S. Ramaswamy, Phys. Rev. Lett. {\bf 89}, 200601 (2002)].Comment: 4 pages, submitted to Phys.Rev.

Simulation of heat transport in low-dimensional oscillator lattices

The study of heat transport in low-dimensional oscillator lattices presents a formidable challenge. Theoretical efforts have been made trying to reveal the underlying mechanism of diversified heat transport behaviors. In lack of a unified rigorous treatment, approximate theories often may embody controversial predictions. It is therefore of ultimate importance that one can rely on numerical simulations in the investigation of heat transfer processes in low-dimensional lattices. The simulation of heat transport using the non-equilibrium heat bath method and the Green-Kubo method will be introduced. It is found that one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) momentum-conserving nonlinear lattices display power-law divergent, logarithmic divergent and constant thermal conductivities, respectively. Next, a novel diffusion method is also introduced. The heat diffusion theory connects the energy diffusion and heat conduction in a straightforward manner. This enables one to use the diffusion method to investigate the objective of heat transport. In addition, it contains fundamental information about the heat transport process which cannot readily be gathered otherwise.Comment: Article published in: Thermal transport in low dimensions: From statistical physics to nanoscale heat transfer, S. Lepri, ed. Lecture Notes in Physics, vol. 921, pp. 239 - 274, Springer-Verlag, Berlin, Heidelberg, New York (2016

Vibro-Impact NES: A Correlation Between Experimental Investigation and Analytical Description

International audienceIn this work the dynamics of a Vibro-Impact Nonlinear Energy Sink (VI-NES) is experimentally investigated via a harmonically forced single-degree-of- freedom linear oscillator (LO) to which a VI-NES is attached. Depending on external force amplitude and frequency, either a Strongly Modulated Response (SMR) or a constant amplitude response (CAR) is observed. In both cases an irreversible transfer of energy occurs from the LO towards the VI-NES: process known as passive Targeted Energy Transfer(TET). Furthermore, the problem is analytically studied by using the multiple scales method. For the fast and the slow time scales the Slow Invariant Manifold (SIM) is obtained. The 0-order SIM shows the existence of a stable and an unstable branch of solution, and of an energy threshold (a saddle-node bifurcation) for the solutions to appear. Subsequently the 1-order SIM is calculated to find the fixed points of the problem. When a stable fixed point exists, the system is naturally drawn to it and a CAR is reached. Otherwise a SMR state is established and no stable point is attained. Finally a good agreement between experimental and analytical results is shown

Performance comparison between a nonlinear energy sink and a linear tuned vibration absorber for broadband control

The performance of a linear tuned vibration absorber (LTVA) and a nonlinear energy sink (NES) for the vibration mitigation of an uncertain linear primary system is investigated. An analytic tuning rule for the LTVA when the primary system contains uncertainty is derived. The behavior of the linear system coupled to the NES is analyzed theoretically. A tuning methodology for the NES in the deterministic as well as for the uncertain case is presented. © The Society for Experimental Mechanics, Inc. 2016