Nonlinear targeted energy transfer and macroscopic analog of the quantum Landau–Zener effect in coupled granular chains

One of the prime focuses in the design of highly adaptive granular material is in ability to passively control the flow of energy through it by means of trapping, redirection and scattering. In this study we demonstrate that one of the possible mechanisms to achieve efficient control over the propagating shock wave in the material is the usage of weakly interacting, non-compressed granular chains. In the latest computational studies we have demonstrated that the shock waves initially localized on a finite amount of chains can be efficiently redirected to the neighboring granular chains. In this work, we present an analytical and numerical approach to the concept of targeted energy transfer (TET) in granular media. We consider two weakly coupled granular chains which have on-site potential. This on-site potential arises if the granular chains are mounted on linear elastic foundation. We propose two different mechanisms for TET in granular media: (i) decouple the coupling, and (ii) stratification of the foundation. Each mechanism provides an efficient way of localization of energy in one of the two chains. For the second mechanism, one chain with varying parameter is excited by an initial impulse but coupled with another chain with constant parameter is initially at rest and we transform the governing equation of the granular chain system into two coupled oscillators and thus made an analogy between strongly nonlinear granular chain with the quantum Landau-Zener tunneling. The revealed phenomena open up the possibility of designing granular media as shock mitigators by efficiently redirecting the incoming energy to the neighboring granular chain, i.e. it gives a passive control over the incoming energy by redirecting among the granular networks.

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A Review on Invariant Manifolds and Targeted Energy Transfer

Oriental Journal of Physical Sciences ◽

10.13005/ojps03.02.02 ◽

2018 ◽

Vol 3 (2) ◽

pp. 75-86

Author(s):

Maaita Jamal Odysseas ◽

Meletlidou Efthymia

Keyword(s):

Energy Transfer ◽

Dynamical Systems ◽

Invariant Manifolds ◽

Singular Perturbation Theory ◽

Targeted Energy Transfer ◽

Transfer Energy ◽

Practical Applications ◽

Nonlinear Targeted Energy Transfer ◽

Self Tuning ◽

Different Time Scales

We present a review on one of the latest developments in the field of dynamical systems, The nonlinear Targeted Energy Transfer (TET). The great significance of the phenomenon lies in the fact that the systems in which Nonlinear TET occurs present a form of self-tuning and can transfer energy over a wide variety of frequencies (resonances). This makes nonlinear TET particularly suitable in practical applications where it is necessary to extract energy from multiple ways of oscillation. Dynamical systems where nonlinear TET occurs are systems with different time scales and are singular. This property allows us to study such systems with the use of singular perturbation theory. It has been shown that Nonlinear TET is related to the bifurcation of the Slow Invariant Manifold of such systems and their slow flow.

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