טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentBen Meir Yitzhak
SubjectIntrinsic Dynamics of Coupled Anharmonic Lattices
in the State of Sonic Vacuum
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Yuli Starosvetsky
Full Thesis textFull thesis text - English Version


Abstract

 

Intrinsic dynamics of purely anharmonic lattices has driven considerable attention in various aspects of applied physics and engineering sciences. For instance, dynamic response of granular materials has attracted substantial interest from researchers due to their unique dynamical properties. Recent studies have shown that granular materials can exhibit a very peculiar dynamical behavior such as energy localization, entrapment, anomalous reflections, uni- directional propagating wave-guides as well as an enhanced mitigation of shock waves. This class of dynamical system defines a special state which is referred to in the literature as sonic vacuum due to the absence of harmonic terms. The vast majority of recent studies have been mostly concerned with the analysis of stationary solutions i.e. periodic waves, breathers, solitons as well as their weak modulations (weakly nonstationary regimes). In many mechanical and physical systems formation of highly nonstationary oscillatory regimes leading to massive energy transport from one fragment of the structure to another can be of primary engineering importance.

First part of the study considers the mechanism of formation of a highly nonstationary response characterized by complete energy exchanges between anharmonic oscillatory chains in the state of sonic vacuum. Despite the complexity of the systems under consideration, it is still possible to derive an analytical approach revealing the transition from energy localization to a strong energy pulsation by investigating the global bifurcations undergone by this type of highly non-stationary regime. We show analytically and numerically that initial excitation in the form of spatially periodic standing waves as well as strongly localized ones (i.e. breathers, compactons) on one of the chains results in the formation of peculiar patterns of energy localization, as well as the highly non stationary, inter-chain energy transport.

Second part of the study considers the dynamics of solitary like pulses propagating through the perturbed granular scalar model i.e. array of coupled, granular chains subject to on-site perturbation of a general type. Thus, assuming a non-uniform excitation applied to each one of the chains we study the evolution of primary pulses caused by the inter-chain interactions as well as the on-site perturbation. We derive a special analytical procedure revealing a spatial modulation of solitary like pulses on each one of the chains in the array. Special emphasis of the present study is given to the perturbed, granular scalar models subjected to a somewhat peculiar type of on-site perturbation, namely a perturbation containing the dissipative and energy sourcing terms.