טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentYacobi Gil
SubjectResonant Energy Transport in Coupled Granular Crystals
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Yuli Starosvetsky
Full Thesis textFull thesis text - English Version


Abstract

Granular crystals, also known as nonlinear acoustic meta-material, are the assembly of discrete solid granular elements of various shapes, arranged in regular lattice structure. These elements are initially in contact and interact one with another through a nonlinear repulsive contact force (Hertzian contact law). In the past few decades, granular crystals attracted substantial attention for their unique dynamical properties of significant practical importance in addition to their simple fabrication. Granular meta-materials can be used in the various engineering problems such as shock mitigation, vibration absorption, vibration isolation and wave manipulation. In the present work, we study the two fundamental mechanisms of unidirectional energy transfer between the two coupled Hertzian oscillators and oscillatory chains in the passive and semi-active manner.

In the first case, corresponding to the passive mechanism, we consider the response of the two nonlinearly coupled, dissipative Hertzian oscillators. We demonstrated that under particular set of system parameters the model under consideration allows the, irreversible transfer of energy from the initially excited oscillator to the initially resting one. In the second case, corresponding to the semi-active mechanism, we study the response of the two coupled Hertzian oscillators subjected to the different dynamical states. The model under consideration assumes that the initially excited Hertzian oscillator is in an uncompressed state (usually referred to as an ‘acoustic vacuum’) while the coupled oscillator is given to the state of a strong, slowly decreasing compression.

In the second part of the study, we implement the passive mechanism for control of nonlinear wave transfer in coupled granular crystals. The passive mechanism is implemented upon a symmetric system of two dissipative nonlinearly coupled granular chains.

Using some basic asymptotical techniques (multi-scale analysis, averaging) we described both mechanisms analytically and predict the special regions in the space of the system parameters corresponding to the formation of the aforementioned regimes of irreversible energy flow in coupled Hertzian oscillators and chains. Theoretical predictions derived from the simplified asymptotical models are found to be in a good agreement with the results of the direct numerical simulations of the original systems.