טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentKislovsky Victor
SubjectTransition from Energy Localization to Energy Transport in
the System of Three Coupled Anharmonic Oscillators
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Yuli Starosvetsky
Full Thesis textFull thesis text - English Version


Abstract

    Dynamics of granular lattices is a subject of growing interest in various fields of applied physics and engineering. Motivated by the latest developments in the dynamics of two, weakly interacting chains, as well as, by the recent, ground-breaking achievements in the area of the dynamics of one dimensional granular crystals, we aim at studying the dynamics of the extended model comprising the three, weakly coupled, strongly nonlinear granular chains - mounted on linear elastic foundations. Unlike the previous studies of weakly coupled oscillatory chains, the dynamical systems considered herein incorporate both the non-smooth effects due to the possible separations between the interacting neighboring elements (granules), as well as the strongly nonlinear, inter-particle, Hertzian interactions. We show that these systems exhibit very rich and complex dynamics that can be partially captured by analytical approximations.

   In the present study we analyze the governing mechanisms of transition from energy entrapment to the nearly complete, inter-chain energy transport in the system of three coupled, an-harmonic oscillators as well as the oscillatory chains. Two distinct mechanisms leading to the breakdown of energy localization on the first and the second oscillators (oscillatory chains) have been revealed and analyzed in the study. Using the regular multi-scale asymptotic analysis along with the non-smooth temporal transformation procedure (NSTT) we formulate the analytic criteria for the formation of the resonant, inter-chain energy transport.

We confirm the validity of the devised analytical procedure for the two different (smooth and non-smooth) dynamical models: (1) weakly coupled, Hertzian chains (2) weakly coupled, cubic oscillators (Duffing oscillators). Results of the analytical approximation are in a very good agreement with the results of numerical simulations of the full models.