טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentVorotnikov Kirill
SubjectAnalysis of Nonstationary Regimes Emerging in
Two-Dimensional Locally resonant Acoustic
Structures
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Yuli Starosvetsky
Full Thesis textFull thesis text - English Version


Abstract

Over the last several decades, wave propagation in acoustic metamaterials has become a subject of a constantly growing interest in various aspects of modern physics and engineering sciences.  These special dynamical systems have driven a considerable attention for their highly tunable, material properties (e.g. tailored band-gaps) which gave rise to some important acoustical properties such as sound focusing, sound absorption, enhanced spatial-temporal control over the deformation of sound fields and more.

Present study involves the four main parts. The first part concerns the analysis of damped and undamped, resonant energy transport emerging in the strongly nonlinear, locally resonant, two-dimensional unit-cell model. System under consideration comprises an outer mass incorporating internal rotator and subject to the two-dimensional, nonlinear local potential. In the current study, we revealed the emergence and bifurcations of highly nonlinear, nonstationary regimes manifested by the unidirectional energy localization as well as the complete, bidirectional energy transport controlled by the internal rotational device.

The second part of the study is mainly devoted to the analysis of nonlinear phenomena of bidirectional and unidirectional energy channeling emerging in the same structure in the limit of low energy excitations. The presently considered limit of low energy excitations reveals the emergence of quite intriguing, highly nonlinear, transient regimes of unidirectional energy channeling manifested by the partial and complete, unidirectional energy flow from axial to lateral vibrations. We also show that the previously reported phenomena of recurrent energy channeling as well as the unidirectional energy locking persist in the low energy limit as well.

The third part of the study is devoted to the analytical investigation of the bifurcation structure of special class of nonstationary low-energy regimes emerging in the same model. These regimes are characterized by the slow, purely rotational motion of the rotator synchronized with the periodic energy beats between the axial and the lateral vibrations of the outer element. Using the regular multi-scale analysis we derive the slow-flow model. To showcase the evolution of these regimes we used the special Poincaré map technique applied on the slow-flow model. Results of the Poincaré sections unveiled some interesting local bifurcations undergone by these regimes.

The final part of the study concerns two-dimensional nonlinear mechanisms of bidirectional and unidirectional channeling of longitudinal and shear waves emerging in the locally resonant acoustic structure. These regimes are manifested by the two-dimensional energy channeling between the waves in the recurrent as well as the irreversible fashion. We show that the spatial control of the two dimensional energy flow between the longitudinal and the shear waves is solely governed by the motion of the internal rotators.

Present study paves the way for future theoretical and experimental investigations of the emergence of unidirectional energy channeling phenomena in the more complex dynamical systems, e.g., two-dimensional acoustic metamaterials made of many interacting locally resonant units. We believe that present study provides efficient theoretical predictive capacity for the design of locally resonant, acoustic structures with the unique dynamical properties allowing for the efficient energy redirection and wave arrest.