טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentUzan Nissan
SubjectNonlinear Normal Modes in Coupled Limit Cycle Oscillators
System with Time Delay
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Oleg Gendelman
Full Thesis textFull thesis text - English Version


Abstract

In a large variety of oscillatory systems it is crucial to take into account that the coupling can cause time delays. It is most obvious in models that take into account finite speed of the signal propagation, retarded waves, etc. In current research we consider the periodic synchronous regimes of motion in a symmetric homogeneous system of delay-coupled essentially nonlinear phase-only self-excited oscillators. Such regimes turn out to be similar to nonlinear normal modes (NNMs), known for corresponding conservative system without delays, and can be found analytically.

Unlikely the conservative counterpart, the system possesses “oval” modes with constant phase shift between the oscillators, in addition to simple and self-evident symmetric / anti-symmetric modes.

Numerical simulation demonstrates that the “oval” modes may be attractors of the phase flow.

 These attractors are a particular case of phase-locked solutions, rather ubiquitous in the system under investigation. The basins of attraction of these solutions are also investigated in order to discuss the effect of the history function.