טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentTzemah Naor
SubjectAccelerating Oscillatory Fronts In a Chain With Nonlocal
Interactions: Effect Of Linear Spectrum
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Oleg Gendelman


Abstract

Accelerating oscillatory fronts are encountered in forced sonic vacuum with non-local interactions. Such behavior appears in simple model dynamical systems, such as a chain of particles oscillating in the plane and coupled by linear springs with fixed ends. Continuous counterpart of the latter system - elastic string with fixed ends without pre-tension.

The work is devoted to exploration of effect of small linear perturbations (like small pre-tension or nonzero bending elasticity) on the propagation of the oscillatory fronts in the sonic vacuum. This work demonstrates that such perturbations have profound effect on propagation of the oscillatory fronts. We derived the asymptotic relationship that describes the front propagation, with a crossover from constant velocity to acceleration. It was demonstrated numerically that small local perturbations of the bending and elasticity coefficients don't affect the front propagation.

In addition to the propagating oscillatory fronts, we revealed the localized states without profound front propagation, and without clear separation between longitudinal and transversal motion.