טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentNaiger Dan
SubjectEscape of a Forced-Damped Particle from a Potential Well:
Transient Response
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Oleg Gendelman
Full Thesis textFull thesis text - English Version


Abstract

The research thesis is devoted to analysis of the escape of periodically forced and damped particle from one-dimensional potential well. The particle is initially at rest, and the forcing is switched on at a certain time. The present work is an extension of previous results, obtained in a Hamiltonian setting, for much more realistic case with viscous damping.

 Assuming primary 1:1 resonance, one can consider the problem in terms of averaged transient dynamics. It turns out that, similarly to the undamped case, the escape process is reliably described in terms of topology of special trajectories on the resonant manifold. A theoretical prediction of the minimal force required for the escape as a function of the excitation frequency for various damping coefficients is provided. In the explored frequency range, numeric simulations are in complete qualitative and reasonable quantitative agreement with the theoretical predictions except for small frequencies under 0.3. These discrepancies are related to quasistatic asymptotic limit of the model.

This research also compares two types of forcing -  a traditional harmonic excitation and the drive in a form of a symmetric triangle wave. It was found that for both of the excitations the escape mechanism was similar. The effects of a small and fast harmonic perturbation in the sinusoidal drive on the critical forcing amplitude for escape from the well were also explored and found quite minor; this finding further corroborates the reliability of approximation based on the averaging in the vicinity of the primary 1:1 resonance.