טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentErez Ariel
SubjectDynamics of Van Der Pol Oscillator with Rotational
Energy Sink
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Oleg Gendelman
Full Thesis textFull thesis text - English Version


Abstract

Self-excited oscillations is a phenomenon, observed in various branches of engineering in which an autonomous system displays generation and maintenance of a periodic motion.  These oscillations, known as limit cycle oscillations (LCO), may lead to catastrophic failure in mechanical systems due to fatigue.

The goal of this research is to study a proposed model for the mitigation or even elimination of the undesired oscillations using the concept of nonlinear energy sink (NES).  This concept is an essentially nonlinear attachment of relatively small mass coupled to a primary oscillating system.  In spite of its relatively small mass and due to its nonlinearity, NES can change the global dynamics of the combined system.

In this research, we study a system of Van der Pol (VDP) oscillator with attached eccentric rotator.  The VDP is a classic model of the oscillator with self-excitation, which exhibits LCO.  Attaching a small eccentric rotational mass to the VDP oscillator is a possible suggestion for relatively simple (as a mechanical component) NES.  The rotational mass is a variation of the pendulum, a basic yet complicated and extensively studied dynamical model.

Using perturbative and asymptotic methods, analytical models for description of dynamical responses in a certain range of parameters are derived.  Numerical simulations of the model display agreement with the analytical predictions.