טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentEzra Tal
SubjectEscape of Excited Two DOF System from Potential Well
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Oleg Gendelman
Full Thesis textFull thesis text - English Version


Abstract

This thesis addresses the problem of the escape of a dynamical system with two degrees of freedom from a one-dimensional potential well. Dynamics of the escape process is governed by energy exchange between internal degrees of freedom of the system and the potential well. We explore the process for three different model potentials with the same initial conditions, in which only one of the system degrees of freedom is initially excited. Later, the main object of the study is the relationship between critical initial energy required for the escape, and internal coupling in the system.

To find this relationship we will examine the dynamics of the system for two limit cases of small and large coupling. For the case of small coupling we will analyze the forces that the two particles exert on each other and the potential well’s force and find the relation between these forces to the initial energy and the stiffness of the spring. For the case of large coupling we will analyze the system in terms of center of mass and by using methods of averaging and effective potential of the center of mass we will find the energy escape criterion.

Quite surprisingly, results showed that a two limit cases of small and large coupling reliably cover almost the whole range of possible coupling values. Moreover, these limit cases allow for the deriving of simple analytic approximations for the relation between critical escape energy and the coupling. In addition, it is shown that the system between the zones of validity of these two limit asymptotic approximations exhibits chaotic characteristics, and the energy threshold is close to a possible minimum due to presumably ergodic system dynamics.