Date of Completion

Fall 12-2012

Thesis Advisor(s)

Patrick J. McKenna

Honors Major



Applied Mathematics | Non-linear Dynamics


The model of nonlinear spring systems can be applied to deal with different aspect of mechanical problems, such as oscillations in periodic flexing in bridges and ships. The concentration of this research is the bouncing behaviors of nonlinear spring system when the processing time is large, therefore nonlinear ordinary differential equations (ODE) are suitable since researchers can add different variables into the models and solve them by computational methods. Benefit from this, it is easy to check the oscillations or bouncing behaviors that each variable contributes to the model and find the relationship between some important factors: vibrating frequency, external forces and amplitudes. Moreover, analyzing the model can be implemented by plugging different values into the equations characteristics. For example, this research will focus on discussing various initial conditions since they may cause different behaviors to appear. Conducting numerical analysis to check the performance of the model by computing with MATLAB is also necessary during the research procedure, which may help researches to avoid failure results and show the existence of a certain phenomenon.