Date of Award

Spring 2014

Degree Type


Degree Name

Master of Science (MS)


Mechanical Engineering

First Advisor

Charles M. Krousgrill

Committee Member 1

Gregory M. Shaver

Committee Member 2

Stuart J. Bolton


Some mechanical systems with gaps such as in disc brakes and Cardan joints exhibit nonlinearity under certain load conditions, which is unpredictable and highly sensitive to initial conditions. Previous studies were mainly focused on either a single-degree-of-freedom (DOF) system or a flexible beam with uniform elastic foundation. The analysis of this thesis is a combination of these two where gaps are first introduced to a flexible beam model. A model of a beam resting on compliant foundation with gaps has been developed and analyzed. The assumed modes method is used to derive the equations of motion (EOM's) for the system. The responses of both rigid and flexible beam systems with linear piecewise contact vibration is considered. For the rigid beam system with only transverse DOF, the piecewise linear function method and non-dimension analysis are used to determine the solution. For the multi-DOF system, the EOM's are solved by numerical time integration. The pseudo-arc continuation and Floquet multipliers provide the completed frequency response along with relevant stability information. The primary resonance has been analyzed in different parameters. Several types of bifurcations are observed around the resonant frequency, some leading to chaotic motion within a small range of excitation frequencies. For the parametric analysis, the effect of gaps, excitation force, constraint load, damping and number of springs on the response are discussed, which are used to describe the types of nonlinear response (softening/hardening or both) shown on the resonant peaks.