Master of Sciences (Engineering), Case Western Reserve University, 2009, EMC - Mechanical Engineering

The damping force and the self-excited force, which are a part of Heat Exchanger tube vibrations, act in the same (transverse) direction. The wedging process introduces alternating longitudinal coulomb forces that act at double the frequency of transverse vibrations and is defined by the wave equation. The transverse vibrations and the alternating longitudinal coulomb forces are coupled and act orthogonal to each other. Physical observations show that the transverse vibrations cannot exist without longitudinal vibrations. The governing constitutive equations for coupling can be shown theoretically through material non-linearities by considering higher order terms for the elastic energy, and geometric non-linearities by considering non-linear strain displacement relations. This non-linear constitutive equation when used in the equation of motion for transverse vibrations, the Gol'dberg tensorial result emerges. Energy reorganization due to this coupling results in reduced transverse vibration amplitudes. A simple experimental setup simulating this wedging process validates that transverse vibrations cannot occur without longitudinal vibrations.

Committee: Joseph Mansour (Advisor); Winston Perera (Committee Co-Chair); Vassilis Panoskaltsis (Advisor); Joseph Prahl (Committee Member); Roger Quinn (Committee Member) Subjects: Engineering