Dimentberg, Mikhail F.
Tilley, Burt S.
Sommerfeld effect is a common phenomenon for vibration system excited by a limited power supply. It was considered in 1D system and axisymmetric system. The cases between the two extreme cases are 2D vibrations. In this report, we consider a 2D vibration system with two spring sets attached to an unbalanced shaft, excited by a limited power supply. We use the Krylov-Bogoluibov averaging method to access the motor torque for the steady-state response, as well as its stability criteria, and consider the transient case. From a simulation of the equations using the Runge-Kutta-Fehlberg method, the steady-state torque and its stability is validated, as well as a hypothesis of passage technique for the axisymmetric case by raising the spring stiffness of one of the spring sets.
Worcester Polytechnic Institute
Major Qualifying Project
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