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Asymptotic analysis of a nonlinear autonomous vibratory system

A system consisting of a spring, dashpot, and mass upon which is mounted an eccentric driven by a motor with a linear torque-speed characteristic, is analyzed by perturbation procedures based on small reciprocal of rotational inertia. Periodic solutions of the third order system, which arises when the angular position of eccentric mass is taken as the new independent variable, are constructed, and their stability is analyzed. An asymptotic solution is also obtained which is more general than a periodic solution, in that the averaged rotational speed is a slowly varying function, rather than a constant. The results are applicable to the determination of the interaction between the rotational motion of a flexibly mounted motor and the translational vibratory motion of its frame.