The research involved in this paper falls into the area of analytical vibrations applied to planar mechanical linkages. Specifically, a study of the vibrations, associated with an elastic connecting-bar for a high-speed slider-crank mechanism, is made. To simplify the mathematical analysis, the vibrations of an externally viscously damped uniform elastic connecting bar is taken to be hinged at each end (i.e., the moment and displacement are assumed to vanish at each end). The equations governing the vibrations of the elastic bar are derived, a small parameter is found, and the solution is developed as an asymptotic expansion in terms of this small parameter with the aid of the Krylov-Bogoliubov method of averaging. The elastic stability is studied and the steady-state solutions for both the longitudinal and transverse vibrations are found.

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