The research presented in this paper is an analytical study of the vibrations associated with planar mechanical linkages. Specifically, the vibrations of a high-speed slider-crank mechanism with a uniform elastic connecting rod and a rigid crank are studied. The elastic connecting rod, with distributed mass, is taken to be externally, viscously damped with a concentrated mass present at its sliding end. The equations governing the longitudinal and transverse vibrations of the elastic connecting rod 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 of the connecting rod are obtained.

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