ABSTRACT: Small vibrations of a cylindrical shaft caused by inertial excitations are studied in this paper. The shaft is vertically situated. It consists of two sections with different cross sections. It is supported by a spherical and a cylindrical joint. The two supporting devices have horizontal elasticity. Between the two supports, and also at the upper end of the shaft, rotationally movable concentric masses, which are eccentrically situated towards the shaft axis, are mounted. They rotate with a constant angular velocity relative to the rotary axis and they create unfavourable inertial excitations. Due to the elasticity of the shaft, as well as to the elastic horizontal supports, small forced vibrations of the two concentric masses are created in planes perpendicular to the rotary axis. The shaft is modelled as a discrete mechanical system with four degrees of freedom. Differential equations, describing the small vibrations of the system, are derived. A programme of MatLab and Simulink has been compiled and used to integrate numerically derived equations. Calculations have been made for the different unfavourable positions of the concentrated masses relative to a plane perpendicular to the shaft rotary axis. All results are illustrated with appropriate graphs. Some important practice conclusions are presented, which can be used in the design of such shafts.
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