Abstract
The article deals with the tasks of determining the refined values of the frequencies of natural bending vibrations of beams for the design schemes common in engineering practice. The object of study is an elastic beam and an engine located on it with an unbalanced eccentrically mounted mass. The studies were carried out with the aim of obtaining a sufficient dynamism coefficient and a refined formulation of the beam strength condition. To determine the natural frequency, taking into account the mass of the beam, a dynamic model of an object with a reduced mass has been built, located in the beam section through which the gravity force of the engine passes. A method for determining: the coefficient of mass reduction, the reduced coefficient of bending stiffness of the beam, the natural vibration frequency has been proposed. To do this, the equation for the curved beam axis is used, taking into account the change in the coordinate of the mass focusing point. The basic vibration frequency of the system has been determined taking into account the axial moment of inertia of the engine mass relative to its central axis. The solution of the frequency equation for a small ratio of the radius of the motor inertia to the length of the beam makes it possible to obtain a significant correction to the frequency that would take place for a point mass of the motor. Based on the strength conditions of the beam in the absence of a damper, recommendations have been obtained regarding the rotor rotation safe speed in the pre-resonant and post-resonant phases of the object motion. Having the refined amplitude value of stresses, taking into account the given parameters of the beam and the engine, it is recommended to select the characteristic of the viscous friction damper, which will provide a given endurance coefficient with an asymmetric cycle of stress change. The results of the article can be used by both students and engineers to select the optimal, in terms of beam strength, combination of beam and engine parameters
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