Abstract
t. The article deals with the problem of torsional vibrations of circular elastic conical rods in the system of cylindrical coordinates. It is believed that vibrations of the rod are caused by external dynamic loads applied to its surface. The cross-sectional radius is taken as a linear function of the longitudinal coordinates. On the basis of the equation of motion of the theory of elasticity for torsional vibrations, the equation of torsional vibrations of a conical rod with a circular cross-section is derived using the Fouret and Laplace integral substitutions. On the basis of the obtained equation, the problem of harmonic torsional vibrations of a rod is solved. The frequency equation and the relationship between frequency and number of waves are given. Based on the obtained numerical results, appropriate conclusions were drawn
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