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L.D. Akulenko, A.A. Gavrikov, and S.V. Nesterov, "Natural Transverse Oscillations of a Rotating Rod of Variable Cross Section," Mech. Solids. 53 (5), 510-519 (2018)
Year 2018 Volume 53 Number 5 Pages 510-519
DOI 10.3103/S0025654418080058
Title Natural Transverse Oscillations of a Rotating Rod of Variable Cross Section
Author(s) L.D. Akulenko (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia; Bauman Moscow State Technical University, ul. 2-ya Baumanskaya 5 str. 1, Moscow, 105005 Russia)
A.A. Gavrikov (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, gavrikov@ipmnet.ru)
S.V. Nesterov (Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia)
Abstract The problem of natural oscillations of a rotating rod of variable cross section is considered. It is believed that the rod is rigidly attached at one end to a rotor with a constant speed orthogonal to the axis of rotation, the other end is assumed to be free. Flexural movements occur in the plane of rotation or perpendicular to it. To determine the natural oscillations, the Euler rod oscillation model is used, taking into account, in addition to the tensile force, the bond reaction force caused by the movements of the neutral axis. Using an original numerical-analytical method, the lower frequencies were calculated for the power and exponential laws of the cross section change.
Keywords Sturm-Liouville theory, rotating rod, eigenvalues, transverse oscillations, method of accelerated convergence, variable section rod, linear Hamiltonian system, boundary value problem
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Received 20 May 2018
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