Journal of Samara State Technical University, Ser. Physical and Mathematical SciencesJournal of Samara State Technical University, Ser. Physical and Mathematical Sciences1991-86152310-7081Samara State Technical University3471210.14498/vsgtu1158Research ArticleEffect of the influence of rheological beam longitudinal strains on the disc motion statePavlovGeorgiy Vasil'evichCandidate of physico-mathematical sciences, Associate professormishart@samaradom.ru, yumishi@yandex.ru, senitskiy@mail.ruKal'movaMariya Alexandrovnawithout scientific degree, no statuskalmova@inbox.ruVronskayaElena SergeevnaCandidate of technical sciences, Associate professorSamara State University of Architecture and Construction1512201317125325910062020Copyright © 2013, Samara State Technical University2013The paper analyzes the effect that the material of a simple rheological beam has on thedynamics of a moving disc. The hybrid system of the differential equations describing the motion of the systemdisc–rheological beam consisting of the integro-differential equation of beam longitudinal vibrationsand the Lagrange equations of the first kind, defining the motion of the disc, and the equationsof nonholonomic constraints following from the difference between the Lagrange coordinates of thedisc mass center and the beam point contacting with the disc is composed. The paper considersthe mode of the disc steady motion, allowing to integrate the equation of beam vibrations regardlessthe system of equations describing the motion of the disc. It is identified that when the disc movesat a low speed, and in the mode corresponding to the limit value of the relaxation time it causes physically inadequate strain in the beam. When relaxation time is null there is a steady mode of forced beamvibrations at moderate amplitudes.nonholonomic connectionDirac delta functionrelaxation kernelLaplace transformationсвязь неголономнаяфункция Диракаядро релаксациипреобразование Лапласа[О. А. Горошко, "Неголономные системы с телами, что деформируются", Вестн. Киев. ун-та, 1983, № 25, 51-55][O. A. Goroško, K. Hedrih (Stevanovic), Analitička dinamika (mehanika) diskretnih naslednih sistema (in Serbian), University of Niš, Niš, 2001, 426 pp.][А. Р. Ржаницын, Некоторые вопросы механики систем деформирующихся во времени, Гостехиздат, М., 1949, 248 с.][R. M. Dreizler, C. S. Lüdde, Theoretical Mechanics: Theoretical Physics 1, Graduate Texts in Physics, Springer, Berlin, 2011, 402 pp.]