Modelling the stability of compressed and twisted rod
Published: 08.10.2014
Authors: Dubrovin V.M., Butina T.A.
Published in issue: #5(29)/2014
DOI: 10.18698/2308-6033-2014-5-1235
Category: Mathematic modeling | Chapter: Modeling in mechanics of solid media
To calculate the stability of a rod under simultaneous effect of axial compressive force and torque we offer an approximate method. It is assumed that the main rod bending rigidity differs slightly, and the rod torsion is very small. We considered rods with clamped ends, with pivot bearings, and rod in the form of a compressed and twisted console. For all cases we received diagrams of dependence of the rod stability parameter for different values of the ratio of its principal bending rigidities.
References
[1] Feodosyev V.I. Izbrannye zadachi i voprosy po soprotivleniyu materialov [Selected problems and questions on resistance of materials]. Moscow, Nauka Publ., 1973, 400 p.
[2] Ponamarev S.D., ed. Raschety na prochnost’ v mashinostroenii [Strength analysis in engineering]. Moscow, Mashgiz Publ., 1959, vol. 3, 861 p.
[3] Shashkov I.E. Prikladnaya mechanika - Applied Mechanics, 1976, vol. 12, no. 1, pp. 71-76.
[4] Shashkov I.E. Prikladnaya mechanika - Applied Mechanics, 1978, vol. XIV, no. 2, pp. 87-94.
[5] Zhilin P.A. Aktualnye problemy mekhaniki. Sbornik statey [Actual Problems in Mechanics. Coll. papers], St.-Petersburg, Institute of Problems of Mechanical Engineering RAS, 2006, 306 p.
[6] Rabotnov Yu.N. Problemy mekhaniki deformiruemogo tela [Problems of solid mechanics]. Moscow, Nauka Publ., 1991, 194 p.
[7] Dimitrienko Yu.I. Mekhanika sploshnoy sredy. Tom 4. Osnovy mekhaniki tverdogo tela [Continuum Mechanics. Vol. 4. Fundamentals of solid mechanics]. Moscow, BMSTU Publ., 2013, 624 p.
[8] Dimitrienko Yu.I. Mekhanika sploshnoy sredy. Tom 2. Universalnye zakony mekhaniki i elektrodinamiki sploshnoy sredy [Continuum Mechanics. Vol. 2. Universal laws of mechanics and electrodynamics of continuous media]. Moscow, BMSTU Publ., 2011, 560 p.
[9] Frolov K.V. Izbrannye Trudy [Selected Works]. Moscow, Nauka Publ., 2007, 526 p.
[10] Pikovsky A., Rozenblyum M., Kurts Yu. Sinkhronizatsiya: Fundamentalnoe nelineynoe yavlenie [Synchronization: The fundamental non-linear phenomenon]. Moscow, Tekhnosfera Publ., 2003, 496 p.
[11] Volmir A.S. Ustoichivost’ deformiruemykh system [Stability of deformable systems]. Moscow, Nauka Publ., 1967, 987 p.
[12] Butina T.A., Dubrovin V.M. Inzhenernyi zhurnal: nauka i innovatsii - Engineering Journal: Science and Innovations, 2012, iss. 2(2). Available at: http://engjournal.ru/articles/44/44.pdf