539.3 Modelling of torsional vibrations of the viscoelastic round bar rotating with the constant angular velocity

Abdirashidov A. (Samarkand State University)

BAR, TORSIONAL VIBRATIONS, DISPLACEMENT, STRESS, ROTATION, ANGULAR VELOCITY, VISCOELASTICITY


doi: 10.18698/2309-3684-2016-1-3851


The purpose of this article is to deduce general and approximate equations for the torsional vibration of the viscoelastic round bar rotating around the symmetry axis with the constant angular velocity. Within the research we develop the algorithm allowing to define the bar deflected mode. The received approximate equations enabled to numerically solve the problem of the bar torsional vibrations. Moreover, we carry out a comparative analysis of the results obtained for exponential and weakly singular kernels of the viscoelastic operator. As a result, we estimate the rotation influence on the bar vibrations


[1] Bauer H.F. Journal of Sound and Vibration, 1980, vol. 72, no. 2, pp. 177–189.
[2] Munitsyn A.I. Matematicheskoye i kompyuternoe modelirovanie mashin i sistem — Mathematical and Computer Modeling of Machines and Systems, 2008, vol. 3, pp. 64–67.
[3] Gong S.W., Lam K.Y. AIAA Journal, 2002, vol. 41, no. 1, Technical notes, pp. 139–142.
[4] Ng T.Y., Lam K.Y. Applied Acoustics, 1999, no. 56, pp. 273–282.
[5] Rand O., Stavsky Y. International Journal Solids and Structures, 1991, vol. 28, no. 7, pp. 831–843.
[6] Badalov F.B., Abdukarimov A., Xudoyarov B.A. Vychislitelniye tekhnologii — Computing Technologies, 2007, vol. 12, no. 4, pp. 17–26.
[7] Marynowski K. Journal of theoretical and applied mechanics, 2002, vol. 40, no. 2, pp. 465–481.
[8] Gorokhova I.V. Matematicheskiye zametki — Mathematical notes, 2011, vol. 89, no. 6, pp. 825–832.
[9] Dimitriyenko Yu.I., Gubareva E.A., Sborschikov S.V. Matematicheskoye modelirovaniye i chislenniye metody — Mathematical Modeling and Computational Methods, 2014, no. 2, pp. 28–48.
[10]Filippov I.G., Cheban V. G. Matematicheskaya teoriya kolebaniy uprugikh i vyazkouprugikh plastin i sterzhney [Mathematical theory of vibrations of elastic and viscoelastic plates and bars]. Kishinev, Shtiintsa Publ., 1988, 190 p.
[11]Khudoynazarov Kh.Kh. Nestatsionarnoye vzaimodeystviye tsylindricheskikh obolochek i sterzhney s deformiruyemoy sredoy [Non-stationary interaction of cylindrical shells and bars with deformable medium]. Tashkent, Abu Ali ibn Sino Publ., 2003, 326 p.
[12]Guz A.N., Kubenko V.D., Cherevko M.A. Difraktsiya uprugikh voln [Diffraction of elastic waves]. Kiyev, Naukova Dumka Publ., 1973, 308 p.
[13]Sneddon I. Preobrazovaniye Furye [Fourier transforms]. Moscow, Inostrannaya Literatura Publ., 1955, 667 p.
[14]Koltunov M.A. Polzuchest i relaksatsiya [Creep and relaxation]. Moscow, Visshaya Shkola Publ., 1976, 276 p.
[15]Formalyov V.F., Reviznikov D.L. Chislennyye metody [Numerical methods]. Moscow, Fizmatlit Publ., 2004, 400 p.


Khudoynazarov K., Abdirashidov A., Burkutboyev . Torsional vibrations of the viscoelastic round bar rotating with the constant angular velocity. Маthematical Modeling and Coтputational Methods, 2016, №1 (9), pp. 38-51



Download article

Колличество скачиваний: 244