Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2016-3pp.263-272

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212

<< Previous article | Volume 51, Issue 3 / 2016 | Next article >>
A.K. Belyaev, N.F. Morozov, P.E. Tovstik, and T.P. Tovstik, "Buckling Problem for a Rod Longitudinally Compressed by a Force Smaller Than the Euler Critical Force," Mech. Solids. 51 (3), 263-272 (2016)
Year 2016 Volume 51 Number 3 Pages 263-272
DOI 10.3103/S0025654416030031
Title Buckling Problem for a Rod Longitudinally Compressed by a Force Smaller Than the Euler Critical Force
Author(s) A.K. Belyaev (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol'shoy pr. 61, St. Petersburg, 199078 Russia, vice.ipme@gmail.ru)
N.F. Morozov (Saint-Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034 Russia, morozov@nm1016.spb.edu)
P.E. Tovstik (Saint-Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034 Russia, peter.tovstik@mail.ru)
T.P. Tovstik (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol'shoy pr. 61, St. Petersburg, 199078 Russia, tovstik_t@mail.ru)
Abstract It was earlier shown that a rod can buckle under the action of a sudden longitudinal load smaller than the Euler critical load. The buckling mechanism is related to excitation of periodic longitudinal waves generated in the rod by the sudden loading, which in turn lead to transverse parametric resonances. In the linear approximation, the transverse vibration amplitude increases unboundedly, and in the geometrically nonlinear approach, beats with energy exchange from longitudinal to transverse vibrations and back can arise. In this case, the transverse vibration amplitude can be significant. In the present paper, we study how this amplitude responds to the following two factors: the smoothness of application of the longitudinal force and the internal friction forces in the rod material.
Keywords rod, longitudinal impact, lateral bending, parametric resonance
References
1.  L. Euler, Method for Determining Curves with the Maximum or Minimum Property GTTI, Moscow-Leningrad, 1934) [in Russian].
2.  Ya. G. Panovko and I. I. Gubanova, Stability and Vibrations of Elastic Systems (Nauka, Moscow, 1987) [in Russian].
3.  M. A. Lavrentiev and A. Yu. Ishlinskii, "Dynamic Buckling Modes of Elastic Systems," Dokl. Akad. Nauk SSSR 64 (6), 776-782 (1949).
4.  A. S. Volmir, "Stability of Compressed Rods under Dynamic Loading," Stroit. Mekh. Rashch. Sooruzh., No. 1, 6-9 (1960).
5.  V. V. Bolotin, Transverse Vibrations and Critical Velocities, Vols. 1 and 2 (Izdat. AN SSSR, Moscow, 1951, 1953) [in Russian].
6.  N. F. Morozov and P. E. Tovstik, "Dynamics of a Rod on Longitudinal Impact," Vestnik St. Peterzburg. Univ. Ser. I. Mat. Mekh. Astr. No. 2, 105-111 (2009).
7.  A. K. Belyaev, D. N. Il'in, and N. F. Morozov "Dynamic Approach to the Ishlinsky-Lavrent'ev Problem," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 28-33 (2013) [Mech. Solids (Engl. Transl.) 48 (5), 504-508 (2013)].
8.  N. F. Morozov and P. E. Tovstik, "Dynamics of a Rod on Short-Time Longitudinal Impact," Vestnik St. Peterzburg. Univ. Ser. I. Mat. Mekh. Astr. No. 3, 131-141 (2013).
9.  N. F. Morozov and P. E. Tovstik, "Transverse Rod Vibrations under a Short-Term Longitudinal Impact," Dokl. Ross. Akad. Nauk 452 (1), 37-41 (2013) [Dokl. Phys. (Engl. Transl.) 58 (9), 387-391 (2013)].
10.  N. F. Morozov, P. E. Tovstik, and T. P. Tovstik, "Statics and Dynamics of a Rod under Longitudinal Loading," Vestnik Yuzhno-Ural Univ. Ser. Mat. Model. Progr. 7 (1), 76-89 (2014).
11.  N. F. Morozov, P. E. Tovstik, and T. P. Tovstik, "More on the Ishlinskii-Lavrentyev Problem," Dokl. Ross. Akad. Nauk 455 (4), 412-415 (2014) [Dokl. Phys. (Engl. Transl.) 59 (4), 189-192 (2014)].
12.  N. F. Morozov and P. E. Tovstik, "Dynamic Buckling of a Rod under Longitudinal Load Lower Than the Eulerian Load," Dokl. Ross. Akad. Nauk 453 (3), 282-285 (2014) [Dokl. Phys. (Engl. Transl.) 58 (11), 510-513 (2013)].
13.  A. K. Belyaev, N. F. Morozov, P. E. Tovstik, and T. P. Tovstik "Beating in the Problem of Longitudinal Impact on a Thin Rod," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 104-117 (2015) [Mech. Solids (Engl. Transl.) 50 (4), 451-462 (2015)].
14.  V. A. Palmov, Vibrations of Elastoplastic Bodies (Nauka, Moscow, 1976) [in Russian].
15.  A. M. Lyapunov, General Problem of Stability of Motion (GosTekhIzdat., Moscow, 1950) [in Russian].
16.  V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients and Their Applications (Nauka, Moscow, 1972) [in Russian].
17.  T. Hayashi, Forced Vibrations in Nonlinear Systems (Izdat. Inostr. Lit., Moscow, 1964) [in Russian].
18.  N. N. Bogolyubov and Yu. A. Mitropolskii, Asymptotic Methods in Theory of Nonlinear Vibrations (Nauka, Moscow, 1969) [in Russian].
Received 11 October 2015
Link to Fulltext
<< Previous article | Volume 51, Issue 3 / 2016 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100