STUDYING DYNAMICS OF A CANTILEVER BAR WITH VARIABLE BENDING STIFFNESS
DOI:
https://doi.org/10.26577/JMMCS2023v119i3a7Keywords:
triangular plate, numerical method, grid method, dynamic deflections and forces, variable bending stiffness, bar analogy, frequency spectrum, amplitude-frequency characteristicsAbstract
In this paper, there are studied the dynamic processes (free and forced oscillations) of isotropic
cantilever plates in the form of an isosceles (wedge-shaped) triangle. In the study, the finite
difference method has been applied using a regular one-dimensional (linear) grid. The finite-
difference equations developed by the authors for point-distributed masses along the length of
the wedge are presented, taking into account the linearly variable bending stiffness. On this basis,
the results of studies in the form of amplitude-frequency characteristics (frequencies, dynamic
forces and deflections) in the resonant and near-resonant regions have been obtained. The content
of theoretical provisions and applied results can be widely used in the scientific and engineering
fields and in the field of mechanics of structures.
References
Bosakov S.V., Skachek P.D. Static calculation of triangular plates with hinged sides. Mechanics. Research and innovation, 2017, No. 10, pp. 24 - 28.
Akhmediev S.K., Zhakibekov M.E., Kurokhtina I.N. Nuguzhinov Zh.S. Numerical study of the stress-strain state of structures such as thin triangular plates and plates of medium thickness. Structural mechanics and calculation of structures, 2015, No. 2 (259), pp. 28 - 33.
Bosakov S.V., Skachek P.D. Application of the Ritz method in the calculations of triangular plates with different conditions of fastening to the action of a static load. Structural mechanics and calculation of structures, 2018, No. 5 (280), pp. 17 - 23.
Korobko A.V., Kalashnikova N.G., Abashin E.G. Transverse bending and free vibrations of elastic isotropic plates in the form of isosceles triangles. Construction and reconstruction, 2021, No. 6, pp. 20 – 27. https://doi.org/10.33979/2073-7416- 2021-98-6-20-27
Korobko A.V., Chernyaev A.A., Shlyakhov S.V. Application of the MICF method for calculating triangular and quadrangular plates using widely known geometric parameters. Construction and reconstruction, 2016, No. 4, pp. 19 - 28.
Akhmediev S.K. Analytical and numerical methods for calculating machine-building and transport constructions and structures (textbook). Karaganda, KarTU, 2016, 158 p.
Akhmediev S.K., Khabidolda О., Vatin N.I., Yessenbayeva G.A., Muratkhan R. Physical and mechanical state of cantilever triangular plates. JMMCS. 2023 N2 (118). Рр. 64-73. DOI: https://doi.org/10.26577/JMMCS.2023.v118.i2.07
Timoshenko S.P., Voinovsky-Kriger S. Plates and shells. M.: 1963. 635 p.
Reference Book on the Theory of Elasticity. Kiev: Publishing House Budivelnik: 1971. 419 p.
Konczkowski Z. Slabs. Static calculations: translation from Polish. - Moscow: Stroyizdat, 1984. 480p.
Leibenzon L.S. Variation methods for solving problems in the theory of elasticity - Moscow; Leningrad: 1943. 287 p.
Pratusevich Y.A. Variation methods in structural mechanics - Moscow; Leningrad: Gosizdat tekhnikotheoreticheskoy literatury. 1948. 399 p.
Weinberg D.V., Weinberg E.D. Plates, disks, beams. Kyiv: Gosstroyizdat of the Ukrainian SSR, 1959. 1049 p.
Maslennikov A.M. Calculation of Building Structures by Numerical Methods - L: Publishing House of Leningrad University, 1987. 224 p.
Gontkevich V.S. Natural vibrations of plates and shells: Reference book. Kiev: Naukova Dumka, 1964. 288 p.
Bosakov S.V., Skachok P.D. Static calculation of triangular plates with hinged faces. // Mechanics. Research and Innovations. Issue 10, Gomel. 2017. Рp. 24-28.
Bosakov S.V. Ritz Method in Examples and Problems in Structural Mechanics and Theory of Elasticity: Textbook for Students of Building Specialties of Higher Education Institutions. Minsk: publishing house of Belarusian State Pedagogical University, 2000. 142 p.
Korobko A.V. Geometrical modeling of area shape in two-dimensional problems of the theory of elasticity. Moscow: Publishing house ASV, 1999. 302 p.
Kobko V.I., Savin S.Y. Free vibrations of triangular orthotropic plates with uniform and combined boundary conditions // Building and Reconstruction. 2013. No 2. P. 33-40.
Korobko V.I., Savin S.Y., Boyarkina S.V. Bending of triangular orthotropic plates with uniform and combined boundary conditions // Construction and reconstruction. Orel: GU-UNPK. 2012. No1. P. 7-13.
Lalin V.V., Beliaev M.O. Bending of geometrically nonlinear cantilever beam. Results obtained by Cosserat – Timoshenko and Kirchhoff’s rod theories // Magazine of Civil Engineering. 2015. 1(153). Рр. 39-55. DOI: 10.5862/MCE.53.5.
A.V. Indeikin Dynamic stability of eccentrically compressed thin-walled rods of metal structures // Transport, industrial and civil construction. Izvestiya PGUPS. 2008, No. 4. Pp. 24-35.
A.V. Indeikin Bar elements of building structures under the action of stationary and moving dynamic loads // Transport,
industrial and civil construction Proceedings of PGUPS 2014. No. 2. Pp. 92-84.
Mishchenko A.V. Dynamic Analysis of Composite Bar Systems under the Kinematic Influence. Bulletin of the South Ural State University. Ser. Construction Engineering and Architecture. 2015, vol. 15, No. 3. Pp. 5-10.
Karamansky T.D. Numerical methods of structural mechanics; Ed. G. K. Klein. M.: Stroyizdat, 1981. 436 p.
Varvak P.M., Varvak L.P. Method of sets in problems of calculation of building structures. - M.: Stroyzdat, 1971. 154 p.
Akhmediyev S.K., Filippova T.S., Oryntayeva G.Zh., Donenbayev B.S. Analytical and numerical methods for calculating machine-building and transport structures and structures. Karaganda: Publishing House of KSTU. 2016. 158 p.
