Variant Design of Girder-Slab Structure with Different Geometric Cells Under Flexural Vibrations


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Abstract

Girder-slab structures are widely used in industrial buildings, bridge decks, complex combined engineering structures and other objects of construction and mechanical engineering. An important task in their design is to find the most economical structural solution with the least amount of material while ensuring the necessary strength and rigidity. Therefore, the development of methods and algorithms for searching of the most rational and optimal design solutions is of great significance. The authors offer a technique of variant design of girder-slab structures with various cell shapes: rectangular, triangular, rhombic, trapezoidal and other, when analyzing vibrations. The technique is based on the principles of physicomechanical analogies and geometrical methods of structural mechanics. For a numerical example, a cantilever girder-slab structure on trapezoidal base is studied. The bars are of typical sections, the flooring is smooth steel. It is shown that cell geometry affects flexural vibrations of the girder-slab structure and material consumption.

About the authors

Andrey A. Chernyaev

Orel State University named after I.S. Turgenev

Author for correspondence.
Email: chernyev87@yandex.ru
ORCID iD: 0000-0002-0158-7056
SPIN-code: 4803-8464

Candidate of Technical Sciences, Associate Professor of the Department of Industrial and Civil Engineering

95 Komsomolskaya St, Orel, 302026, Russian Federation

Kirill V. Marfin

Orel State University named after I.S. Turgenev

Email: marfinkirill@yandex.ru
ORCID iD: 0000-0001-7646-1258
SPIN-code: 5146-0715

Candidate of Technical Sciences, Associate Professor of the Department of Building Structures and Materials

95 Komsomolskaya St, Orel, 302026, Russian Federation

References

  1. Rees D.W.A. Mechanics of optimal structural design: Minimum weight structures. Uxbridge: A John Wiley & Sons Ltd.; 2009. https://doi.org/10.1002/9780470749784
  2. Pavlov V.P., Kudoyarova V.M., Nusratullina L.R. Eigenfrequency spectrum analysis of bending vibrations for naturally swirled rod. IOP Conference Series Materials Science and Engineering. 2020;709(2):022059. https://doi.org/10.1088/1757-899X/709/2/022059 EDN: SFMDZZ
  3. Mazilu T., Dumitriu M., Sorohan S., Gheti M.A., Apostol I.I. Testing the effectiveness of the anti-bending bar system to reduce the vertical bending vibrations of the railway vehicle carbody using an experimental scale demonstrator. Applied Sciences. 2024;14(11):4687. https://doi.org/10.3390/app14114687 EDN: NECUOI
  4. Zak A., Krawczuk M. Certain numerical issues of wave propagation modelling in rods by the spectral finite element method. Finite Elements in Analysis and Design. 2011;47(9):1036-1046. https://doi.org/10.1016/j.finel.2011.03.019
  5. Serpik I.N., Shvyryaev M.V. Finite element modeling of operation for thin-walled open cross section bars to analyze plate-rod systems. Russian Aeronautics. 2017;60(1):34-43. https://doi.org/10.3103/S1068799817010068 EDN: XMZQHR
  6. Dmitrieva T. Algorithm of numerical optimization of steel structures on basis of minimum weight criterion. MATEC Web of Conferences. 2018;1212:01024. https://doi.org/10.1051/matecconf/201821201024 EDN: NFHAYZ
  7. Zvorygina S.V., Viktorova O.L. Determination of rational geometrical parameters of spatial plate-core systems using adaptive method. Regional architecture and engineering. 2019;38(1):105-111. (In Russ.) EDN: MDXKBD
  8. Simões T.M., Ribeiro P., António C.C. Maximisation of bending and membrane frequencies of vibration of variable stiffness composite laminated plates by a genetic algorithm. Journal of Vibration Engineering and Technologies. 2023;12: https://doi.org/10.1007/s42417-023-01022-3 EDN: VGZFEJ
  9. Poshyvach D., Lukianchenko O. Research of stochastic stability of constructions parametric vibrations by the MonteCarlo method. Strength of Materials and Theory of Structures. 2024:(112):32-331. https://doi.org/10.32347/2410-2547.2024. 112.327-331 EDN: NAGQPV
  10. Dmitrieva T.L., Ulambayar Kh. Algorithm for building structures optimization based on Lagrangian functions. Magazine of Civil Engineering. 2022;109(1):10910. https://doi.org/10.34910/MCE.109.10 EDN: DEHQHE
  11. Korobko V.I., Korobko A.V. Quantification of symmetry. Moscow: ASV Publ.; 2008. (In Russ.) ISBN 978-5-93093-544-8
  12. Korobko A.V., Prokurov M.Yu. Automated calculation of form factor of simply connected plane domains with convex polygonal contour. Building and Reconstruction. 2016;6(68):29-40. (In Russ.) EDN: XBKCAN
  13. Pólya G., Szegö G. Isoperimetric inequalities in mathematical physics. Princeton, New Jersey: Princeton Univ. Press.; 1951. ISBN: 1400882664, 9781400882663
  14. Chernyaev A.A. Construction of algorithms and development of computer programs in design variant plate-core power structures of conditions by reinforcement plate geometric modeling form. International Journal for Computational Civil and Structural Engineering, 2016;12(2):147-157. (In Russ.) EDN: WCYGAF
  15. Chernyaev A.A. Alternative engineering of steel girder cages by geometrical methods. Magazine of Civil Engineering. 2018;78(2):3-15. https://doi.org/10.18720/MCE.78.1 EDN: XPKZRB
  16. Chernyaev A.A. Geometric modeling of a shape of parallelogram plates in a problem of free vibrations using conformal Radii. Tomsk State University journal of mathematics and mechanics. 2021;(70):139-159. (In Russ.) https://doi.org/10.17223/19988621/70/12 EDN: ISHAER
  17. Kazantsev V.P., Zolotov O.A., Dolgopolova M.V. Electrostatics on the plane. Potential normalization. Capacities of the lonely conductor and the line concerning a point. Conformal radiuses. Bulletin of the Krasnoyarsk State University. Series: physical and mathematical sciences. 2005;(1):32-38. (In Russ.) EDN: KLNDRX
  18. Soninbayar J.A. Sequential method conformal mappings. Annals Of Mathematics And Physics. 2023;6(2):154-155. https://doi.org/10.17352/amp.000095 EDN: IBNACY
  19. Chernyayev A.A. Solving two-dimensional problems of the theory of elasticity and structural mechanics by interpolation using conformal radii. Structural mechanics and structures. 2017;2(15):32-44. (In Russ.) EDN: ZXMGSP
  20. Mazja V.G., Nazarov S.A. Paradoxes of limit passage in solutions of boundary value problems involving the approximation of smooth domains by polygonal domains. Mathematics of the USSR-Izvestiya. 1987;29(3):511-533. https://doi.org/10.1070/IM1987v029n03ABEH000981
  21. Korobko A.V., Chernyayev A.A. Determination of the fundamental frequency of free vibrations of plates using conformal radii. Building and Reconstruction. 2011;1(33):12-18. (In Russ.) EDN: OIJZKN
  22. Ibrahim S.M., Alsayed S., Abbas H. Carrera E., Al-Salloum Y., Almusallam T. Free vibration of tapered beams and plates based on unified beam theory. Journal of Vibration and Control. 2013;20(16):2450-2463. https://doi.org/10.1177/1077546312473766
  23. He X.C., Yang J.S., Mei G.X., Peng L.X. Bending and free vibration analyses of ribbed plates with a hole based on the FSDT meshless method. Engineering Structures. 2022;272(2):114914. https://doi.org/10.1016/j.engstruct.2022.114914 EDN: MQVIBS
  24. Eltaş S., Guler M.A., Tsavdaridis K.D., Sofias C., Yildirim B. On the beam-to-beam eccentric end plate connections: a Numerical Study. Thin-Walled Structures. 2023;188(2):110787. https://doi.org/10.1016/j.tws.2023.110787 EDN: MUPUYO
  25. Karpilovskiy V.S., Kriksunov E.Z., Malyarenko A.A., Fialko S.Yu., Perel’muter A.V., Perel’muter M.A. SCAD Office. Version 21. Moscow: SKAD SOFT Publ.; 2015. (In Russ.) Available from: https://djvu.online/file/msHDERp3z3XOE (accessed: 20.12.2024)

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