Skip to main content
SpringerLink
Log in

Models of Spatial and Planar Light Bar Structures in the Maple System

  • Conference paper
  • First Online:
International Scientific Siberian Transport Forum TransSiberia - 2021 (TransSiberia 2021)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 403))

Included in the following conference series:

  • 666 Accesses

Abstract

Models of planar and spatial statically determinate regular trusses and analytical solutions of the problem of calculating natural frequencies are considered. A beam planar truss with triangular lattice, planar and spatial cantilever trusses are considered. To calculate the forces in the elements of the structure and calculate the rigidity of the structure in an analytical form, the computer mathematics system Maple was used. The dependence of the solutions on the number of panels was found by the induction method. To do this, we looked for common members of the sequences of coefficients included in solutions for trusses with a sequentially increasing number of panels. An algorithm for calculating the estimate of the first frequency by Dunkerley is given. In the spectra of eigenfrequencies of regular structures, frequencies are found that are the same for structures of any order (spectral constants) and frequencies with the same number in ordered spectra, forming curves in the axes “frequency number in the spectrum - order of construction” curves tending to spectral constants.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 219.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 279.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Popova, M., Sergeev, M., Lukina, A., et al.: Strength and deformability of lightweight metal trusses with elements from cut I-beams. In: IOP Conference Series: Materials Science and Engineering, vol. 896, no. 1, p. 012061 (2020). https://doi.org/10.1088/1757-899X/896/1/012061

  2. Itam, Z., Beddu, S., Mohd Kamal, N.L., et al.: Finite element analysis of the maximum stress at the joints of the transmission tower. In: IOP Conference Series: Earth and Environmental Science, vol. 32, no. 1, p. 012044 (2016). https://doi.org/10.1088/1755-1315/32/1/012044

  3. Cao, L., Li, J., Zheng, X., et al.: Vibration behavior of large span composite steel bar truss-reinforced concrete floor due to human activity. Steel Compos. Struct. 37(4), 391–404 (2020). https://doi.org/10.12989/scs.2020.37.4.391

  4. Hoseini Vaez, S.R., Mehanpour, H., Fathali, M.A.: Reliability assessment of truss structures with natural frequency constraints using metaheuristic algorithms. J. Build. Eng. 28, 101065 (2020). https://doi.org/10.1016/j.jobe.2019.101065

  5. Huang, J., Losa, M., Leandri, P., et al.: Potential anti-vibration pavements with damping layer: finite element (FE) modeling, validation, and parametrical studies. Constr. Build. Mater. 281, 122550 (2021). https://doi.org/10.1016/j.conbuildmat.2021.122550

  6. Khodzhaev, D., Abdikarimov, R., Vatin, N.: Nonlinear oscillations of a viscoelastic cylindrical panel with concentrated masses. In: MATEC Web of Conferences, vol. 245, p. 01001 (2018). https://doi.org/10.1051/matecconf/201824501001

  7. Ufimtcev, E.: Dynamic calculation of nonlinear oscillations of flat trusses Part 2: examples of calculations. Procedia Eng. 206, 850–856 (2017). https://doi.org/10.1016/j.proeng.2017.10.562

    Article  Google Scholar 

  8. Hutchinson, R.G., Fleck, N.A.: The structural performance of the periodic truss. J. Mech. Phys. Solids 54(4), 756–782 (2006). https://doi.org/10.1016/j.jmps.2005.10.008

    Article  MathSciNet  MATH  Google Scholar 

  9. Hutchinson, R.G., Fleck, N.A.: Microarchitectured cellular solids - The hunt for statically determinate periodic trusses. ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik 85(9), 607–617 (2005). https://doi.org/10.1002/zamm.200410208

    Article  MathSciNet  MATH  Google Scholar 

  10. Zok, F.W., Latture, R.M., Begley, M.R.: Periodic truss structures. J. Mech. Phys. Solids 96, 184–203 (2016). https://doi.org/10.1016/j.jmps.2016.07.007

    Article  Google Scholar 

  11. Petrenko, V.F.: The natural frequency of a two-span truss, taking into account the stiffness of the supports. AlfaBuild 20(2001). https://doi.org/10.34910/ALF.20.1

  12. Dai, Q.: Analytical dependence of planar truss deformations on the number of panels. AlfaBuild 17(1701) (2021). https://doi.org/10.34910/ALF.17.1

  13. Zotos, K.: Performance comparison of Maple and Mathematica. Appl. Math. Comput. 188(2), 1426–1429 (2007). https://doi.org/10.1016/j.amc.2006.11.008

    Article  MATH  Google Scholar 

  14. Rapp, B.E.: Introduction to Maple. Microfluidics: Modelling, Mechanics and Mathematics. Elsevier, Amsterdam (2017)

    Google Scholar 

  15. Zawidzki, M.: Retrofitting of pedestrian overpass by Truss-Z modular systems using graph-theory approach. Adv. Eng. Softw. 81(C), 41–49 (2015). https://doi.org/10.1016/j.advengsoft.2014.11.004

  16. Vorobev, O.V.: Bilateral analytical estimation of the first frequency of a plane truss. Constr. Unique Build. Struct. 92(7), 9204–9204 (2020). https://doi.org/10.18720/CUBS.92.4

  17. Trainor, P.G.S., Shah, A.H., Popplewell, N.: Estimating the fundamental natural frequency of towers by Dunkerley’s method. J. Sound Vib. 109(2), 285–292 (1986). https://doi.org/10.1016/S0022-460X(86)80009-8

    Article  Google Scholar 

  18. Low, K.H.: Modified Dunkerley formula for eigenfrequencies of beams carrying concentrated masses. Int. J. Mech. Sci. 42(7), 1287–1305 (2000). https://doi.org/10.1016/S0020-7403(99)00049-1

    Article  MATH  Google Scholar 

  19. Kirsanov, M., Serdjuks, D., Buka-Vaivade, K.: Analytical expression of the dependence of the multi-lattice truss deflection on the number of panels. Constr. Unique Build. Struct. 90, 9003 (2020). https://doi.org/10.18720/CUBS.90.3

  20. Kirsanov, M.N.: Analytical assessment of the frequency of natural vibrations of a truss with an arbitrary number of panels. Struct. Mech. Eng. Constr. Build. 16(5), 351–360 (2020). https://doi.org/10.22363/1815-5235-2020-16-5-351-360

  21. Kirsanov, M.N., Vorobev, O.V.: Calculating of a spatial cantilever truss natural vibration frequency with an arbitrary number of panels: analytical solution. Constr. Unique Build. Struct. 94(1), 9402 (2021). https://doi.org/10.4123/CUBS.94.2

    Article  Google Scholar 

  22. Kirsanov, M.N., Qiao, D.: Dependence of the natural oscillation frequency of the half-tilt console on the number of panels. Struct. Mech. Struct. 28(1), 39–44 (2021)

    Google Scholar 

Download references

Acknowledgements

The research is partially funded by the Ministry of Science and Higher Education of the Russian Federation under the strategic academic leadership program ‘Priority 2030’ (Agreement 075-15-2021-1333 dated 30.09.2021).

Author information

Authors and Affiliations

  1. Peter the Great St. Petersburg Polytechnic University, 195251, St. Petersburg, Russia

    Mikhail Kirsanov

  2. Institute of Structural Engineering and Reconstruction, Riga Technical University, Kipsalas Street, 6A/6B, Riga, 1048, Latvia

    Karina Buka-Vaivade

  3. NRU “MPEI”, Krasnokazarmennya Street, 14, 111250, Moscow, Russia

    Alexander Shirokov

Authors
  1. Mikhail Kirsanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karina Buka-Vaivade
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alexander Shirokov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Rector of the Siberian Transport University, Siberian Transport University, Novosibirsk, Russia

    Aleksey Manakov

  2. Far Eastern State Transport University, Ulitsa, Khabarovsk Territory, Russia

    Arkadii Edigarian

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kirsanov, M., Buka-Vaivade, K., Shirokov, A. (2022). Models of Spatial and Planar Light Bar Structures in the Maple System. In: Manakov, A., Edigarian, A. (eds) International Scientific Siberian Transport Forum TransSiberia - 2021. TransSiberia 2021. Lecture Notes in Networks and Systems, vol 403. Springer, Cham. https://doi.org/10.1007/978-3-030-96383-5_133

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-96383-5_133

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-96382-8

  • Online ISBN: 978-3-030-96383-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation