Formula for natural frequency oscillation truss with an arbitrary number of panels

Formula for natural frequency oscillation truss with an arbitrary number of panels

Автор: Kirsanov M.N.

Журнал: Строительство уникальных зданий и сооружений @unistroy

Статья в выпуске: 4 (109), 2023 года.

Бесплатный доступ

The object of research is the problem of the first frequency of free vibrations of a planar statically determinate regular beam truss with a mass uniformly distributed over the nodes.

Truss, induction, maple, fundamental frequency, dunkerley method, simplified solution, spectral constants, resonant safety regions

Короткий адрес: https://sciup.org/143182711

IDR: 143182711   |   DOI: 10.4123/CUBS.109.18

Список литературы Formula for natural frequency oscillation truss with an arbitrary number of panels

  • Colajanni, P., La Mendola, L., Latour, M., Monaco, A. and Rizzano, G. (2015) FEM Analysis of Push-out Test Response of Hybrid Steel Trussed Concrete Beams (HSTCBs). Journal of Constructional Steel Research, Elsevier, 111, 88–102. https://doi.org/10.1016/J.JCSR.2015.04.011.
  • Han, Q.H., Xu, Y., Lu, Y., Xu, J. and Zhao, Q.H. (2015) Failure Mechanism of Steel Arch Trusses: Shaking Table Testing and FEM Analysis. Engineering Structures, Elsevier, 82, 186–198. https://doi.org/10.1016/J.ENGSTRUCT.2014.10.013.
  • Zotos, K. (2007) Performance Comparison of Maple and Mathematica. Applied Mathematics and Computation, Elsevier, 188, 1426–1429. https://doi.org/10.1016/j.amc.2006.11.008.
  • Ignatiev, V.A. (1973) Calculation of Regular Rod Systems. Saratov Higher Military Chemical Military School, Saratov. https://elibrary.ru/item.asp?id=28958501.
  • Kaveh, A. (2013) Optimal Analysis of Structures by Concepts of Symmetry and Regularity. Optimal Analysis of Structures by Concepts of Symmetry and Regularity, Springer-Verlag Wien, 9783709115, 1–463. https://doi.org/10.1007/978-3-7091-1565-7.
  • Hutchinson, R.G. and Fleck, N.A. (2005) Microarchitectured Cellular Solids - The Hunt for Statically Determinate Periodic Trusses. ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 85, 607–617. https://doi.org/10.1002/zamm.200410208.
  • Hutchinson, R.G. and Fleck, N.A. (2006) The Structural Performance of the Periodic Truss. Journal of the Mechanics and Physics of Solids, Pergamon, 54, 756–782. https://doi.org/10.1016/j.jmps.2005.10.008.
  • Kirsanov, M. (2019) Planar Trusses: Schemes and Formulas. Cambridge Scholars Publishing Lady Stephenson Library, Newcastle upon Tyne, GB. https://www.cambridgescholars.com/product/978-1-5275-5976-9.
  • Levy, C. (1991) An Iterative Technique Based on the Dunkerley Method for Determining the Natural Frequencies of Vibrating Systems. Journal of Sound and Vibration, Academic Press, 150, 111–118. https://doi.org/10.1016/0022-460X(91)90405-9.
  • Low, K.H. (2000) A Modified Dunkerley Formula for Eigenfrequencies of Beams Carrying Concentrated Masses. International Journal of Mechanical Sciences, Pergamon, 42, 1287–1305. https://doi.org/10.1016/S0020-7403(99)00049-1.
  • Vorobev, O.V. (2020) Bilateral Analytical Estimation of the First Frequency of a Plane Truss. Construction of Unique Buildings and Structures, 92, 9204–9204. https://doi.org/10.18720/CUBS.92.4.
  • Kirsanov, M. and Ivanitskii, A. (2023) Bilateral Analytical Estimation of the Natural Oscillation Frequency of a Planar Triangular Truss. AlfaBuild, 26, 2601. https://doi.org/10.57728/ALF.26.1.
  • Kirsanov, M. (2023) Simplified Dunkerley Method for Estimating the First Oscillation Frequency of a Regular Truss. Construction of Unique Buildings and Structures, 108. https://doi.org/10.4123/CUBS.108.1.
  • Kirsanov, M.N. (2022) Energy Collocation Method for the Truss Fundamental Frequency Estimation. Structural mechanics and structures, 36, 27–37. https://doi.org/10.36622/VSTU.2023.36.1.003.
  • Galileev, S.M. and Matrosov, A. V. (1995) Method of Initial Functions in the Computation of Sandwich Plates. International Applied Mechanics, Kluwer Academic Publishers-Plenum Publishers, 31, 469–476. https://doi.org/10.1007/BF00846800.
  • Goloskokov, D.P. and Matrosov, A. V. (2016) A Superposition Method in the Analysis of an Isotropic Rectangle. Applied Mathematical Sciences, 10. https://doi.org/10.12988/ams.2016.67211.
  • Galishnikova V.V. (2019) Nonlinear Numerical Stability Analysis of Space Trusses. EG-ICE 2010 - 17th international workshop on intelligent computing in engineering. https://www.elibrary.ru/item.asp?id=43274656.
  • Komerzan, E. V., Maslov, A.N. (2023) Analytical Evaluation of a Regular Truss Natural Oscillations Fundamental Frequency. Structural Mechanics and Structures, 37, 17–26. https://doi.org/10.36622/VSTU.2023.37.2.002.
  • Komerzan, E. V., Maslov, A.N. (2023) Estimation of the L-Shaped Spatial Truss Fundamental Frequency Oscillations. Structural Mechanics and Structures, 37, 35–45. https://doi.org/10.36622/VSTU.2023.37.2.004.
  • Petrichenko, E.A. (2020) Lower Bound of the Natural Oscillation Frequency of the Fink Truss. Structural Mechanics and Structures, 26, 21–29. https://www.elibrary.ru/item.asp?id=44110287.
  • Dai, Q. (2021) Analytical Dependence of Planar Truss Deformations on the Number of Panels. AlfaBuild, 17, 1701. https://doi.org/10.34910/ALF.17.1.
  • Petrenko, V.F. (2021) The Natural Frequency of a Two-Span Truss. AlfaBuild, 2001. https://doi.org/10.34910/ALF.20.1.
  • Manukalo, A.S. (2023) Analysis of a Planar Sprengel Truss First Frequency Natural Oscillations Value. Structural Mechanics and Structures, 37, 54–60. https://doi.org/10.36622/VSTU.2023.37.2.006.
  • Buka-Vaivade, K., Kirsanov, M.N. and Serdjuks, D.O. (2020) Calculation of Deformations of a Cantilever-Frame Planar Truss Model with an Arbitrary Number of Panels. Vestnik MGSU, 4, 510–517. https://doi.org/10.22227/1997-0935.2020.4.510-517.
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