The first natural frequency and deflection of a two-hinged truss arch

Строительные конструкции, здания и сооружения
Авторы:
Kirsanov, Mikhail Nikolaevich
Аннотация:

The object of research is a statically determinate model of a planar, regular, arched truss on two fixed, hinged supports. Using the induction method in a computer mathematics system, calculation formulas for the structure's deflection under a uniform vertical nodal load on the lower or upper chord are derived. An approximate analytical dependence of the truss's first natural frequency of oscillation on the number of panels is found. The forces in the rods are calculated for an arbitrary number of panels. Method. The truss's inertial properties are modeled using concentrated masses at the nodes. The truss's natural frequency of oscillation is calculated using the Dunkerley method and its simplified version. Vertical node oscillations are assumed. Results. A comparison of the analytical calculations with numerical results, performed taking into account all degrees of freedom of vertical mass oscillations, shows good agreement between the methods.

Ключевые слова:
Arched trussFundamental frequencyInductionDeflectionMapleDunkerley method
  • Список литературы

    1         Wu, Y., Cao, D., Liu, M., Li, Y. and Chen, Z. (2022) Natural Characteristic and Vibration Analysis of Nonlinear Articulated Multi-Beam Ring Structure for Modeling Ring Truss Antenna under Base Excitation. Applied Mathematical Modelling, 108, 787–806. https://doi.org/10.1016/J.APM.2022.04.027

    2         Embaby, M. and El Naggar, M.H. (2025) Experimental and Analytical Investigation for Modular Double Truss Bridge. Engineering Structures, 322, 119087. https://doi.org/10.1016/J.ENGSTRUCT.2024.119087

    3         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

    4         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

    5         Kirsanov, M. and Safronov, V. (2022) Analytical Estimation of the First Natural Frequency and Analysis of a Planar Regular Truss Oscillation Spectrum. Magazine of Civil Engineering, 111. https://doi.org/10.34910/MCE.111.14

    6         Kirsanov, M. (2021) Model and Analytical Calculation of a Spatial Truss. Lecture Notes in Civil Engineering, 150 LNCE, 496–503. https://doi.org/10.1007/978-3-030-72404-7_48

    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

    8         Hutchinson, R.G. and Fleck, N.A. (2006) The Structural Performance of the Periodic Truss. Journal of the Mechanics and Physics of Solids, 54, 756–782. https://doi.org/10.1016/j.jmps.2005.10.008

    9         Kooshkbaghi, M. and Kaveh, A. (2020) Sizing Optimization of Truss Structures with Continuous Variables by Artificial Coronary Circulation System Algorithm. Iranian Journal of Science and Technology - Transactions of Civil Engineering, 44. https://doi.org/10.1007/s40996-019-00254-2

    10       Kaveh, A. (2013) Optimal Analysis of Structures by Concepts of Symmetry and Regularity. Optimal Analysis of Structures by Concepts of Symmetry and Regularity, 9783709115, 1–463. https://doi.org/10.1007/978-3-7091-1565-7

    11       Ignatyev, A. V. and Ignatyev, V.A. (2016) On the Efficiency of the Finite Element Method in the Form of the Classical Mixed Method. Procedia Engineering, 150, 1760–1765. https://doi.org/10.1016/J.PROENG.2016.07.167

    12       Galishnikova, V. (2010) Nonlinear Numerical Stability Analysis of Space Trusses. Geometrically Nonlinear Analysis of Plane Trusses and Frames. https://doi.org/10.18820/9781920109998.

    13       Goloskokov, D.P. and Matrosov, A. V. (2018) Approximate Analytical Approach in Analyzing an Orthotropic Rectangular Plate with a Crack. Materials Physics and Mechanics, 36, 137–141. https://doi.org/10.18720/MPM.3612018_15

    14       Goloskokov, D.P. (2014) Analyzing Simply Supported Plates Using Maple System. 2014 International Conference on Computer Technologies in Physical and Engineering Applications, ICCTPEA 2014 - Proceedings, Institute of Electrical and Electronics Engineers Inc., 55–56. https://doi.org/10.1109/ICCTPEA.2014.6893273

    15       Dai, Q. (2026) Derivation of a Formula for Calculating the First Frequency of Natural Oscillations of a Trapezoidal Truss. Structural Mechanics and Structures, 48, 55–62. https://doi.org/10.36622/2219-1038.2026.48.1.005

    16       Seleznev, K. (2025) Formula for the First Frequency of Natural Oscillations of a Flat Truss with an Arbitrary Number of Panels. Structural Mechanics and Structures, 46, 33–40. https://doi.org/10.36622/2219-1038.2025.46.3.004

    17       Seleznev, K. (2026) Formulas for the Deflection and First Frequency of Natural Oscillations of a Flat Truss with an Arbitrary Number of Panels. Structural Mechanics and Structures, 49, 71–79. https://doi.org/10.36622/2219-1038.2026.49.2.006

    18       Luong, C.L. (2024) Resonance Safety Zones of a Truss Structure with an Arbitrary Number of Panels. Construction of Unique Buildings and Structures, 114, 11304–11304. https://doi.org/10.4123/CUBS.113.4

    19       Maslov, A.N. (2023) The First Natural Frequency of a Planar Regular Truss. Analytical Solution. Construction of Unique Buildings and Structures, 110, 10912–10912. https://doi.org/10.4123/CUBS.109.12

    20       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

    21       Petrenko, V.F. (2021) The Natural Frequency of a Two-Span Truss. AlfaBuild, 2001. https://doi.org/10.34910/ALF.20.1

    22       Degertekin, S.O., Yalcin Bayar, G. and Lamberti, L. (2021) Parameter Free Jaya Algorithm for Truss Sizing-Layout Optimization under Natural Frequency Constraints. Computers and Structures, 245, 106461. https://doi.org/10.1016/j.compstruc.2020.106461

    23       Tyukalov, Y. (2020) Optimal Shape of Arch Concrete Block Bridge. Construction of Unique Buildings and Structures, 93, 9307. https://doi.org/10.18720/CUBS.93.7

    24       Marutyan, A., Abovyan, A. and Kravchenko, A. (2023) Optimization of the Assembly of Cross-Truss Structures. E3S Web of Conferences, 410. https://doi.org/10.1051/E3SCONF/202341004003

    25       Tinkov, D. V. and Safonov, A.A. (2017) Design Optimization of Truss Bridge Structures of Composite Materials. Journal of Machinery Manufacture and Reliability, 46, 46–52. https://doi.org/10.3103/S1052618817010149

    26       Tinkov, D. V. (2016) The Optimum Geometry of the Flat Diagonal Truss Taking into Account the Linear Creep. Magazine of Civil Engineering, 61, 25–32. https://doi.org/10.5862/MCE.61.3

    27       Luong, C.L. (2024) Dependence of the Region of Resonantly Safe Frequencies on the Dimensions of a Statically Determinate Flat Truss. Structural Mechanics and Structures, 41, 16–26. https://doi.org/10.36622/2219-1038.2024.41.2.002

    28       Gribova O.V. (2025) Formulas for Calculating the Deflection and Natural Frequency of a Flat Truss with an Arbitrary Number of Panels. Structural Mechanics and Structures, 44, 31–39. https://doi.org/10.36622/2219-1038.2025.44.1.003

    29       Komerzan E. V., Ninalalov I. G., Sviridenko O. V. (2023) Calculation of the Fundamental Frequency of Natural Oscillations of a Planar Model of a Composite Truss. Structural Mechanics and Structures, 39, 27–34. https://doi.org/10.36622/VSTU.2023.39.4.003

    30       Efimchuk A.V. (2025) Analytical Derivation of the Formula for the First Frequency of Oscillations of a Hinge-Rod Structure. Structural Mechanics and Structures, 46, 25–32. https://doi.org/10.36622/2219-1038.2025.46.3.003

    31       Astakhov, S.V. (2024) Analytical Assessment of the Deflection of the Rod Model of a Four-Slope Roof Frame. Structural mechanics and structures, 43, 34–41. https://doi.org/10.36622/2219-1038.2024.43.4.003

    32       Kirsanov, M.N. (2023) Deformations of a Three-Dimensional Model of a Trihedral Double Lattice Rod Tower. Vestnik MGSU. Monthly Journal on Construction and Architecture, 18, 1032–1038. https://doi.org/10.22227/1997-0935.2023.7.1032-1038

    33       Kirsanov, M.N. and Luong, C.L. (2024) Simplified Method for Estimating the First Natural Frequency of a Symmetric Arch Truss. Magazine of Civil Engineering., 17, 13001. https://doi.org/10.34910/MCE.130.1

    34       Kirsanov, M.N. (2024) Formulas for Calculating Deformations and Natural Frequency of Free Vibrations of a Hexagonal Tower. Russian Journal of Building Construction and Architecture, 1, 101–109. https://doi.org/10.36622/VSTU.2024.61.1.009

    35       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

     

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Предыдущая статья