Free Vibrations of Thin-Walled Box-Section Bars Allowing for Shear Strains

  • Authors

    • Aleksandr Gavrilov
    • Grigoriy Grebenyuk
    • Nikolay Morozov
    • Andrey Grehov
    2018-04-15
    https://doi.org/10.14419/ijet.v7i2.13.11570
  • thin-walled bar, free vibrations, warping, vibration frequency.

  • Purpose. The purpose is to study free vibrations of thin-walled bar with combined bisymmetrical section allowing for the effects of shear strains.

    Methods. We used the main hypothesis of V.Z. Vlasov concerning thin-walled bars. Solving motion equations analytically, we used the method of initial parameters and the known methods for differential equations solution. In the natural experiment we applied Autodesk Inventor system. In the course of the natural experiment on shaker, we used the method of smooth change in the frequency of sinusoidal vibrations.

    Results. We provide the analytical solutions of the shapes and the natural frequencies of thin-walled bar with combined bisymmetrical section allowing for shears caused by bends and constrained torsion. We compared the results of the calculations conducted in CAE system and the results of the full-scale experiment to determine the frequencies of vibrations of box beam.

    Conclusions. The results showed that the analytical calculations are in good compliance with the results of numerical and physical experiments and can be used for dynamic calculations of thin-walled structural elements, in particular, for the prevention of the destruction of structures in the event of resonance phenomena.

     

     

  • References

    1. [1] Gunda J. B., Gupta R. K., Janardhan G. R., Rao G. V. Large amplitude free vibration analysis of Timoshenko beams using a relatively simple finite element formulation / // International Journal of Mechanical Sciences. – 2010. – vol. 52. – no. 12. P. 1597–1604.

      [2] Ambrosini D. Experimental validation of free vibrations from nonsymmetrical thin walled beams // Engineering Structures. – 2010. – vol. 32. – no. 5. – P. 1324–1332.

      [3] Ambrosini D. On free vibration of nonsymmetrical thin-walled beams // Thin-Walled Structures. – 2009. – vol. 47. – no. 6-7. P. 629–636.

      [4] Tanaka M., Bercin A. N. Free vibration solution for uniform beams of nonsymmetrical cross section using Mathematica // Computers and Structures. – 1999. – vol. 71. – no. 1. – P. 1–8.

      [5] Giunta G., Belouettar S. Higher-Order Hierarchical Models for the Free Vibration Analysis of Thin-Walled Beams // Hindawi Publishing Corporation Mathematical Problems in Engineering Volume. – 2015. Access: http://dx.doi.org/10.1155/2015/940347

      [6] Akulenko L.D., NesterovS.V Anomalous dependence of the vibration frequencies of a rod in an elastic medium on the rod length // Mechanics of solids. – 2010. – vol. 45. – no. 2. P. 257-263.

      [7] Attarnejad R., Semnani S.J., Shahba A. Basic displacement functions for free vibration analysis of non-prismatic Timoshenko beams // Finite Elements in Analysis and Design. – 2010. – vol. 46. – no. 10. P. 916–929.

      [8] Chernov S. A. Thin-walled bar system dynamics tasks modeling // Software products and systems. – 2014. – number 106. P. 171 –176.

      [9] Beilin, E. A. Elements of the torsion theory of thin-walled bars of arbitrary profile [text] / E. A. Beilin. – SPSUACE Press- 2003. 113 p.

      [10] Khosravi M., Mosaddeghi F., Oveisi, M., khodayari-b, A., Aerodynamic drag reduction of heavy vehicles using append devices by CFD analysis, Journal of Central South University, Volume 22, 2015, pp 4645–4652.

      [11] Grebenyuk G. I., Gavrilov A. A., Yankov E. V. Calculation and optimization of continuous beam with thin–walled profile // Proceedings of the higher educational institutions. Building. – 2013. – number 7 (655) P. 3–11.

      [12] Seyedhosseini, S. M., Esfahani, M. J., & Ghaffari, M. A novel hybrid algorithm based on a harmony search and artificial bee colony for solving a portfolio optimization problem using a mean-semi variance approach. Journal of Central South University, 23(1), 2016, 181-188.

      [13] Gavrilov A. A., Kudina L. I., Kucha G. V., Morozov N. A. Influence of geometrical characteristics of sections on the frequency values of the free flexural vibrations of thin-walled straight bars // Bulletin of Orenburg State University. – 2011. – number 5 (124) P. 146–150.

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    Gavrilov, A., Grebenyuk, G., Morozov, N., & Grehov, A. (2018). Free Vibrations of Thin-Walled Box-Section Bars Allowing for Shear Strains. International Journal of Engineering & Technology, 7(2.13), 7-12. https://doi.org/10.14419/ijet.v7i2.13.11570