Modeling a Viscoelastic Support Considering Its Mass-Inertial Characteristics During Non-Stationary Vibrations of the Beam | Journal of Engineering Sciences

Modeling a Viscoelastic Support Considering Its Mass-Inertial Characteristics During Non-Stationary Vibrations of the Beam

Author(s): Voropay A. V.1*, Menshykov O. V.2, Povaliaiev S. I.1, Sharapata A. S.1, Yehorov P. A.1

Affiliation(s):
1 Kharkiv National Automobile and Highway University, 25, Yaroslava Mudrogo St., 61002 Kharkiv, Ukraine;
2 School of Engineering, University of Aberdeen, AB243UE Scotland, United Kingdom

*Corresponding Author’s Address: [email protected]

Issue: Volume 10, Issue 1 (2023)

Dates:
Submitted: February 27, 2023
Received in revised form: May 10, 2023
Accepted for publication: May 16, 2023
Available online: May 19, 2023

Citation:
Voropay A. V., Menshykov O. V., Povaliaiev S. I., Sharapata A. S., Yehorov P. A. (2023). Modeling a viscoelastic support considering its mass-inertial characteristics during non-stationary vibrations of the beam. Journal of Engineering Sciences, Vol. 10(1), pp. D8-D14, doi: 10.21272/jes.2023.10(1).d2

DOI: 10.21272/jes.2023.10(1).d2

Research Area:  MECHANICAL ENGINEERING: Dynamics and Strength of Machines

Abstract. Non-stationary loading of a mechanical system consisting of a hinged beam and additional support installed in the beam span was studied using a model of the beam deformation based on the Timoshenko hypothesis with considering rotatory inertia and shear. The system of partial differential equations describing the beam deformation was solved by expanding the unknown functions in the Fourier series with subsequent application of the integral Laplace transform. The additional support was assumed to be realistic rather than rigid. Thus it has linearly elastic, viscous, and inertial components. This means that the effect of a part of the support vibrating with the beam was considered such that their displacements coincide. The beam and additional support reaction were replaced by an unknown concentrated external force applied to the beam. This unknown reaction was assumed to be time-dependent. The time law was determined by solving the first kind of Volterra integral equation. The methodology of deriving the integral equation for the unknown reaction was explained. Analytic formulae and results of computations for specific numerical parameters were given. The impact of the mass value on the additional viscoelastic support reaction and the beam deflection at arbitrary points were determined. The research results of this paper can be helpful for engineers in designing multi-span bridges.

Keywords: Timoshenko multi-span beam, additional viscoelastic support, non-stationary vibration, concentrated mass, Volterra integral equation.

References:

  1. Smetankina, N.V., Shupikov, A.N., Sotrikhin, S.Yu., Yareschenko, V.G. (2008). A noncanonically shape laminated plate subjected to impact loading: Theory and experiment. Journal of Applied Mechanics, Transactions ASME, Vol. 75, No 5. Pp. 051004-1–051004-9. https://doi.org/10.1115/1.2936925.
  2. Timoshenko, S. P. (1937). Vibration problems in engineering. D. Van Nostrand Company INC. 497 p.
  3. Filippov, A.P., Kokhmanyuk, S. S., Yanyutin, Ye. G. (1978). Deformation of structural elements under impact and impulse loads. Kyiv, Naukova dumka. 184 p.
  4. Freundlich, J. (2013). Vibrations of a Simply Supported Beam with a Fractional Viscoelastic Material Model – Supports Movement Excitation. Shock and Vibration, 20, Article ID 126735, https://doi.org/10.3233/SAV-130825.
  5. Qiao, G, Rahmatalla, S. (2019). Identification of the viscoelastic boundary conditions of Euler-Bernoulli beams using transmissibility. Engineering Reports, 1:e12074, https://doi.org/10.1002/eng2.12074.
  6. Kokhmanyuk, S. S., Yanyutin, Ye. G., Romanenko, L. G. (1980). Vibrations of deformable systems under pulse and moving loads. Naukova Dumka, Kyiv.
  7. Yanyutin, Ye. G., Gnatenko, G. O., Grishakin, V. T. (2007). Solving non-stationary direct and inverse problems for beams with additional elastic supports. Mashynoznavstvo, 8, pp. 18–23.
  8. Yanyutyn, Ye. G., Grishakin, V. T. (2008). Identification of mobile load for viscoelastic beams. Bulleting of the National Technical University “Kharkiv Polytechnic Institute”. 47, pp. 178–184.
  9. Borji, A., Movahedian, B., Boroomand, B. Implementation of time-weighted residual method for simulation of flexural waves in multi-span Timoshenko beams subjected to various types of external loads: from stationary loads to accelerating moving masses. (2022). Archive of Applied Mechanics, 92 (4), pp. https://doi.org/10.1007/s00419-021-02103-z.
  10. Dan Stancioiu, Huajiang Ouyang, John E. Mottershead, Simon James, Experimental investigations of a multi-span flexible structure subjected to moving masses, Journal of Sound and Vibration, Volume 330, Issue 9, 2011, Pages 2004-2016, ISSN 0022-460X, https://doi.org/10.1016/j.jsv.2010.11.011.
  11. Taehyun, K., Usik, L. (2017). Dynamic analysis of a multi-span beam subjected to a moving force using the frequency domain spectral element method. Computers & Structures. 192, pp. 181–195. https://doi.org/10.1016/j.compstruc.2017.07.028.
  12. Szyłko-Bigus, O., Śniady, P., Zakęś, F. (2019). Application of Volterra integral equations in the dynamics of a multi-span Rayleigh beam subjected to a moving load. Mechanical Systems and Signal Processing, Vol. 121, pp. 777-790, ISSN 0888-3270, https://doi.org/10.1016/j.ymssp.2018.11.056.
  13. Vesali, F., Rezvani, M.A., Shadfar, M. (2023). Attuned dynamic response of double track Multi-span railway bridges under the delayed entry of a second train. Journal of Vibration Engineering and Technologies. https://doi.org/10.1007/s42417-023-00884-x.
  14. Liu, S., Jiang, L., Zhou, W., Xilin, C., Zhang, Y. (2021). Dynamic response analysis of multi-span bridge-track structure system under moving loads. Mechanics Based Design of Structures and Machines.
  15. Zhao, Z., Wen, S., Li, F., Zhang, C. (2018). Free vibration analysis of multi-span Timoshenko beams using the assumed mode method. Archive of Applied Mechanics, Vol. 88, no. 7, pp. 1213–1228. https://doi.org/10.1007/s00419-018-1368-8.
  16. Cong Gao, Fuzhen Pang, Haichao Li, Hongfu Wang, Jie Cui, Jisi Huang. (2021). Free and Forced Vibration Characteristics Analysis of a Multispan Timoshenko Beam Based on the Ritz Method. Shock and Vibration, Vol. 2021, Article ID 4440250. https://doi.org/10.1155/2021/4440250.
  17. Chen, X., Zeng, X., Liu, X. and Rui, X. (2020). Transfer matrix method for the free and forced vibration analyses of multi-step Timoshenko beams coupled with rigid bodies on springs. Applied Mathematical Modelling, 87, pp. 152–170.
  18. Kantor, B.Ya., Smetankina, N.V., Shupikov, A. N. (2001) Analysis of non-stationary temperature fields in laminated strips and plates. International Journal of Solids and Structure. Vol. 38, No 48/49, pp. 8673-8684. https://doi.org/10.1016/S0020-7683(01)00099-3.
  19. Voropay, A.V., Povaliaiev, S.I., Yehorov, P.A. (2022) Simulation of intermediate viscoelastic support under non-stationary vibrations of Timoshenko beams. Bulletin of the National Technical University “KhPI”. Series: Mathematical modeling in engineering and technology, №1, pp. 36-44 (2022). https://doi.org/10.20998/2222-0631.2022.01.05.
  20. Voropay, A. V., Yegorov, P. A. (2020). The influence of mass and inertial characteristics of an additional viscoelastic support in the non-stationary deforming of a rectangular plate. Bulletin of the National Technical University “Kharkiv Polytechnic Institute”, 1, pp. 15–23. https://doi.org/10.20998/2222-0631.2020.01.02.
  21. Yang, F., Sedaghati, R., Esmailzadeh, E. (2021). Vibration suppression of structures using tuned mass damper technology: A state-of-the-art review. Journal of Vibration and Control, 28 (7-8), pp. 812-836. https://doi.org/10.1177/1077546320984305.
  22. Zhang, L., Chen, Q., Zhang, R., Lei, T. (2023). Vibration control of beams under moving loads using tuned mass inerter systems. Engineering Structures, 275, art. no. 115265. https://doi.org/10.1016/j.engstruct.2022.115265.
  23. Beerends, R. J., Ter Morsche, H. G., Van Den Berg, J. C., Van De Vrie, E. M. (2003). Fourier and Laplace Transforms. Cambridge University Press. 458 p. ISBN: 0521534410, 9780521806893.
  24. Voropay, A., Gnatenko, G., Yehorov, P., Povaliaiev, S., Naboka, O. (2022). Identification of the pulse axisymmetric load acting on a composite cylindrical shell, inhomogeneous in length, made of different materials. Eastern-European Journal of Enterprise Technologies, 5(7 (119), pp. 21–34. https://doi.org/10.15587/1729-4061.2022.265356.

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