On the Dual Nature of Forced Transverse Vibrations of Bridges Under the Action Moving Load

Karush Mkrtchyan Shirak

doi:doi:10.11648/j.ijse.20220601.12

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On the Dual Nature of Forced Transverse Vibrations of Bridges Under the Action Moving Load

Karush Mkrtchyan Shirak

Published in International Journal of Systems Engineering (Volume 6, Issue 1)

Received: 28 April 2021 Accepted: 20 January 2022 Published: 28 February 2022

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Abstract

In this paper, forced transverse vibrations of an elastic hinge-supported Timoshenko beam are considered, taking into account the rotational motion caused by a periodically oscillating concentrated load moving along the beam at a constant speed v. This problem is of practical interest in connection with the study of forced transverse vibrations of bridges. The bridge span is considered here as a Timoshenko beam of constant transverse cross-section. The problem is solved by the method proposed earlier using combined conditions, including dynamic action on the Timoshenko beam and rotational motion relative to the bending wave front. The solution of the problem is built in the form of a number of own forms of vibrations. Two types of forced transverse vibrations and new resonance frequencies are obtained. The purpose of this study is to assess the effect of the identified new forced transverse vibrations for bridges and compare these results. With the solutions obtained by previous authors. To show at which new resonant frequency obtained in bridges new resonance phenomena arise. New dynamic phenomena in bridges caused by a periodically oscillating concentrated load moving along the beam at a constant speed, play an important role in bridge design. This work is a new calculation scheme for the design of bridges.

Published in	International Journal of Systems Engineering (Volume 6, Issue 1) This article belongs to the Special Issue Recent Trends in Machine Intelligence in Medical Imaging
DOI	10.11648/j.ijse.20220601.12
Page(s)	10-17
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Bridge, Centrifugal Force, Cross Section, Gravity, Transverse Oscillations, Natural Frequencies, Natural Forms

References

[1]	G. G. Stokes “Discussion of a differential Equation relating to the breaking Railway Bridges.” “Mathematical and Physical Papers", 1883, vol. II, p. 178—220. Grambride University Press (From the Transactions of the Cambridge Philosopical sosiety, 1849, vol. 8, p. 707, May, 21).
[2]	A. N. Kriloff, Ober die erzwungenen Schwingungen von gleichfor- •migen elastischen Staben. „Mathematishe Annalen", 1905, b. 61, p. 211-234.
[3]	S. P. Timoshenko, On forced vibrations of prismatic rods. "Izvestia of the Kiev Polytech, in-ta", book 4, pp. 205—248, 1909 [in Russian].
[4]	(1957). S. P. Timoshenko, History of science on the strength of materials. M. [in Russian].
[5]	(1967). S. P. Timoshenko, Vibration Problems in Engineering (Nauka, Moscow) [in Russian].
[6]	S. P. Timoshenko, On the transverse vibrations of Bars uniform crossiction". Philosophical IVlagazine and Journal of science", 1922, vol. 43, ser. 6, p. 125-131.
[7]	A. L. Florence, Traveling force on a Timoshenko beam. Trans. ASME. 1965. E32. № 2. pp. 351-358.
[8]	J. D. Achenbach, C. T. Sun, Moving load on a flexibly supported Timoshenko beam. Internat. J. Solids and Struct., 1965, 1, №4, pp. 353-370.
[9]	Tang Sing-Chih. A solution to the Timoshenko beam under a moving force. AIAA Journal, 1966, 4, №4, pp. 711-713.
[10]	B. A. Во1eу and Chi-Chang Сhao. An Approximate Analysis of Timoshenko beams under dynamic loads. „Journal Appl. Mech"., 1958. vol. 25, № 1, pp. 31—36.
[11]	H. H. Pan, Vibration of a viscoelastic Timoshenko beam. J. Engng Mech. Div. Proc. Amer. Soc. Civil Engrs, 1966, 92, №2. pp. 213-234.
[12]	P. M. Mathews, «Vibration of a Beam on Elastic Foundation», Zeitschrift fur angewandte Mathematik und Mechanik, Vol. 38, 1958. pp. 105-115.
[13]	(1973). E. I. Grigolyuk and I. T. Selezov, “Nonclassical Theories of Rod, Plate, and Shell Vibrations,” in Results in Science and Technology. Mechanics of Solids, Vol. 5 (VINITI, Moscow) [in Russian].
[14]	K. Sh. Mkrtchyan, The Dual Nature of the Transverse Vibrations of an Elastic Rod. Prikl. Mat. Mekh. 63 (6), 1055–1058 (1999) [J. Appl. Math. Mech. (Engl. Transl.) 63 (6), 989–992 (1999)].
[15]	K. Sh. Mkrtchyan, Study of Forced Transverse Vibrations of Elastic Hinge-Operated Rod Taking Into Account Rotative Movement. Mech. Solids 54, 112–121 (2019). https://doi.org/10.3103/S0025654419010096.

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Karush Mkrtchyan Shirak. (2022). On the Dual Nature of Forced Transverse Vibrations of Bridges Under the Action Moving Load. International Journal of Systems Engineering, 6(1), 10-17. https://doi.org/10.11648/j.ijse.20220601.12

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ACS Style

Karush Mkrtchyan Shirak. On the Dual Nature of Forced Transverse Vibrations of Bridges Under the Action Moving Load. Int. J. Syst. Eng. 2022, 6(1), 10-17. doi: 10.11648/j.ijse.20220601.12

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AMA Style

Karush Mkrtchyan Shirak. On the Dual Nature of Forced Transverse Vibrations of Bridges Under the Action Moving Load. Int J Syst Eng. 2022;6(1):10-17. doi: 10.11648/j.ijse.20220601.12

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@article{10.11648/j.ijse.20220601.12,
  author = {Karush Mkrtchyan Shirak},
  title = {On the Dual Nature of Forced Transverse Vibrations of Bridges Under the Action Moving Load},
  journal = {International Journal of Systems Engineering},
  volume = {6},
  number = {1},
  pages = {10-17},
  doi = {10.11648/j.ijse.20220601.12},
  url = {https://doi.org/10.11648/j.ijse.20220601.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijse.20220601.12},
  abstract = {In this paper, forced transverse vibrations of an elastic hinge-supported Timoshenko beam are considered, taking into account the rotational motion caused by a periodically oscillating concentrated load moving along the beam at a constant speed v. This problem is of practical interest in connection with the study of forced transverse vibrations of bridges. The bridge span is considered here as a Timoshenko beam of constant transverse cross-section. The problem is solved by the method proposed earlier using combined conditions, including dynamic action on the Timoshenko beam and rotational motion relative to the bending wave front. The solution of the problem is built in the form of a number of own forms of vibrations. Two types of forced transverse vibrations and new resonance frequencies are obtained. The purpose of this study is to assess the effect of the identified new forced transverse vibrations for bridges and compare these results. With the solutions obtained by previous authors. To show at which new resonant frequency obtained in bridges new resonance phenomena arise. New dynamic phenomena in bridges caused by a periodically oscillating concentrated load moving along the beam at a constant speed, play an important role in bridge design. This work is a new calculation scheme for the design of bridges.},
 year = {2022}
}

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TY - JOUR
T1 - On the Dual Nature of Forced Transverse Vibrations of Bridges Under the Action Moving Load
AU - Karush Mkrtchyan Shirak
Y1 - 2022/02/28
PY - 2022
N1 - https://doi.org/10.11648/j.ijse.20220601.12
DO - 10.11648/j.ijse.20220601.12
T2 - International Journal of Systems Engineering
JF - International Journal of Systems Engineering
JO - International Journal of Systems Engineering
SP - 10
EP - 17
PB - Science Publishing Group
SN - 2640-4230
UR - https://doi.org/10.11648/j.ijse.20220601.12
AB - In this paper, forced transverse vibrations of an elastic hinge-supported Timoshenko beam are considered, taking into account the rotational motion caused by a periodically oscillating concentrated load moving along the beam at a constant speed v. This problem is of practical interest in connection with the study of forced transverse vibrations of bridges. The bridge span is considered here as a Timoshenko beam of constant transverse cross-section. The problem is solved by the method proposed earlier using combined conditions, including dynamic action on the Timoshenko beam and rotational motion relative to the bending wave front. The solution of the problem is built in the form of a number of own forms of vibrations. Two types of forced transverse vibrations and new resonance frequencies are obtained. The purpose of this study is to assess the effect of the identified new forced transverse vibrations for bridges and compare these results. With the solutions obtained by previous authors. To show at which new resonant frequency obtained in bridges new resonance phenomena arise. New dynamic phenomena in bridges caused by a periodically oscillating concentrated load moving along the beam at a constant speed, play an important role in bridge design. This work is a new calculation scheme for the design of bridges.
VL - 6
IS - 1
ER -

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Author Information

Karush Mkrtchyan Shirak

Alexander Nazarov Institute of Geophysics and Engineering Seismology of National Academy of Sciences of Armenia, Gyumri, Armenia

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APA Style

Karush Mkrtchyan Shirak. (2022). On the Dual Nature of Forced Transverse Vibrations of Bridges Under the Action Moving Load. International Journal of Systems Engineering, 6(1), 10-17. https://doi.org/10.11648/j.ijse.20220601.12

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ACS Style

Karush Mkrtchyan Shirak. On the Dual Nature of Forced Transverse Vibrations of Bridges Under the Action Moving Load. Int. J. Syst. Eng. 2022, 6(1), 10-17. doi: 10.11648/j.ijse.20220601.12

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AMA Style

Karush Mkrtchyan Shirak. On the Dual Nature of Forced Transverse Vibrations of Bridges Under the Action Moving Load. Int J Syst Eng. 2022;6(1):10-17. doi: 10.11648/j.ijse.20220601.12

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@article{10.11648/j.ijse.20220601.12,
  author = {Karush Mkrtchyan Shirak},
  title = {On the Dual Nature of Forced Transverse Vibrations of Bridges Under the Action Moving Load},
  journal = {International Journal of Systems Engineering},
  volume = {6},
  number = {1},
  pages = {10-17},
  doi = {10.11648/j.ijse.20220601.12},
  url = {https://doi.org/10.11648/j.ijse.20220601.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijse.20220601.12},
  abstract = {In this paper, forced transverse vibrations of an elastic hinge-supported Timoshenko beam are considered, taking into account the rotational motion caused by a periodically oscillating concentrated load moving along the beam at a constant speed v. This problem is of practical interest in connection with the study of forced transverse vibrations of bridges. The bridge span is considered here as a Timoshenko beam of constant transverse cross-section. The problem is solved by the method proposed earlier using combined conditions, including dynamic action on the Timoshenko beam and rotational motion relative to the bending wave front. The solution of the problem is built in the form of a number of own forms of vibrations. Two types of forced transverse vibrations and new resonance frequencies are obtained. The purpose of this study is to assess the effect of the identified new forced transverse vibrations for bridges and compare these results. With the solutions obtained by previous authors. To show at which new resonant frequency obtained in bridges new resonance phenomena arise. New dynamic phenomena in bridges caused by a periodically oscillating concentrated load moving along the beam at a constant speed, play an important role in bridge design. This work is a new calculation scheme for the design of bridges.},
 year = {2022}
}

Copy | Download