Numerical Evaluation of the Forced Vibration Response of a Timoshenko Beam Subjected to a Moving Force Using the Modal Analysis Approach
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Abstract
The dynamic response of a structure subjected to moving loads is an interesting and meaningful research subject in various engineering fields such as bridges, roadways, railways and aircrafts. The present paper deals with the dynamic response of an uniform Timoshenko beam under the action of a moving force. Properties of the natural frequencies and modes of the Timoshenko beam are discussed. It is shown that the solution of the forced vibration for the transverse displacement and the rotation of the cross section of the beam can be expressed in form of a sum of two infinite series. The numerical simulation result shows that the speed change of the moving force has little effect on the beam deflection, but its magnitude change greatly affects the beam deflection.
Keywords
Timoshenko beam, moving force, vibrations, modal analysis
Article Details
References
[1] P. Hagedorn, A. DasGupa (2007), Vibrations and Waves in Continuous Mechanical Systems, John Woley & Sons, Chichester. https://doi.org/10.1002/9780470518434
[2] A. W. Leissa, M. S. Qatu (2011), Vibration of Continuous Systems, McGraw-Hill, New York.
[3] Nguyen Van Khang (2005), Engineering Vibration (4th Edition), (in Vietnamese).
[4] P. Sniady (2008), Dynamic response of a Timoshenko beam to a moving force, Journal of Applied Mechanics, vol.75, pp. 024503-1-.024503-4 https://doi.org/10.1115/1.2775500
[5] L. Majkut (2009), Free and forced vibrations of Timoshenko beams described by single difference equation, Journal of Theoretical and Applied Mechanics, Vol. 47(1), pp. 193-210, Warsaw
[6] S.E. Azam, M. Mofid, R. A. Khoraskani (2013), Dynamic response of Timoshenko beam under moving mass, Scientia Iranica A, vol. 20(1), pp. 50-56.
[7] D. Roshandel, M. Mofid, and A. Ghannadiasl (2015), Modal analysis of the dynamic response of Timoshenko beam under moving mass, Scientia Iranica A, vol. 22(2), pp. 331-344.
[8] T. Kim, I. Park, U. Lee (2017), Forced vibration of Timoshenko beam subjected to stationary and moving loads using the modal analysis method, Hindawi Shock and Vibration, vol. 2017, Article ID 3924921 https://doi.org/10.1155/2017/3924921
[9] T.I. Zhdan (2019), Action of moving loads on the Bernoulli-Euler and Timoshenko beams, Moscow University Mechanics Bulletin, vol. 74 (5), pp. 123-127. https://doi.org/10.3103/S0027133019050042
[2] A. W. Leissa, M. S. Qatu (2011), Vibration of Continuous Systems, McGraw-Hill, New York.
[3] Nguyen Van Khang (2005), Engineering Vibration (4th Edition), (in Vietnamese).
[4] P. Sniady (2008), Dynamic response of a Timoshenko beam to a moving force, Journal of Applied Mechanics, vol.75, pp. 024503-1-.024503-4 https://doi.org/10.1115/1.2775500
[5] L. Majkut (2009), Free and forced vibrations of Timoshenko beams described by single difference equation, Journal of Theoretical and Applied Mechanics, Vol. 47(1), pp. 193-210, Warsaw
[6] S.E. Azam, M. Mofid, R. A. Khoraskani (2013), Dynamic response of Timoshenko beam under moving mass, Scientia Iranica A, vol. 20(1), pp. 50-56.
[7] D. Roshandel, M. Mofid, and A. Ghannadiasl (2015), Modal analysis of the dynamic response of Timoshenko beam under moving mass, Scientia Iranica A, vol. 22(2), pp. 331-344.
[8] T. Kim, I. Park, U. Lee (2017), Forced vibration of Timoshenko beam subjected to stationary and moving loads using the modal analysis method, Hindawi Shock and Vibration, vol. 2017, Article ID 3924921 https://doi.org/10.1155/2017/3924921
[9] T.I. Zhdan (2019), Action of moving loads on the Bernoulli-Euler and Timoshenko beams, Moscow University Mechanics Bulletin, vol. 74 (5), pp. 123-127. https://doi.org/10.3103/S0027133019050042