Abstract
A parametric survey was conducted to capture the dynamic response of a thin beam subjected to a varying speed moving mass. The existing literature lacks a comprehensive study on the beam dynamic behavior under a varying speed moving mass with arbitrary constant acceleration and mass ratio. The current work represents midpoint response spectra for a thin beam acted upon by a varying speed moving mass for a wide range of design parameters. Findings show that for a given mass ratio, higher response amplitudes are observed in decelerating motion compared to accelerating one. Moreover, increasing the mass ratio of the moving mass generally leads to higher beam dynamic response. Among the methods that can be utilized to calculate beam response, the Eigenfunction expansion method (EFM) and Orthonormal polynomial series expansion method (OPSEM) were used. Then an improvement technique was applied on both aforementioned methods and computational efficiency and convergence rate of all utilized methods was compared.
Similar content being viewed by others
References
H. Ouyang, Moving-load dynamics problems: A tutorial (with a brief overview), Mechanical Systems and Signal Processing, 25 (6) (2011) 2039–2060.
L. Fryba, Vibration of solids and structures under moving loads, Thomas Telford, London (1999).
S. Eftekhar Azam, M. Mofid and R. A. Khoraskani, Dynamic response of Timoshenko beam under moving mass, J. of Scientia Iranica, 20 (1) (2013) 50–56.
C. P. S. Kumar, C. Sujatha and K. Shankar, Vibration of simply supported beams under a single moving load: a detailed study of cancellation phenomenon, International J. of Mechanical Science, 99 (2015) 40–47.
A. Nikkhoo, M. E. Hassanabadi and S. Mariani, Simplified modeling of beam vibrations induced by a moving mass by regression analysis, Acta Mechanica, 226 (7) (2015) 2147–2157.
M. E. Hassanabadi, A. Nikkhoo, J. V. Amiri and B. Mehri, A new orthonormal polynomial series expansion method in vibration analysis of thin beams with non-uniform thickness, J. of Applied Mathematical Modelling, 37 (18-19) (2013) 8543–8556.
A. Nikkhoo, A. Farazandeh and M. E. Hassanabadi, On the computation of moving mass/beam interaction utilizing a semi-analytical method, J. of Brazilian Society of Mechanical Sciences and Engineering, 38 (3) (2016) 761–771.
Y. H. Lee and S. S. Kim, Combined analytical and numerical solution for an elastically supported Timoshenko beam to a moving load, JMST, 28 (7) (2014) 2549–2559.
M. R. Nami and M. Janghorban, Dynamic analysis of isotropic nanoplates subjected to moving load using statespace method based on nonlocal second order plate theory, JMST, 29 (6) (2015) 2423–2426.
Kh. Youcef, T. Sabiha, D. El Mostafa, D. Ali and M. Bachir, Dynamic analysis of train-bridge system and riding comfort of trains with rail irregularities, JMST, 27 (4) (2013) 951–962.
M. E. Hassanabadi, J. V. Amiri and M. R. Davoodi, On the vibration of a thin rectangular plate carrying a moving oscillator, J. of Scientia Iranica, 21 (2) (2014) 284–294.
M. Ebrahimi, S. Gholampour, H. J. Kafshgarkolaei and I. M. Nikbin, Dynamic behavior of a multispan continuous beam traversed by a moving oscillator, Acta Mechanica, 226 (12) (2015) 4247–4257.
M. E. Hassanabadi, N. K. Attari, A. Nikkhoo and M. Baradaran, An optimum modal superposition approach in the computation of moving mass induced vibrations of distributed parameter system, Proceeding of the Institution of Mechanical Engineers, Part C: J. of Mechanical Engineering Science, 229 (6) (2015) 1015–1028.
U. Lee, Revisiting the moving mass problem: Onset of separation between the mass and the beam, ASME, J. of Vibration and Acoustics, 118 (3) (1996) 516–521.
D. Stancioiu, H. Ouyang and J. E. Mottershead, Vibration of a beam excited by a moving oscillator considering separation and reattachment, J. of sound and Vibration, 310 (4-5) (2008) 1128–1140.
H. P. Lee, On the dynamic behavior of a beam with an accelerating mass, J. of Applied Mechanics, 65 (8) (1995) 564–571.
H. P. Lee, Transverse vibration of Timoshenko beam acted on by an accelerating mass, J. of Applied Acoustics, 47 (4) (1996) 319–330.
I. Esen, Dynamic response of a beam due to an accelerating moving mass using moving finite element approximation, J. of Mathematical and Computational Applications, 16 (1) (2011) 171–182.
B. Dyniewicz and C. I. Bajer, New consistent numerical modelling of a travelling accelerating concentrated mass, World J. of Mechanics, 2 (2012) 281–287.
A. Karlstrom, An analytical model for ground vibrations from accelerating trains, J. of Sound and Vibration, 293 (3-5) (2006) 587–598.
G. T. Michaltsos, Dynamic behavior of a single-span beam subjected to loads moving with variable speeds, J. of sound and Vibration, 258 (2) (2002) 359–372.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Junhong Park
Morteza Tahmasebi Yamchelou received his B.S. in Civil Engineering from Qom University. In 2014, he began his M.Sc. in Earthquake Engineering at Kharazmi University. His research interests include structural dynamics and numerical mechanics.
Gholamreza Nouri is currently an assistant professor in Civil Engineering at Kharazmi University. His research mainly focuses on earthquake engineering, geotechnical engineering and bridge engineering.
Rights and permissions
About this article
Cite this article
Yamchelou, M.T., Nouri, G. Spectral analysis of dynamic response of a thin beam subjected to a varying speed moving mass. J Mech Sci Technol 30, 3009–3017 (2016). https://doi.org/10.1007/s12206-016-0609-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-016-0609-4