Abstract
Compared with the moving concentrated load model, it is more realistic and proper to use the moving distributed mass and load model to simulate the dynamics of a train moving along a railway track. In the problem of a moving concentrated load, there is only one critical velocity, which divides the load moving velocity into two categories: subcritical and supercritical. The locus of a concentrated load demarcates the space into two parts: the waves in these two domains are called the front and rear waves, respectively. In comparison, in the problem of moving distributed mass and load, there are two critical velocities, which results in three categories of the distributed mass moving velocity. Due to the presence of the distributed mass and load, the space is divided into three domains, in which three different waves exist. Much richer and different variation patterns of wave shapes arise in the problem of the moving distributed mass and load. The mechanisms responsible for these variation patterns are systematically studied. A semi-analytical solution to the steady-state is also obtained, which recovers that of the classical problem of a moving concentrated load when the length of the distributed mass and load approaches zero.
Similar content being viewed by others
References
S. P. Timoshenko, Method of Analysis of Statical and Dynamical Stresses in Rail (Proceedings of the Second International Congress for Applied Mechanics, Zurich, Switzerland, 1926).
J. J. Labra, Acta Mech. 22, 113 (1975).
A. D. Kerr, Int. J. Mech. Sci. 14, 71 (1972).
S. P. Timoshenko, and B. F. Langer, J. Appl. Mech. 54, 277 (1932).
M. T. Tran, K. K. Ang, and V. H. Luong, J. Sound Vib. 333, 5427 (2014).
K. K. Ang, and J. Dai, J. Sound Vib. 332, 2954 (2013).
N. H. Lim, N. H. Park, and Y. J. Kang, Comput. Struct. 81, 2219 (2003).
A. V. Metrikine, and H. A. Dieterman, Eur. J. Mech. A-Solids 16, 295 (1997).
Y. G. Chen, and B. Jin, Sci. China Ser. G-Phys. Mech. Astron. 51, 883 (2008).
B. Jin, Archive Appl. Mech. 74, 277 (2004).
A. K. Mallik, S. Chandra, and A. B. Singh, J. Sound Vib. 291, 1148 (2006).
J. T. Kenney, J. Appl. Mech. 21, 359 (1954).
Z. Dimitrovová, and J. N. Varandas, Comput. Struct. 87, 1224 (2009).
Z. Dimitrovová, Int. J. Solids Struct. 122–123, 128 (2017).
A. Nobili, J. Eng. Mech. 139, 1470 (2013).
R. Bogacz, and W. Czyczula, J. Theor. Appl. Mech. 46, 763 (2008).
A. V. Vostroukhov, and A. V. Metrikine, Int. J. Solids Struct. 40, 5723 (2003).
D. G. Duffy, J. Appl. Mech. 57, 66 (1990).
A. V. Metrikine, and H. A. Dieterman, J. Sound Vib. 201, 567 (1997).
Z. Dimitrovová, Int. J. Mech. Sci. 127, 142 (2017).
H. D. Nelson, and R. A. Conover, J. Appl. Mech. 38, 1003 (1971).
G. A. Benedetti, J. Appl. Mech. 41, 1069 (1974).
E. Esmailzadeh, and M. Ghorashi, J. Sound Vib. 184, 9 (1995).
Y. H. Lin, J. Sound Vib. 199, 697 (1997).
X. Bian, H. Jiang, C. Cheng, Y. Chen, R. Chen, and J. Jiang, Soil Dyn. Earthquake Eng. 66, 368 (2014).
W. L. Luo, Y. Xia, and S. Weng, Sci. China-Phys. Mech. Astron. 58, 084601 (2015).
K. D. Murphy, and Y. Zhang, J. Sound Vib. 237, 319 (2000).
X. M. Zhou, and Y. C. Zhao, Sci. China-Phys. Mech. Astron. 62, 014612 (2019).
J. H. Yang, Q. Z. Yuan, and Y. P. Zhao, Sci. China-Phys. Mech. Astron. 62, 124611 (2019).
J. D. Achenbach, and C. T. Sun, Int. J. Solids Struct. 1, 353 (1965).
L. Frýba, Vibration of Solids and Structures under Moving Loads (No-ordhoff International Publishing, Groningen, Netherland, 1972).
M. A. Biot, J. Appl. Mech. 4, 1 (1937).
M. Hetényi, Beams on Elastic Foundation (The University of Michigan Press, Ann Arbor, Michigan, USA, 1946).
P. M. Mathews, Z. Angew. Math. Mech. 38, 105 (1958).
Y. Zhang, and K. D. Murphy, Int. J. Solids Struct. 41, 6745 (2004).
Y. H. Chen, Y. H. Huang, and C. T. Sun, J. Sound Vibr. 241, 809 (1997).
J. S. Chen, and Y. K. Chen, Int. J. Non-Linear Mech. 46, 180 (2011).
B. Tabarrok, C. Tezer, and M. Stylianou, Acta Mech. 107, 137 (1994).
C. Y. Wang, Acta Mech 228, 357 (2017).
Y. Zhang, and K. D. Murphy, Acta Mech. Solid Sin. 20, 236 (2007).
K. F. Graff, Wave Motions in Elastic Solids (Clarendon Press, Oxford, UK, 1975).
C. R. Steele, J. Appl. Mech. 35, 481 (1968).
A. D. Kerr, J. Appl. Mech. 31, 491 (1964).
Y. Zhang, and X. Liu, Eur. J. Mech. A-Solids 77, 103819 (2019).
S. C. Dutta, and R. Roy, Comput. Struct. 80, 1579 (2002).
U. Lee, J. Vib. Acoust. 118, 516 (1996).
H. Zhu, Y. Zhao, Z. He, R. Zhang, and S. Ma, Sci. China-Phys. Mech. Astron. 61, 054611 (2018).
Y. Zhang, X. Liu, and Y. Wei, Eur. J. Mech. A-Solids 71, 394 (2018).
Y. Zhang, Sci. China-Phys. Mech. Astron. 59, 624602 (2016).
G. A. Korn, and T. M. Korn, Mathematical Handbook for Scientist and Engineers, 2nd ed. (McGraw-Hill Book Company, New York, USA, 1968).
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by the National Natural Science Foundation of China (Grant No. 11772335), the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB22020201), the National Key Research and Development Program of China (Grant Nos. 2016YFB1200602-09, and 2016YFB1200602-10
Rights and permissions
About this article
Cite this article
Zhang, Y. Steady state response of an infinite beam on a viscoelastic foundation with moving distributed mass and load. Sci. China Phys. Mech. Astron. 63, 284611 (2020). https://doi.org/10.1007/s11433-019-1513-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11433-019-1513-5