Steady state response of an infinite beam on a viscoelastic foundation with moving distributed mass and load
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August 2020 Vol. 63 No. 8: 284611 https://doi.org/10.1007/s11433-019-1513-5
Steady state response of an infinite beam on a viscoelastic foundation with moving distributed mass and load Yin Zhang1,2* 1 State
Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China; 2 School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China Received December 15, 2019; accepted January 14, 2020; published online April 3, 2020
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. steady state, beam, viscoelastic foundation, moving distributed mass PACS number(s): Citation:
02.30.Oz, 46.40.-f, 46.40.Ff, 46.70.De
Y. Zhang, 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
1 Introduction The steady state solution of an infinite beam on an elastic foundation under a moving concentrated load was first obtained, in connection with the stress analysis of railway tracks, by Timoshenko in 1926 [1]. Timoshenko found that there is a critical velocity at which the vibration amplitude of the undamped beam approaches infinity [1]. This critical velocity is found to be around 1800 km/h [1, 2], which is much larger than the highest train speed at that time and nowadays. At a first look, the dynamic effect should be little because of this very high critical velocity [3]. While, this moving load induced vibration can cause very significant dynamic *Corresponding author (email: [email protected])
effect in conjunction with the track irregularities [4-6]. Recent analysis shows that the difference between the static and dynamic wheel-track contact stress can be as large as twenty times [5]. Nowadays
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