Table of Contents Author Guidelines Submit a Manuscript
Shock and Vibration
Volume 2014 (2014), Article ID 848536, 9 pages
http://dx.doi.org/10.1155/2014/848536
Research Article

Analysis of Critical Velocities for an Infinite Timoshenko Beam Resting on an Elastic Foundation Subjected to a Harmonic Moving Load

1School of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai 200093, China
2College of Hydraulic and Environmental Engineering, China Three Gorges University, Yichang 443002, China
3School of Aerospace Engineering and Mechanics, Tongji University, Shanghai 200092, China

Received 28 February 2014; Accepted 27 June 2014; Published 14 July 2014

Academic Editor: Toshiaki Natsuki

Copyright © 2014 Bin Zhen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Critical velocities are investigated for an infinite Timoshenko beam resting on a Winkler-type elastic foundation subjected to a harmonic moving load. The determination of critical velocities ultimately comes down to discrimination of the existence of multiple real roots of an algebraic equation with real coefficients of the 4th degree, which can be solved by employing Descartes sign method and complete discrimination system for polynomials. Numerical calculations for the European high-speed rail show that there are at most four critical velocities for an infinite Timoshenko beam, which is very different from those gained by others. Furthermore, the shear wave velocity must be the critical velocity, but the longitudinal wave velocity is not possible under certain conditions. Further numerical simulations indicate that all critical velocities are limited to be less than the longitudinal wave velocity no matter how large the foundation stiffness is or how high the loading frequency is. Additionally, our study suggests that the maximum value of one group velocity of waves in Timoshenko beam should be one “dangerous” velocity for the moving load in launching process, which has never been referred to in previous work.