Please cite this article in press as: Zarfam, R., et al., On the response spectrum of Euler–Bernoulli beams with a moving mass and horizontal support excitation. Mech. Re. Commun. (2012), http://dx.doi.org/10.1016/j.mechrescom.2012.09.006 ARTICLE IN PRESS G Model MRC-2677; No. of Pages 7 Mechanics Research Communications xxx (2012) xxx–xxx Contents lists available at SciVerse ScienceDirect Mechanics Research Communications j o ur nal homep age: www.elsevier.com/locate/mechrescom On the response spectrum of Euler–Bernoulli beams with a moving mass and horizontal support excitation Raham Zarfam a , Ali Reza Khaloo a,∗ , Ali Nikkhoo b a Department of Civil Engineering, Sharif University of Technology, Tehran, Iran b Department of Civil Engineering, University of Science and Culture, Tehran, Iran a r t i c l e i n f o Article history: Received 12 April 2012 Received in revised form 22 September 2012 Available online xxx Keywords: Moving mass Vibration of beams Response spectrum Seismic excitation a b s t r a c t In this study, the response spectrum of a time-varying system such as a beam subjected to moving masses under a harmonic and earthquake support excitations is explored. The excitations are supposed to act on the horizontal directions of the beam axis. The inertial effect of the moving masses on the natural frequencies of the beam for different cases of loading is investigated and a critical value of a so called parameter “mass staying time” is presented to avoid dynamic instability of the system. Finally, some 3D response spectra for different supports excitations as well as the beam natural frequencies are depicted. © 2012 Elsevier Ltd. All rights reserved. 1. Introduction Investigating a system traversed by moving vehicles is one of the important concerns for structural engineers in the design of highway and railway bridges (Fr ´ yba, 1999). Kenney (1954), pre- sented the constitutive equation of an infinite beam on an elastic foundation subjected to the moving load and derived the criti- cal velocity of the moving load for the first time. By introducing the inertial effects of the moving loads into the problem formu- lation, more realistic results would be gained especially for loads with relative large weights traveling at high speeds. However, this would lead to a more complicated problem solution in comparison with the moving load. Akin and Mofid (1989) developed a numer- ical scheme named as discrete element technique (DET) to cope with the problem of Euler–Bernoulli beams with various boundary conditions acted upon by a moving mass. This method was suc- cessfully applied to a Timoshenko beam excited by a moving mass (Yavari et al., 2001) and a viscoelastic beam subjected to the moving mass (Mofid et al., 2010). Nikkhoo et al. (2007) reported an exten- sive study on the effects of convective acceleration components of the moving mass on dynamic behavior of an Euler–Bernoulli beam. They showed the importance of these components on the response of the structure for those masses travel at speeds higher than some certain limits. This fact is re-emphasized by Sharbati ∗ Corresponding author. E-mail addresses: r zarfam@civil.sharif.edu, zraham@gmail.com (R. Zarfam), khaloo@sharif.ir (A.R. Khaloo), nikkhoo@usc.ac.ir (A. Nikkhoo). and Szyszkowski (2011) by proposing a FEM approach to deal with the problem. Shear deformable beams excited by a moving mass is the subject of Kiani et al. (2009a) paper. They applied the repro- ducing kernel particle method (RKPM) to solve Euler–Bernoulli, Timoshenko and higher order beams with different boundary con- ditions under a moving mass. Their results were indicatory of the load inertia importance for the all assumed beam theories. They also signified the significance of opting proper beam theory based on the beam slenderness. The problem of moving mass traveling on a thin multi-span beam is also scrutinized by Ichikawa et al. (2000) via eigenfunction expansion method. Their results revealed the sig- nificance of moving mass inertial for heavier masses traveling at high speeds. Numerical methods have been effectively utilized to deal with the problem of multi-span viscoelastic thin (Kiani et al., 2010) and thick beams (Kiani et al., 2009b) traversed by a mov- ing mass. On the other hand, the problem of single-span (Bilello et al., 2004) and multi-span (Stancioiu et al., 2011) beams carrying moving masses are examined experimentally and good agreement is achieved between the theoretically determined and the experi- mental results. The problem of a beam under the simultaneous moving loads and horizontal support motions is a recently developed field of study. Yau and Fr ´ yba (2007) explored a model of suspended bridges subjected to a row of equidistant moving forces and earthquake excitations acted as horizontal motions to the beam supports. They studied the significance of higher mode contribution on the maximum acceleration of such structure when the supports excita- tion interacts with the moving forces excitation. In another study, Fr ´ yba and Yau (2009) investigated the same problem for long-span 0093-6413/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.mechrescom.2012.09.006