Journal of Mechanical Science and Technology 30 (7) (2016) 3009~3017 www.springerlink.com/content/1738-494x(Print)/1976-3824(Online) DOI 10.1007/s12206-016-0609-4 Spectral analysis of dynamic response of a thin beam subjected to a varying speed moving mass † Morteza Tahmasebi Yamchelou 1,* and Gholamreza Nouri 2 1 Faculty of Civil Engineering, Kharazmi University, Karaj, Iran 2 Faculty of Civil Engineering, Kharazmi University, Tehran, Iran (Manuscript Received September 24, 2015; Revised February 15, 2016; Accepted March 21, 2016) ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 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 con- stant 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. Keywords: Computational efficiency evaluation; Dynamic response spectrum; Eigenfunction expansion method; Orthonormal polynomial series expansion method; Varying speed moving mass ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction Investigating the dynamic response of structures excited by a moving mass encompasses a wide range of engineering problems. Vibration of beams, circular plates and rotating shafts traversed by moving masses, vehicle-bridge interaction, vehicle road/ground-interaction and train-railway interaction are just a few examples. The contact force between the mov- ing load and the beam could be considered as constant gravita- tional force of the moving load; this approach is known as the moving force problem. Taking into account inertial loads re- sulting from transverse acceleration of the moving mass trav- elling upon the deformed path of the beam is moving mass approach. The higher the mass and speed of the moving load, the more considerable difference between beam responses resulting from these two approaches is observed. A variety of fundamental concepts related to moving load problem could be found in Ouyang’s review article [1]. A thorough investiga- tion of simple moving load problems can be found in Fryba’s monograph [2]. Eftekhar Azam et al. [3] studied the dynamic response of Timoshenko beam under moving mass. Kumar et al. [4] investigated cancellation phenomenon in a simply sup- ported beam under a single moving load. Nikkhoo et al. [5, 7] proposed some new methods to capture the dynamic response of a beam acted upon by a moving mass. Hassanabadi et al. [6] proposed OPSEM to calculate the dynamic response of a beam subjected to a moving mass with different boundary conditions. Lee and Kim [8] used an analytical-numerical solution to calculate the response of a Timoshenko beam to a moving load. Nami and Janghorban [9] presented dynamic analysis of nanoplates subjected to moving loads. Train-track interaction and the effect of railway irregularities on riding comfort has been studied by Youcef et al. [10]. Vibration of thin rectangular plate carrying a moving oscillator has been scrutinized by Ebrahimzadeh Hassanabadi et al. [11]. Dy- namic response of multi-span beams traversed by a moving oscillator is investigated by Ebrahimi et al. [12]. Ebra- himzadeh Hassanabadi et al. [13] introduced an improved method to enhance computational efficiency in capturing the dynamic response of a circular plate carrying a moving mass. Most reported papers consider that the moving mass and sup- porting beam stay attached constantly. Lee [14] investigated the dynamic response of a beam subjected to a moving mass, considering separation between the moving mass and the sup- porting beam. Stancioiu et al. [15] studied vibration of a beam excited by a moving oscillator considering separation and reattachment. Most investigations on the subject are based on the assump- * Corresponding author. Tel.: +98 2188826502, Fax.: +98 2188826502 E-mail address: std_tahmasbi@khu.ac.ir † Recommended by Associate Editor Junhong Park © KSME & Springer 2016