J. KSIAM Vol.20, No.1, 17–35, 2016 http://dx.doi.org/10.12941/jksiam.2016.20.017 DYNAMIC CHARACTERISTICS OF A ROTATING TIMOSHENKO BEAM SUBJECTED TO A VARIABLE MAGNITUDE LOAD TRAVELLING AT VARYING SPEED BABATOPE OMOLOFE 1† AND SEGUN NATHANIEL OGUNYEBI 2 1 DEPARTMENT OF MATHEMATICAL SCIENCES,SCHOOL OF SCIENCES,FEDERAL UNIVERSITY OF TECH- NOLOGY, PMB 704, AKURE,ONDO STATE,NIGERIA E-mail address: babatope omolofe@yahoo.com; bomolofe@futa.edu.ng 2 DEPARTMENT OF MATHEMATICAL SCIENCES,FACULTY OF SCIENCES,EKITI STATE UNIVERSITY,ADO- EKITI ,EKITI STATE,NIGERIA E-mail address: segunogunyebi@yahoo.com ABSTRACT. In this study, the dynamic behaviour of a rotating Timoshenko beam when under the actions of a variable magnitude load moving at non-uniform speed is carried out. The effect of cross-sectional dimension and damping on the flexural motions of the elastic beam was neglected. The coupled second order partial differential equations incorporating the effects of rotary and gyroscopic moment describing the motions of the beam was scrutinized in order to obtain the expression for the dynamic deflection and rotation of the vibrating system using an elegant technique called Galerkin’s Method. Analyses of the solutions obtained were carried out and various results were displayed in plotted curve. It was found that the response amplitude of the simply supported beam increases with an increase in the value of the foundation reaction modulus. Effects of other vital structural parameters were also established. 1. I NTRODUCTION Studies concerning vibrating bodies resting on an elastic foundation carrying moving loads are of considerable practical importance and have been a subject of numerous scientific inves- tigations by different authors in past few years [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20]. In most of the studies available in literature, such as the work of Sadiku and Leipolz [21], Oni and Awodola [22], the scope of the problem of assessing the dynamic response of a structural member under the passage of moving load has been limited to that of thin beam or thick beam. Kolousek et al. [23] studied works on uniform thin beam. In their analysis the adopted a normal modes method, effects of damping and foundation were not Received by the editors January 21 2015; Revised March 21 2015; Accepted in revised form September 3 2015; Published online March 23 2016. 2000 Mathematics Subject Classification. 74H45, 70K40, 74K10. Key words and phrases. Timoshenko beam, flexural motion, dynamic deflection, rotation, rotary inertia, gyro- scopic moment, response amplitude. † Corresponding author. 17