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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.

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In this present paper, the dynamic analysis of nonprismastic beams subjected to moving concentrated forces is investigated at constant speed. Two cases of load- beam interaction problems described by the Dirac delta function with constant and harmonic magnitude mobile forces are studied. The technique called Galerkin’s method in conjunction with integral transform method was employed to solve the motion equation. From the numerical results, it is evidently seen that an increase in the foundation stiffness provides reduction on the beam deflection. And furthermore, the issue of resonance is closely monitored and observed to have reached earlier in constant magnitude than harmonic variable magnitude problem. Results presented in this work are useful in constructions engineering designs.