Dynamic Response to Moving Load of Prestressed Damped Shear Beam Resting on Bi-Parametric Elastic Foundation

The dynamic behaviour of damped shear beam resting on bi-parametric elastic foundation when traversed by moving load travelling at constant velocity is investigated in this present study. The beam-type structure has a uniform cross-sectional area and it is assumed to be simply supported. The governing equations are coupled second order partial differential equations. The method of integral transformation called Finite Fourier series was first used to reduce the sets of coupled second order partial differential equations governing the motion of this class of dynamical problem to sequence of coupled second order ordinary differential equations. Thereafter, the simplified coupled equations describing the motion of the beam-load system were then solved by Laplace transformation in conjunction with convolution theory to obtain the solution. The closed form solution obtained was analyzed to obtain the conditions under which the beam-load system will experience resonance phenomenon and speeds at which this may occur are also established. The effects of pertinent structural parameters on the response of a damped shear beam when under the action of the moving load were presented in plotted curves. From the graphs, it is interestingly found that increase in the values of vital structural parameters, such as axial force Nf, circular frequency CF, foundation stiffness K and shear modulus G, reduces the transverse displacement of the damped shear beam when under the action of the moving load. Practically speaking, increase in the values of these structural parameters significantly enhances the stability of the beam and increases the critical speed of the dynamical system. Consequently, the resonance risk of the vibrating system is reduced and thus the safety of the occupant of this structural member is guaranteed.