On the Resolution of Existing Discontinuities in the Dynamic Responses of an Euler-Bernoulli Beam Subjected to the Moving Mass

The dynamic response of a one-dimensional distributed parameter system subjected to a moving mass with constant speed is investigated. An Euler-Bernoulli beam with the uniform cross-section and finite length with specified boundary support conditions is assumed. In this paper, rather a new method based on the time dependent series expansion for calculating the bending moment and the shear force due to motion of the mass is suggested. Governing differential equations of the motion are derived and solved. The accuracy of the numerical results primarily is verified and further the rapid convergence of this new technique was illustrated over other existing methods. Finally, it is shown that a considerable improvement is obtained in capturing the incurred discontinuities at the contact point of traveling concentrated mass.