New improved series expansion for solving the moving oscillator problem

A new method able to evaluate the dynamic stress response of an elastic beam subject to moving oscillators is presented. The proposed procedure improves the convergence and accuracy of the conventional eigenfunction series expansion of beam response taking into account the gravitational, inertial and damping effects due to the moving oscillators. The improvement of the conventional solution is obtained by means of an extension to continuous systems of the dynamic correction method, originally proposed for discretized structures. The proposed method is able to account for the truncated higher order eigenfunctions by adding a pseudo-static term to the conventional series expansion. Numerical results are presented to demonstrate the capability of the method to accurately determine the discontinuity and jump in bending moment and shear force distributions, respectively.