New Semi-analytical Solution for a Moving Mass Problem: The Effect of Initial Conditions and Abrupt Change in Foundation Stiffness

In this contribution, the new semi-analytical solution for the moving mass problem from [1] is extended to account for the influence of initial conditions. The essential part of the new closed-form formula derived in [1] is the term governed by the mass-induced frequencies, which cannot be obtained when a common solution method for this kind of problems like double Fourier transform is used. Apart the term given by the closed-form formula, there is a transient part of natural vibrations originated by a line discontinuity in the Laplace image of the displacement under the load. Analytical expression is derived for such a defined line cut. Then the transient part is determined by numerical integration and added to the response given by the closed-form formula. Very good coincidence between results on finite and infinite beams is obtained, which is further exploited for the analysis of the influence of the abrupt change in the foundation stiffness.