Complete semi-analytical solution for a uniformly moving mass on a beam on a two-parameter visco-elastic foundation with non-homogeneous initial conditions

In this paper the new semi-analytical solution for the moving mass problem, published by the author of this paper, is extended to account for the non-homogeneous initial conditions. Derivations are presented for infinite homogeneous beams placed on a two-parameter visco-elastic foundation. Methods of integral transforms and contour integration are exploited to obtain the final closed-form solution, which is presented in form of a sum of the truly steady-state part, mass induced harmonic part, initial conditions induced harmonic part and transient vibration. Except for the transient part that is obtained by numerical integration, full evolution of the transversal vibrations can be quickly and accurately obtained by simple evaluation of the presented closed-form results. Newly derived formulas for infinite beams are validated by analysis of long finite beams, where the problem is solved by the eigenmode expansion method. Excellent agreement between the results is obtained validating the new formulas.