Analysis of vibrations induced by proximate masses traversing a beam supported by a finite depth foundation with partial shear resistance

In this paper, analysis of vibrations induced by proximate moving masses traversing a beam supported by a finite-depth foundation with partial shear resistance is presented. This model is simple enough to be handled by semi-analytical approaches and has a counterpart in modal expansion, which is suitable for finite beams [I]. The model can acceptably approximate vibrations recorded experimentally as shown in [2] and provides results sufficiently close to the ones obtained on more sophisticated models [3]. The semi-analytical analysis is based on developments related to massless foundation presented in [4-7]. The method is extended, and additional aspect of dynamic amplification due to the proximity of moving masses are included. Final solution is presented in convenient form where most terms are analytical, and thus can be easily evaluated. This form also clearly identifies each part contribution. Main part of the solution is harmonic, composed from steady and unsteady parts of the solution. The unsteady part needs identification of induced frequencies. These frequencies are also important indicators of the onset of instability of the moving masses. Generally insignificant transient part of the solution has to be obtained numerically. The possibility of analysing same situation on finite beams is very important for results validation. In addition, because it is easy to determine vibration modes for beams with abrupt change in foundation stiffness, this additional feature can also be analysed. The main new contribution of this paper is detailed analysis of dynamic amplification effects due to masses proximity and conclusion that, as far as the instability is concerned, its onset is not influenced by increasing number of masses.