Previous results, which indicate reduced propogation along the rail due to stiffer pads [1], and yet the increased parametric excitation due to the same [1], suggest the possibility of an optimal pad stiffness. Results also indicate thatparametric excitation becomes more broad-banded by adding randomness to the pad stiffness [6], while this same randomness will likely broaden the stop-bands [3]; thus, an optimum tolerance is also suggested. This paper, in anticipation of seeking suchoptima, provides methodology to analyze the randomness. The random stiffness of the rail foundation is regarded as the superposition of a noise spectrum of wavenumber contributions; from these, the broad-band parametric excitation is obtained as thesidebands from the various modulations of the fundamental solution. Finally, to lend confidence to eventual optimization results, refinement of the model for roughness-induced vibration is attempted: a correction term incorporating a 2nd parametricexcitation, arising from the contact stiffness variation along the rail, as well as a theoretical 'geometric' filter, is derived.
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