Models of track vibration representing the rail as a beam are insufficiently detailed for high frequencies where the rail cross-sectional deformation is significant. A double Timoshenko beam model is developed for vertical vibration analysis at high frequencies. Although simple, this model includes the essential cross-sectional deformation of a rail in vertical vibration at high frequencies. Based on this model, the dispersion relation of propagating waves in a free and a continuously supported rail is studied. Vertical vibration receptances of the rail are calculated using both continuously and discretely supported models. The results show good agreement with an FE model and measurement data in terms of frequency-wavenumber curves, point receptance and vibration decay rate.
We present an optimization-based model to gain insights into the integrated inventory and transportation problem for a single-echelon, multi-facility service parts logistics system with time-based service level constraints. As an optimization goal we minimize the relevant inventory and transportation costs while ensuring that service constraints are met. The model builds Shoes Nike FS Lite Run Men Black Fluorescent Green Professional
on stochastic base-stock
inventory model and integrates it with transportation options and service responsiveness that can be achieved using alternate modes Nike Free Sale Run 3 Women Blue Green
(namely slow, medium and fast). The results obtained through different networks show that significant benefits can be obtained from transportation mode and inventory integration.