Determining capacity of multimodal multi-commodities freight transportation network from critical link volumes

The commodity transportation capacity between all origin-destination （ OD ） pairs over the multimodal multi-commodities freight transportation network （MMFTN） is determined. A multi-ob- jectives mathematical model is formulated for determining the OD capacity over the MMFTN accord- ing to a transporting capacity matrix that increased from the reference matrixes. The corresponding incremental factor for estimating the capacity matrix is obtained via the maximal likelihood estima- tion method that samples data of differences between the estimated commodity volumes and carrying capacities of the critical links. The proposed formulations are tested by an experimental highway and railroad freight transportation network in an existing literature. The relevant results of OD capacities are displayed and applicability of the algorithm is certified.

Analytical analysis for vibration of longitudinally moving plate submerged in infinite liquid domain

The vibration of a longitudinally moving rectangular plate submersed in an infinite liquid domain is studied analytically with the Rayleigh-Ritz method. The liquid is assumed to be incompressible, inviscid, and irrotational, and the velocity potential is used to describe the fluid velocity in the whole liquid field. The classical thin plate theory is used to derive mechanical energies of the traveling plate. As derivative of transverse displacement with respect to time in the compatibility condition equation exists, an exponential function is introduced to depict the dynamic deformation of the moving plate. It is shown that this exponential function works well with the Rayleigh- Ritz method. A convergence study shows a quick convergence speed for the immersed moving plate. Furthermore, the parametric study is carried out to demonstrate the effect of system parameters including the moving speed, the plate location, the liquid depth, the plate-liquid ratio, and the boundary condition. Results show that the above system parameters have significant influence on the vibration characteristics of the immersed moving plate. To extend the study, the method of added virtual mass incremental （AVMI） factor is used. The results show good agreement with those from the Rayleigh-Ritz method.