The deflection of thin orthotropic rectangular plate under moving loads is a classic problem in solid mechanics. However, the equations are challenging to solve due to their non linearity and complexity. At the same time, this equation is a coupled fourth order partial differential equation having variables and singular coefficients. In this research article, the partial differential equation is converted to a set of coupled second order ordinary differential equations by using a special technique adopted by Shadnam et al., [19]. This transformed set of second order ordinary differential equations is then reduced using modified asymptotic method of Struble and Laplce transformation. The closed form solution is evaluated, resonance conditions are obtained and the results are showed in plotted curves to solve the variations in amplitudes for some varying orthotropic plate parameters with elastically supported ends under moving loads for both cases of moving distributed force and moving distributed mass.

This research article considers the flexural rigidity influence along both x and y axes on the dynamic response of orthotropic rectangular plate resting on constant elastic foundation with elastic end conditions. The orthotropic rectangular plate model is a coupled fourth order partial differential equation having variables and singular coefficients. The solutions to this model are arrived at by reconstructing the fourth order partial differential. This partial differential equation model is converted to a set of coupled second order ordinary differential equations by using a special technique adopted by Shadnam et al., [11]. This set of second order ordinary differential equations is then reduced using modified asymptotic method of Struble. The closed form solution is evaluated, resonance conditions are obtained and the results are showed in plotted curves to depict the influence of flexural rigidities along both x and y axes on the dynamic response of orthotropic rectangular plate resting on constant elastic foundation with elastic end conditions for both cases of moving distributed mass and moving distributed force.

In a typical watershed area such as the Federal University of Technology, Owerri, Nigeria, watershed modelling is essential for the sustainable management of water resources, protection of ecosystems and more. In this study, we will be creating a watershed model for FUTO, this study will also cover other aspects such as estimating the depression-less flow direction, delineating the flow accumulation, extracting realistic drainage network using the Strahler’s stream order method and we will also delineate the watershed’s boundary and identify possible outlets / pour points, using the digital elevation model (DEM) gotten from Alaska satellite facility used as a main data source in combination with the PC version of ArcGIS software (ArcMap 10.7) and then we extract the hydrologic information from the DEM in ArcGIS using Hydrology tools. The estimation of depression-less flow direction is done by filling the digital elevation model (DEM). This includes performing fill on sinks to ensure proper delineation of basins and streams. If the sinks are not filled, a derived drainage network may be discontinuous. After the DEM has been filled, then we can now move on to delineating the flow accumulation in the study area. The results shows that by using watershed function in ArcGIS for watershed flow direction and accumulation in FUTO can be determined. The results also shows the drainage network that was extracted by Strahler’s method, showing different orders of streams and it also shows the watershed boundary and pour point / outlets along the Otamiri River which the watershed drains into. This work simply shows the applicability of GIS as a tool of watershed delineation and drainage extraction.