In this work, polynomial deflection expression was used in the free-vibration investigation of thick rectangular plates with two different boundary conditions; one with its four edges clamped denoted with the acronym (CCCC) and another with two adjacent edges fixed and having simple supports at the other two adjacent edges denoted with the acronym (CCSS). The edge conditions of the various plates were fulfilled and used in generating the stiffness coefficients which were substituted into the analytical equation to obtain the non-dimensional frequency functions for the plates at different span-depth ratio (a/t) and aspect ratio (b/a). It was observed that at the same value of (b/a), there is an increase in the value of the non-dimensional frequency parameter as (a/t) increases. Also, at the same value of (a/t), there is a decrease in the value of the non-dimensional frequency parameter as (b/a) increases. The results obtained for the all edges clamped plate were compared with similar works by other researchers in the literature and were found to follow similar pattern and trend and were quite close.

California bearing ratio (CBR) is an important property used to express the quality and strength of the unbound granular materials. Moreover, it is one of the material inputs for the empirical pavement design procedure. CBR is also conducted on the unbound materials for the quality control/quality assurance during construction. Because of its importance, this paper presents a mathematical approach to the problem of estimating the strength of local sand-aggregate material usually obtained from riverbed and banks and used as subbase layer for road construction. Based on simple and easy to determine physical parameters such as particles size distribution, modified proctor dry density (MDD), and moisture content, such estimation could be determined. The study can help in understanding the nature and the properties of sand-aggregate mixture and provide a reasonable and simple statistical method for assessing the strength from simple physical tests, and assist in considerable reduction of the bulk testing of samples on a project, thus affect economy, choice of material and quality control. The model obtained is capable to explain 73% of the variation in log CBR predicted from gradation and density parameters.