Natural frequencies and mode shapes of rectangular and circular plates are well studied as they are common for many engineering applications. It is possible to utilize different approximate methods. However implementation of such methods in case of a distributed structural in homogeneity frequently leads to very complex procedure. The goal of the present work is to find comparatively simple solution for clamped rectangular plates with rectangular segment placed on its surface. Such sort of design is very important for installation of equipment on deck and floor. Influence of the in homogeneity on the plate fundamental frequency is explored in the paper. An analytical solution is developed for calculation of fundamental frequency of a clamped rectangular plate. The solution is gathered in a dimensionless form as a function of the plate dimensions and material properties. Influence of an added plinth- like structure on the plate fundamental frequency is considered utilizing two approaches. First one is based on the modal stiffness and mass concept. Another one employs the perturbation method technique. Simulation runs were performed to verify accuracy of the developed methods. Deviation between fundamental frequencies determined by the derived formulas and FEM calculations is within reasonable limits. However formula based on the perturbation approach gives more accurate result. Nonetheless any of the proposed methods can be employed in engineering practice for approximate calculations to determine influence of plinth in homogeneity on the fundamental frequency of the clamped rectangular plate.
展开▼
