Vibration of Rectangular Plates on Elastic Foundations by Finite Grid Solution

Abstract: Assessment of stress conditions created by vertical or horizontal forces to the supporting medium is a frequent problem of design. In engineering practice, beside static case often dynamic effects must be taken into consideration for plate design problems. Plate vibration solutions have been available for regular geometries for a long time, but it will be necessary to describe the governing equation of motion in a general mathematical form. This is not easy. The intention of this study is to extend analytical solutions of the discrete one-dimensional beam elements resting on elastic foundation for solution of plate vibration problems. The solution can be stated as an extension of the so-called discrete parameter approach where the physical domain is broken down into discrete sub-domains, each endowed with a response suitable for the purpose of mimicking problem at hand.