- INTRODUCTION Plates supported by elastic foundations present very common technical problems in structural and geotechnical engineering. The majority of research work in this area has been done using the classical Winkler model [1] where a coef®cient k called the subgrade reaction of the foundation is employed [2]. Many other models have been used but the Winkler model is often adapted [3] because of its simplicity. The problems of vibrations and stability of beams on elastic foundations by using a Winkler model are solved by several researchers such as Clastornik et al. [4], Eisenberger et al. [5], Eisenberger and Clastornik [6], De Rosa [7] and Ding [3]. Recognizing the behavioural inconsistency of the Winkler model, many researchers attempted to make the model more realistic by providing some interaction among the Winkler springs, and introducing a two parameter foundation model. Despite their simplicity, two parameter foundation models failed to gain acceptance in the engineering community [8] because of their lack of consistency. Dynamic analysis of beams resting on elastic foundations using two parameter models have been performed by Franciosi and Masi [9], De Rosa [10] and Yokoyama [11]. Vlasov and Leont 'ev [12] introduced an improved model by introducing a third parameter, g, to represent the distribution of the displacements in the vertical direction. This Vlasov model is applied to the dynamic analysis of beams on elastic foundations by Ayvaz and DalogAE olu [13] and DalogAE lu and Ayvaz [14]. But no references have been found for the application of a consistent Vlasov model to dynamic analysis of plates resting on elastic foundations subjected to external loads.
The authors have developed a mathematical model for the dynamic analysis of rectangular plates on elastic foundations using three parameters such as k, t, and g. A computer program is coded in FORTRAN for the dynamic out-of-plane response of plates resting on elastic foundations. Rectangular ®nite elements are used to model the plate±soil system and the Newmark-b method is used for time integration. The computational technique is an iterative process which is dependent upon the g parameter. A number of graphs are presented to show the effects of the subsoil depth, plate dimensions, and their ratios on the dynamic response of rectangular plates on elastic foundations subjected to both uniformly distributed load and concentrated load at the center of the plates.