JOURNAL OF SOUND AND VIBRATION Journal of Sound and Vibration 301 (2007) 495–509 Axisymmetric forced vibrations of an elastic free circular plate on a tensionless two parameter foundation Z. Celep à , K. Gu¨ler Department of Civil Engineering, Faculty of Civil Engineering, Istanbul Technical University, TR-34469 Maslak, Istanbul, Turkey Received 26 July 2004; received in revised form 17 August 2006; accepted 4 September 2006 Available online 22 December 2006 Abstract The static and dynamic responses of a circular elastic plate on a two-parameter tensionless foundation are investigated by assuming that the external load is rotationally symmetric and the plate experiences axially symmetric displacements. In the solution procedure, the vertical displacement of the foundation is determined by the corresponding governing equation, whereas the vertical displacement of the plate is expressed in series in terms of the mode shapes of the completely free circular plate. For the case of complete contact, the corresponding governing equation of the plate incorporated with the edge reaction from the foundation is satisfied through the Galerkin’s approximation technique. The contact radius is obtained by requiring that the surface of the foundation satisfies the corresponding continuity equations. It is shown that the problem displays a highly nonlinear character due to the lift-off of the plate from the foundation and the numerical treatment of the governing equation is accomplished by adopting iterative processes in terms of the contact radius. The governing equation of the problem is solved numerically for the static and dynamic cases and the results are presented in figures to demonstrate the nonlinear behavior of the plate for various values of the parameters of the problem comparatively. r 2006 Elsevier Ltd. All rights reserved. 1. Introduction The response of elastic plates, such as slabs and pavements, on an elastic foundation of earthquake response of footings is structural engineering problem of theoretical and practical interest. It is therefore natural that a large number of studies has been devoted to the subject. Since the soil exhibits a very complex behavior, a number of different foundation models with various degrees of sophistication have been proposed. In the analysis of structures on soil the simplest model is the Winkler model. The Winkler model represents the soil medium as a system of identical but mutually independent elastic springs. The model has various shortcomings. The most serious deficiency of the model is the one pertaining to the independence of the springs. On the other hand, elastic continuum model is a conceptual approach of the infinite soil media. The second model provides much more information on the stresses and deformations within the soil mass than Winkler model. However, this modeling of the soil by semi-infinite elastic continuum model leads to ARTICLE IN PRESS www.elsevier.com/locate/jsvi 0022-460X/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jsv.2006.09.029 à Corresponding author. E-mail address: celep@itu.edu.tr (Z. Celep).