JOURNAL OF SOUND AND VIBRATION Journal of Sound and Vibration 297 (2006) 457–476 Buckling and vibration of polar orthotropic circular plate resting on Winkler foundation U.S. Gupta à , A.H. Ansari, S. Sharma Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247667, India Received 13 July 2004; received in revised form 20 September 2005; accepted 31 January 2006 Available online 10 July 2006 Abstract Buckling and vibrational behavior of polar orthotropic circular plates of linearly varying thickness is presented on the basis of classical plate theory. The plate is resting on Winkler-type foundation. An approximate solution has been obtained by Ritz method, which employs basis functions based upon static deflection of polar orthotropic plates. The effect of elastic foundation and that of orthotropy on the natural frequency of plate has been illustrated for different values of taper parameter, flexibility parameter, in-plane force and nodal diameter. The critical buckling load for clamped and simply supported plates have been obtained. A comparison of results with those available in literature has been presented. r 2006 Elsevier Ltd. All rights reserved. 1. Introduction The increasing use of orthotropic materials in modern aerospace structures has necessitated the study of vibrational characteristics of plate-type components fabricated by these materials. Circular and annular plates are extensively used as structural components for diaphragms and deckplates in launch vehicles. The consideration of thickness variation together with anisotropy not only reduces the size and weight of components, but also meets the desirability of high strength, corrosion resistance and high-temperature performance. A considerable amount of work dealing with vibration of polar orthotropic circular/annular plates of uniform/non-uniform thickness is available in literature and few of them are reported in Refs. [1–11]. The problem of plates resting on an elastic foundation finds application in foundation engineering such as reinforced concrete pavements of high runways, foundation of deep wells, storage tanks and slabs of buildings(Szilard [12, p. 136]). Various models such as Winkler (Chonan [13], Gupta et al. [14] and Liew et al. [15]), Pasternak (Wang and Stephans [16]) and Vlasov (Bhattacharya [17]) have been proposed in the literature. 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.2006.01.073 à Corresponding author. E-mail address: usgptfma@iitr.ernet.in (U.S. Gupta).