On the application of the constant deflection-contour method in nonlinear vibrations of elastic plates M. M. Banerjee, G. A. Rogerson Summary This paper concerns the application of the constant deflection-contour method to problems involving nonlinear vibrations. Two specific problems are considered: a clamped circular plate and an annular plate with free inner boundary. For the linear case, the results obtained offer excellent agreement with previous studies, indicating significant potential for the utilization of this method in different nonlinear cases. The analysis may be applied to other types of geometrical structures. Notwithstanding the fact that only a first-term approximation has been made for the deflection function, in conjunction with the Galerkin procedure, excellent agreement has been found. Additional analytical calculations could be made to improve accuracy, indicating that the method could prove particularly useful when employed with a symbolic manipulation package. Keywords Elastic plate, Vibration, Non linearity, Deflection, Large amplitude 1 Introduction The nonlinear analysis of elastic plates has received considerable attention in literature since the 1960’s. However, the number of such studies is relatively few when compared with similar linear investigations. Book [1] provides a detailed study of linear problems, and numerous references of significant contributions, within the linear framework, may be found. The paucity of literature concerning nonlinear (large amplitude) vibration analysis is, probably, due to the fact that the two basic von Karman field equations, extended to the dynamic case, involve the deflection and stress functions in a coupled form. Moreover, these equations are of fourth order, posing analytical problems and more often than not necessitating a numerical approach. Several methods are available to investigate such problems and thereby elucidate nonlinear response for some simpler cases. For one type of method, the analytical difficulties are over- come by using modern high-speed computers and finite element or finite difference methods. An analytical approach, revealing qualitative features, is still preferable, even for some approximate solution wherever possible. Many authors have investigated large amplitude vibrations, mostly for plates and shells having regular shapes, [2–7]. Almost all problems involve a considerable amount of compu- tation. Attempts have always been made to offer new approaches to solve such nonlinear dynamical problems, [8, 9], using Karman-type field equations for solution of plate problems having uncommon boundaries. However, it is a difficult task, which is further complicated Archive of Applied Mechanics 72 (2002) 279–292 Ó Springer-Verlag 2002 DOI 10.1007/s00419-002-0206-0 279 Received 13 June 2001; accepted for publication 6 November 2001 M. M. Banerjee Department of Mathematics, A.C. College, Jalpaiguri-735101, W.B., India G. A. Rogerson (&) Department of Computer and Mathematical Sciences, University of Salford, M5 4WT, UK This work was completed while one of the authors (MMB) visited the University of Salford, UK. The support of the University of Salford and UGC are very gratefully acknowledged. The authors would also like to thank the Referee of the AAM for many perceptive and instructive comments.