DISPERSION OF TORSIONAL WAVES IN INITIALLY STRESSED MULTILAYERED CIRCULAR CYLINDERS A. Cilli a,* and A. Ozturk b Keywords: propagation of torsional waves, initial stress, Murnaghan potential, multilayered cylinder Within the framework of a piecewise homogeneous body model, with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the propagation of torsional waves in prestressed multilayered circular cylinders is investigated. The elasticity relations for cylinder components are given through the Murnaghan potential. The influence of variations in the geometric and mechanical parameters of the cylinders on the dispersion curves is analyzed. Introduction The problem on the propagation of torsional waves in compound circular cylinders has been considered in a number of investigations, such as [1-6] and many others, and solutions to it were obtained within the framework of the classical linear theory of elastodynamics by using a piecewise homogenous body model. The present level of all areas of natural sciences and engineering require investigations of these problems with account of the nonlinear dynamical effects too. Among them, the elastodynamics problems of initially stressed bodies can be mentioned. At present, by the theory of elastodynamics for initially stressed bodies is meant the theory constructed using the linearization principle known from the general nonlinear theory of elasticity or its simplified modifications. Within the framework of certain conditions, the linearized equations make it possible to investigate all kinds of dynamical problems for initially stressed bodies. Almost all the investigations carried out by employing the three-dimensional linearized theory of elastic waves in initially stressed body (TLTEWISB) (except [7-10] and some other listed therein) refer to the influence of the initial stress on the speed and dispersion of various types of waves; see, for example, [11-22]. A systematic analysis of these investigations is given in monographs [23-25] and reviewed in [26, 27]. Most of these studies deal with layered composite materials. There is also a considerable number of investigations on prestressed cylinders. These investigations are analyzed in monographs [19, 23-25]. The pioneer works on wave propagation in prestretched cylinders are the investigations carried out in [18, 20] and some others. But the torsional waves in cylindrical bodies are considered only in [18, 20] and some other papers listed and detailed in [24, 25]. However, only homogeneous circular cylinders are examined in them. Thus, up to now, investigations on wave propagation in prestressed multilayered 227 0191-5665/10/4602-0227 © 2010 Springer Science+Business Media, Inc. a Department of Physics, Faculty of Arts and Sciences, Yildiz Technical University,Davutpasa Campus, Esenler, Is- tanbul 34210, Turkey. b Department of Physics, Gebze Institute of Technology,Gebze, Kocaeli 41400, Turkey. Russian transla- tion published in Mekhanika Kompozitnykh Materialov, Vol. 46, No. 2, pp. 327-338, March-April, 2010. Original article sub- mitted October 6, 2009. *Corresponding author; e-mail: acilli@yildiz.edu.tr . Mechanics of Composite Materials, Vol. 46, No. 2, 2010