Structural Mechanics of Engineering Constructions and BuildingsStructural Mechanics of Engineering Constructions and Buildings1815-52352587-8700Peoples’ Friendship University of Russia (RUDN University)2020610.22363/1815-5235-2018-14-5-404-413Research ArticleInvestigation of the distribution of elastic waves in the composite cylinder with the initial torchGuliyevMugan S<p>Dr Sci. (Phys.-Math.), Professor, Faculty of General Technical Disciplines, Department of Physics</p>a.seyfullayev@yahoo.comSeyfullayevAlizade I<p>Cand. Sci. (Phys.Math.), Chief Research Fellow, Professor Assistant, Department of Wave Dynamics, Institute of Mathematics and Mechanics</p>a.seyfullayev@yahoo.comAbdullayevaJamile N<p>Lecturer, Department of Methodology for Mathematics</p>a.seyfullayev@yahoo.comGanja State UniversityInstitute of Mathematics and Mechanics of the Azerbaijan National Academy of SciencesAzerbaijan State Pedagogical University1512201814540441321122018Copyright © 2018, Guliyev M.S., Seyfullayev A.I., Abdullayeva J.N.2018<p>The aim of work. The work is devoted to the study of the propagation of axisymmetric longitudinal waves in a compound cylinder with initial torsion. Solution technique. The initial stresses in the cylinder are determined using the classical linear theory of elasticity. Methods for solving corresponding problems of intrinsic significance are proposed. Numerical results are given and their analysis is carried out. Results. It was found that the presence of initial torsion in cylinders does not exclude the appearance of an axisymmetric longitudinal and axisymmetric waves in a compound cylinder separately. It is found that, in the absence of initial torsion in the compound cylinder, there are intersection points between the dispersion curves corresponding to the modes of axially symmetric longitudinal and torsional waves. It is shown that in the case when initial torsion takes place on at least one cylinder, the axisymmetric longitudinal and torsional waves can not propagate separately, i.e. there is an interference between these two types of axisymmetric waves in a composite cylinder. Methods for solving the problem are developed and corresponding dispersion equations for a compound cylinder are obtained. Dispersion equations are solved and dispersion curves are obtained, an algorithm is developed for constructing these curves.</p>elastic wavestorsionstressBessel functionMacDonald functionупругие волныкручениенапряжениефункция Бесселяфункция Макдональда[Guz A.N. (2004). Uprugiye volni v telakh s nachalnimi (ostatochnimi) napryajeniyami [Elastic waves in bodies with initial (residual) stresses]. Kiev, A.S.K. Publ., 672. (In Russ.)][Akbarov S.D. (2007). Resent investigations on the dynamical problems of the elastic body with initial (residual) stresses (review). Int. Appl. Mechanics, 43(12), 3–27.][Akbarov S.D., Guliev M.S. (2009). Axisymmetric longitudinal wave propagation in a finite pre-strained compound circular made from compressible materials. CMES – Computer Modeling in Engineering and Sciences, 39(2), 155–177, doi.org/10.1007/s10778-010-0255-y.][Akbarov S.D., Guliev M.S. (2008). Propagation of axisymmetric longitudinal waves in afinitely pre-strained circular cylinder embedded in a finitely pre-strained infinite elastic body. Mechanics of Composite Materials, 44(5), 465–478, doi.org/10.1007/s11029-008-9045-6.][Demiray H., Suhubi E.S. (1970). Small torsional oscilattion in initially twisted circular rubber cylinder. International Jounal of Engineering Sciences, 8, 19–30.][Ozturk A., Akbarov S.D. (2009). Torsional wave propagation in a pre-stressed circular cylinder embedde in a pre-stressed elastic medium. Applied Mathematical Modelling, 33, 3636–3649.][Seyfullayev A.I., Guliyev M.S. (2010). On the axisymmetric wave propagation in a finite restrained compound circular cylinder made from compressible materials. International Journal of Nanosystems, 2(2), 33–42.]