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http://dx.doi.org/10.12989/sem.2019.72.5.597

Dispersion of axisymmetric longitudinal waves in a "hollow cylinder + surrounding medium" system with inhomogeneous initial stresses  

Akbarov, Surkay D. (Yildiz Technical University, Faculty of Mechanical Engineering, Department of Mechanical Engineering)
Bagirov, Emin T. (Institute of Mathematics and Mechanics of National Academy of Sciences of Azerbaijan)
Publication Information
Structural Engineering and Mechanics / v.72, no.5, 2019 , pp. 597-615 More about this Journal
Abstract
The paper studies the dispersion of the axisymmetric longitudinal wave propagating in the "hollow cylinder + surrounding medium" system with inhomogeneous initial stresses caused by the uniformly distributed radial compressional forces acting at infinity. Up to now in the world literature, there exist only a few investigations related to the wave dispersion in a hollow cylinder with inhomogeneous initial stresses. Therefore, this paper is one of the first attempts in this field in the sense of the development of investigations for the case where the cylinder is surrounded with an infinite medium. The three-dimensional linearized theory of elastic waves is used for describing the considered wave propagation problem and, for a solution to the corresponding mathematical problem, the discrete-analytical solution method is developed and employed. The corresponding dispersion equation is obtained and this equation is solved numerically and, as a result of this solution, the dispersion curves are constructed for the first and second modes. By analyzing these curves, the character of the influence of the inhomogeneous initial stresses on the dispersion curves is established. In particular, it is established that as a result of the inhomogeneity of the initial stresses both new dispersion curves and the "band gap" for the wave frequencies can appear.
Keywords
inhomogeneous initial stresses; "hollow cylinder + surrounding medium" system; discrete-analytical method; wave dispersion; dispersion curves; band gap;
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Times Cited By KSCI : 5  (Citation Analysis)
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1 Pozhuev, V.I. (1980), "Reaction of a cylindrical shell in a transversely isotropic medium when acted upon by a moving load", Soviet. App. Mech., 16(11), 958-964. https://doi.org/10.1007/BF00884875.   DOI
2 Abdulkadirov, S.A. (1981), "Low-frequency resonance waves in a cylindrical layer surrounded by an elastic medium", J. Min. Sci., 80, 229-234.
3 Akbarov, S.D. (2006), "Frequency response of the axisymmetrically finite pre-stretched slab from incompressible functionally graded material on a rigid foundation", Int. J. Eng. Sci., 44, 93-112. https://doi:10.1016/j.ijengsci.2005.10.003.   DOI
4 Akbarov, S.D. (2015), Dynamics of Pre-strained Bi-material Elastic Systems: Linearized Three-dimensional Approach, Springer, Heidelberg, New York, U.S.A.
5 Akbarov, S.D. (2018), "Forced vibration of the hydro-viscoelastic and -elastic systems consisting of the viscoelastic or elastic plate, compressible viscous fluid and rigid wall: A review", Appl. Comput. Math., 17(3), 221-245.
6 Akbarov, S.D. and Bagirov, E.T. (2019). "Axisymmetric longitudinal wave dispersion in a bi-layered circular cylinder with inhomogeneous initial stresses", J. Sound Vib., 450, 1-27. https://doi.org/10.1016/j.jsv.2019.03.003.   DOI
7 Akbarov, S.D. and Mehdiyev, M.A. (2018b), "The interface stress field in the elastic system consisting of the hollow cylinder and surrounding elastic medium under 3D non-axisymmetric forced vibration", CMC: Comput. Mater. Contin., 54(1), 61-81. http://doi:10.3970/cmc.2018.054.061.
8 Akbarov, S.D., Guliyev, H.H. and Yahnioglu, N. (2017), "Three-dimensional analysis of the natural vibration of the three-layered hollow sphere with middle layer made of FGM", Struct. Eng. Mech., 61(5), 563-576. http://dx.doi.org/10.12989/sem.2017.61.5.563.   DOI
9 Akbarov, S.D., Guliyev, H.H., Sevdimaliyev, Y.M. and Yahnioglu, N. (2018), "The Discrete-Analytical Solution Method for Investigation Dynamics of the Sphere with Inhomogeneous Initial Stresses", CMC: Cont. Mater. Comp. 55(2), 359-380. http://doi:10.3970/cmc.2018.00173.
10 Akbarov S.D. and Mehdiyev M.A. (2018a), "Influence of initial stresses on the critical velocity of the moving load acting in the interior of the hollow cylinder surrounded by an infinite elastic medium", Struct. Eng. Mech., 66(1), 45-59. http://dx.doi.org/10.12989/sem.2018.66.1.045.   DOI
11 Akbarov S.D. and Guliev M.S. (2010), "The influence of the finite initial strains on the axisymmetric wave dispersion in a circular cylinder embedded elastic medium", Inter. J. Mech. Sci., 52, 89-95. https://doi.org/10.1016/j.ijmecsci.2009.10.012.   DOI
12 Shearer, I.D. Abrahams,W.J. Parnell, C.H. Daros, (2013), "Torsional wave propagation in a pre-stressed hyperelastic annular circular cylinder", Q. J. Mech. Appl. Math., 66, 465-487. https://doi:10.1093/qjmam/hbt014.   DOI
13 Watson, G.N. (1966), A Treatise on the Theory of Bessel Functions, Cambridge University Press, United Kingdom.
14 Wu, B., Su, Y., Liu, D., Chen, W. and Zhang, C. (2018), "On propagation of axisymmetric waves in pressurized functionally graded elastomeric hollow cylinders", J. Sound Vib., 421, 17-47. https://doi.org/10.1016/j.jsv.2018.01.055.   DOI
15 Akbarov, S.D. and Mehdiyev, M.A. (2018c), "Dynamics of the system consisting of the hollow cylinder and surrounding infinite elastic medium under action an oscillating moving load on the interior of the cylinder", Coupl. Syst. Mech., 7(5), 525-554. https://doi.org/10.12989/csm.2018.7.5.525.   DOI
16 Akbarov, S.D., Mehdiyev, M.A. and Ozisik, M. (2018), "Three-dimensional dynamics of the moving load acting on the interior of the hollow cylinder surrounded by the elastic medium", Struct. Eng. Mech., 67(2), 185-206. https://doi.org/10.12989/sem.2018.67.2.185.   DOI
17 Engin, H. and Suhubi, E.S. (1978), "Torsional oscillations of an infinite cylindrical elastic tube under large internal and external pressure, Int. J. Eng. Sci., 16, 387-396. https://doi.org/10.1016/0020-7225(78)90028-9.   DOI
18 Yuan, Z., Bostrom, A. and Cai, Y. (2017), "Benchmark solution for vibration from a moving point source in a tunnel embedded in a half-space", J. Sound Vib., 387, 177-193. https://doi.org/10.1016/j.jsv.2016.10.016.   DOI
19 Batra, R.C. and Bahrami, A. (2009), "Inflation and eversion of functionally graded non-linear elastic incompressible circular cylinders", Int. J. Non-Lin. Mech., 44, 311-323. https://doi.org/10.1016/j.ijnonlinmec.2008.12.005.   DOI
20 Chen, W.Q., Liu, D.Y., Kitipornchai, S. and Yang, J. (2017), "Bifurcation of pressurized functionally graded elastomeric hollow cylinders", Compos. Part B Eng., 109, 259-276. https://doi.org/10.1016/j.compositesb.2016.10.063.   DOI
21 Eringen, A.C. and Suhubi, E.S. (1975), Elastodynamics, Finite Motion, Vol. I; Linear Theory, Vol. II, Academic Press, New-York, U.S.A.
22 John, F. (1960), "Plane strain problems for an elastic material of harmonic type", Common Pur. Appl. Mathem., 13(2), 239-296. https://doi.org/10.1002/cpa.3160130206.   DOI
23 Guz, A.N. (1986a), Elastic waves in bodies with initial stresses: Vol. 1. General questions, Naukova Dumka, Kiev, Ukraine.
24 Guz, A.N. (1986b), Elastic Waves in Bodies with Initial Stresses: Vol. 2. Propagation Laws, Naukova Dumka, Kiev, Ukraine.
25 Guz, A.N. (1999), Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer, Berlin, Germany.
26 Guz, A.N. (2004), Elastic Waves in Bodies With Initial (residual) Stresses, A.C.K. Kiev, Ukraine.
27 Hussein, M.F.M., Francois, S., Schevenels, M., Hunt, H.E.M., Talbot, J.P. and Degrande, G. (2014), "The fictitious force method for efficient calculation of vibration from a tunnel embedded in a multi-layered half-space", J. Sound Vib., 333, 6996-7018. https://doi.org/10.1016/j.jsv.2014.07.020.   DOI
28 Negin, M. (2018), "Seismic surface waves in a pre-stressed imperfectly bonded covered half-space", Geomech. Eng., 16(1), 11-19. http://dx.doi.org/10.12989/gae.2018.16.1.011.   DOI
29 Hasheminejad, S.M. and Komeili, M. (2009), "Effect of imperfect bonding on axisymmetric elastodynamic response of a lined circular tunnel in poroelastic soil due to a moving ring load", Int. J. Solid Str., 46, 398-411. https://doi.org/10.1016/j.ijsolstr.2008.08.040.   DOI
30 Li, G.Y., He, Q., Mangan, R., Xu, G.Q., Mo, C., Luo, J.M., Destrade, M. and Cao, Y.P. (2017), "Guided waves in pre-stressed hyperelastic plates and tubes: application to the ultrasound elastography of thin-walled soft materials", J. Mech. Phys. Solids 102, 67-79. https://doi.org/10.1016/j.jmps.2017.02.008.   DOI
31 Ozisik, M., Mehdiyev, M.A. and Akbarov, S.D. (2018), "The influence of the imperfectness of contact conditions on the critical velocity of the moving load acting in the interior of the cylinder surrounded with elastic medium", CMC: Comput. Mater. Contin., 54(2), 103-136. http://doi:10.3970/cmc.2018.054.103.
32 Parnes, R. (1969), "Response of an infinite elastic medium to traveling loads in a cylindrical bore", J. Appl. Mech., Trans., ASME, 36(1), 51-58. https://doi.org/10.1115/1.3564585.   DOI
33 Parnes, R. (1980), "Progressing torsional loads along a bore in an elastic medium", Int. J. Sol. Struct., 36(1), 653-670. https://doi.org/10.1016/0020-7683(80)90024-4.   DOI
34 Parnes, R. (1981), "Dispersion relation of waves in a rod embedded in an elastic medium", J Sound. Vibr., 76(1), 65-75. https://doi.org/10.1016/0022-460X(81)90291-1.   DOI