Abstract
Influence of identical applied initial pressures on the radial surfaces of a hollow cylinder which is compose of materials with first power hypo-elastic constitutive model was investigated. The basic equations of the problem were built up based on the framework of piecewise homogeneous body model with the use of three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB). With the method proposed previously, this problem was then solved numerically. Moreover, the dispersion group velocity of the lowest order mode with different initial pressures was also studied. It can be concluded that the initial pressure and the geometry parameters will induce considerable changes of different degrees in dispersive relation between phase velocity and wave number in opposite trend (positive in initial pressure and negative in thickness).
Similar content being viewed by others
References
CAUCHY A L. Exercise de mathematique [M]. Paris: Bure Feres, 1827.
BIOT M A. Mechanics of incremental deformation [M]. New York: John Wiley, 1965: 260–271.
GUZ A N. Fundamentals of the three-dimensional theory of stability of deformable bodies [M]. Berlin Heidelberg: Springer-Verlag, 1999; 155–256.
AKBAROV S D, GUZ A N. Axisymmetric longitudinal wave propagation in pre-stressed compound circular cylinders [J]. International Journal of Engineering Science, 2004, 42: 769–779.
AKBAROV S D, GULIEV M S. Axisymmetric longitudinal wave propagation in a finite pre-strained compound circular cylinder made from compressible materials [J]. Computer Modeling in Engineering & Sciences, 2009, 39: 155–177.
AKBAROV S D, GULIEV M S. The influence of the finite initial strains on the axisymmetric wave dispersion in a circular cylinder embedded in a compressible elastic medium [J]. International Journal of Mechanical Sciences, 2010, 52: 89–95.
AKBAROV S D, GULIEV M S. Propagation of axisymmetric longitudinal waves in a finitely prestrained circular cylinder imbedded in a finitely prestrained infinite elastic body [J]. Mechanics of Composite Materials, 2008, 44: 465–478.
AKBAROV S D, GULIEV M S, KEPCELER T. Propagation of axisymmetric waves in an initially twisted circular compound bimaterial cylinder with a soft inner and a stiff outer constituents [J]. Mechanics of Composite Materials, 2011, 46: 627–638.
AKBAROV S D, GULIEV M S, KEPCELER T. Dispersion relations of axisymmetric wave propagation in initially twisted bi-material compounded cylinders [J]. Journal of Sound and Vibration, 2011, 330: 1644–1664.
AKBAROV S D, KEPCELER T, EGILMEZ M M. Torsional wave dispersion in a finitely pre-strained hollow sandwich circular cylinder [J]. Journal of Sound and Vibration, 2011, 330: 4519–4537.
OZTURK A, AKBAROV S D. Propagation of torsional waves in a prestretched compound hollow circular cylinder [J]. Mechanics of Composite Materials, 2008, 44: 77–86.
AKBAROV S D, KEPCELER T, EGILMEZ M M, DIKMEN F. Torsional wave propagation in the finitely pre-stretched hollow bi-material compound circular cylinder [J]. Computers Materials & Continua, 2011, 26: 91–109.
OZTURK A, AKBAROV S D. Torsional wave propagation in a pre-stressed circular cylinder embedded in a pre-stressed elastic medium [J]. Applied Mathematical Modelling, 2009, 33: 3636–3649.
KEPCELER T. Torsional wave dispersion relations in a pre-stressed bi-material compounded cylinder with an imperfect interface [J]. Applied Mathematical Modelling, 2010, 34: 4058–4073.
AKBAROV S D, IPEK C. Dispersion of axisymmetric longtudinal waves in a pre-strained imperfectly bonded bi-layered hollow cylinder [J]. Computers Materials & Continua, 2012, 30: 99–144.
AKBAROV S D, IPEK C. The influence of the imperfectness of the interface ionditions on the dispersion of the axisymmetric longitudinal waves in the pre-strained compound cylinder [J]. Computer Modeling in Engineering & Sciences, 2010, 70: 93–121.
COON M D, EVANS R J. Incremental constitutive laws and their associated failure criteria with application to plain concrete [J]. International Journal of Solids and Structures, 1972, 8: 1169–1183.
COON M D, EVANS R J. Recoverable deformation of cohesionless soils [J]. Journal of the Soil Mechanics and Foundations Division, 1971, 97: 375–391.
GAZIS D C. Three-dimensional investigation of the propagation of waves in hollow circular cylinders: I. Analytical foundation [J]. Journal of the Acoustical Society of America, 1959, 31: 568–573.
TRUSDELL C. Hypoelasticity [J]. Indiana University Mathematics Journal, 1955, 4: 83–133.
ERINGEN A C, SUHUBI E S. Elastodynamics, Vol. I [M]. New York: Academic, 1974: 246–295.
FOLLAND G B. Fourier analysis and its applications [M]. Calif: Pacific Grove, 1992: 127–143.
BURDEN R L, FAIRES J D. Numerical analysis [M]. 9th ed. Brooks Cole: Cengage Learning, 2010: 48–54.
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item: Project(51378463) supported by National Natural Science Foundation of China
Rights and permissions
About this article
Cite this article
Hu, Wt., Xia, Td. & Chen, Wy. Influence of lateral initial pressure on axisymmetric wave propagation in hollow cylinder based on first power hypo-elastic model. J. Cent. South Univ. 21, 753–760 (2014). https://doi.org/10.1007/s11771-014-1998-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11771-014-1998-0