Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

An analytical solution for finitely long hollow cylinder subjected to torsional impact

  • Wang, X. (Department of Engineering Mechanics, The School of Civil Engineering and Mechanics, Shanghai Jiaotong University) ;
  • Wang, X.Y. (Department of Engineering Mechanics, The School of Civil Engineering and Mechanics, Shanghai Jiaotong University) ;
  • Hao, W.H. (Department of Engineering Mechanics, The School of Civil Engineering and Mechanics, Shanghai Jiaotong University)
  • Received : 2003.08.11
  • Accepted : 2004.10.21
  • Published : 2005.02.20
⟨ Previous Next ⟩

Abstract

An analytical method is presented to solve the elastodynamic problem of finitely long hollow cylinder subjected to torsional impact often occurs in engineering mechanics. The analytical solution is composed of a solution of quasi-static equation satisfied with the non-homogeneous boundary condition and a solution of dynamic equation satisfied with homogeneous boundary condition. The quasi-static solution is obtained directly by solving the quasi-static equation satisfied with the non-homogeneous boundary condition. The solution of the non-homogeneous dynamic equation is obtained by means of finite Hankel transform on the radial variable, r, Laplace transform on time variable, t, and finite Fourier transform on axial variable, z. Thus, the solution for finitely long, hollow cylinder subjected to torsion impact is obtained. In the calculating examples, the response histories and distributions of shear stress in the finitely long hollow cylinder subjected to an exponential decay torsion load are obtained, and the results have been analyzed and discussed. Finally, a dynamic finite element for the same problem is carried out by using ABAQUS finite element analysis. Comparing the analytical solution with the finite element solution, it can be found that two kinds of results obtained by means of two different methods agree well. Therefore, it is further concluded that the analytical method and computing process presented in the paper are effective and accurate.

Keywords

References

  1. Armenaakas, A.E. (1965), 'Torsional waves in composite rods', J. Acoustical Soc. Am., 38, 439-446 https://doi.org/10.1121/1.1909709
  2. Carcione, J.M. and Seriani, G. (1998), 'Torsional waves in lossy cylinders', J. Acoustical Soc. Am., 103, 760-765 https://doi.org/10.1121/1.421199
  3. Carcione, J.M. and Flavio, P. (2000), 'Simulation of stress waves in attenuating drill strings including piezoelectric sources and sensors', J. Acoustical Soc. Am., 108, 53-64 https://doi.org/10.1121/1.429443
  4. Cho, H., Kardomateas, G.A. and Valle, C.S. (1998), 'Elastodynamic solution for the thermal shock stress in an orthotropic thick cylinder shell', J. Appl. Mech., ASME, 65(1), 184-193 https://doi.org/10.1115/1.2789024
  5. Cinelli, G. (1965), 'An extension of the finite Hankel transform and application', Int. J. Engng. Sci., 3, 539-550 https://doi.org/10.1016/0020-7225(65)90034-0
  6. Cinelli, G. (1966), 'Dynamic vibrations and stress in the elastic cylinders and spheres', J. Appl. Mech., ASME, 825-830
  7. Clark, S.K. (1956), 'Torsional wave propagation in hollow cylindrical bars', J. Acoustical Soc. Am., 28, 1163-1165 https://doi.org/10.1121/1.1908581
  8. Eringen, A.C. and Suhubi, E.S. (1975), Elastodynamics, Vol. 2, (Linear Theory) Academic Press. New York
  9. Gazis, D.C. (1959a), 'Three-dimensional investigation of the propagation of waves in hollow circular cylinders, 1. Analytic foundation', J. Acoustical Soc. Am., 31, 568-573 https://doi.org/10.1121/1.1907753
  10. Gazis, D.C. (1959b), 'Three-dimensional investigation of the propagation of waves in hollow circular cylinders, II. Analytic foundation', J. Acoustical Soc. Am., 31, 573-578 https://doi.org/10.1121/1.1907754
  11. Haines, D.W. and Lee, P.C.Y (1971), 'Approximate theory of torsional wave propagation in elastic circular composite cylinders', J. Acoustical Soc. Am., 49, 211-219 https://doi.org/10.1121/1.1912319
  12. Kim, J.O. and Haim, H.H. (1991), 'Torsional stress waves in a circular cylinder with a modulated surface', J. Appl. Mech., ASME, 58, 710-715 https://doi.org/10.1115/1.2897252
  13. Lighthill, M.J. (1958), An Introduction to Fourier Analysis and Generalized Function, Cambridge University Press
  14. Liu, C.G. and Wang, D. (1995), 'Spread problem on torsion wave in a infinite long elastic hollow cylinder', Science Publisher in China
  15. Pao, Y.H. and Ceranoglu, A.N. (1978), 'Determination of transient responses of a thick-walled spherical shell by the ray theory', J. Appl. Mech., ASME, 45, 114-122 https://doi.org/10.1115/1.3424212
  16. Soldatos, K.P. and Ye, J.Q. (1994), 'Wave propagation in anisotropic laminated hollow cylinders of infinite extent', J. Acoustics Soc. Am., 96(5), 744-752
  17. Wang, X., Zhang, K. and Zhang, W. (2000), 'Theoretical solution and finite element solution for an orthotropic thick cylindrical shell under impact load', J. Sound Vib., 236, 129-140 https://doi.org/10.1006/jsvi.2000.2961

Cited by

  1. Transient torsional wave in finite hollow cylinder with initial axial stress vol.21, pp.6, 2008, https://doi.org/10.1007/s10338-008-0864-8