The combination of Flüggeʼs shell theory, the transfer matrix approach and the Romberg integration method are used to investigate the free vibration behaviour of stepped orthotropic cylindrical shells. The hoop step on the shell surface is described by a reduced thickness over part of its circumference. Modal displacements of the shell can be described by trigonometric functions and Fourierʼs approach is used to separate the variables. The vibration equations of the shell are reduced to eight first-order differential equations in the circumferential coordinate, and by using the transfer matrix of the shell, these equations can be written in a matrix differential equation. The transfer matrix is derived from the non-linear differential equations of the cylindrical shells by introducing the trigonometric functions in the longitudinal direction and applying the numerical integration in the circumferential direction. The proposed model is used to get the vibration frequencies and the corresponding mode shapes for symmetrical and antisymmetrical type-modes. Computed results indicate the sensitivity of the frequency parameters and the bending deformations to the geometry of stepped shell, and also to the axial and circumferential rigidities of the shell.
Accepté le :
Publié le :
@article{CRMECA_2011__339_11_708_0,
author = {Ahmed Mousa Khalifa},
title = {Exact solutions for the vibration of circumferentially stepped orthotropic circular cylindrical shells},
journal = {Comptes Rendus. M\'ecanique},
pages = {708--718},
publisher = {Elsevier},
volume = {339},
number = {11},
year = {2011},
doi = {10.1016/j.crme.2011.08.001},
language = {en},
}
TY - JOUR AU - Ahmed Mousa Khalifa TI - Exact solutions for the vibration of circumferentially stepped orthotropic circular cylindrical shells JO - Comptes Rendus. Mécanique PY - 2011 SP - 708 EP - 718 VL - 339 IS - 11 PB - Elsevier DO - 10.1016/j.crme.2011.08.001 LA - en ID - CRMECA_2011__339_11_708_0 ER -
Ahmed Mousa Khalifa. Exact solutions for the vibration of circumferentially stepped orthotropic circular cylindrical shells. Comptes Rendus. Mécanique, Volume 339 (2011) no. 11, pp. 708-718. doi : 10.1016/j.crme.2011.08.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2011.08.001/
[1] Stress in Shells, Springer-Verlag, Berlin, 1934
[2] Mathematical Theory of Elasticity, Dover, New York, 1944
[3] The Theory of Sound, Dover, New York, 1945
[4] A.W. Leissa, Vibration of shells, NASA, SP-288, Washington, 1973.
[5] Vibrations of thin circular cylindrical shell, J. Mech. Eng. Sci., Volume 7 (1965), pp. 399-407
[6] Mode shapes and frequencies of clamped-clamped cylindrical shells, AIAA J., Volume 12 (1974), pp. 1755-1756
[7] The Mechanics of Vibrations of Cylindrical Shells, Elsevier, New York, 1988
[8] Vibration analysis of thin cylindrical shells using wave propagation approach, J. Sound Vib., Volume 239 (2001) no. 3, pp. 397-403
[9] A new approach for free vibration of thin circular cylindrical shell, J. Sound Vib., Volume 296 (2006), pp. 91-98
[10] Vibrations of circular cylindrical shells: theory and experiments, J. Sound Vib., Volume 303 (2007), pp. 154-170
[11] Free vibration of thin cylindrical shells with a discontinuity in the thickness, J. Sound Vib., Volume 9 (1969), pp. 373-382
[12] Construction of solutions of the equations for free vibration of a cylindrical shell of variable thickness along the directrix, J. Mech. Solids, Volume 14 (1979), pp. 127-134
[13] Free vibration of circular cylinders of variable thickness, J. Sound Vib., Volume 62 (1979) no. 2, pp. 165-180
[14] Axisymmetric vibrations of cylindrical shell with varying thickness, Bull. Japan Soc. Mech. Eng., Volume 24 (1981), pp. 2122-2132
[15] Free vibration of circular cylindrical shells with axially varying thickness, J. Sound Vib., Volume 147 (1991), pp. 165-180
[16] Exact solutions for vibration of stepped circular cylindrical shells, J. Sound Vib., Volume 299 (2006), pp. 948-964
[17] Axisymmetric transverse vibrations of circular cylindrical shells with variable thickness, J. Sound Vib., Volume 317 (2008), pp. 1035-1041
[18] A study of free vibration of a circumferentially non-uniform cylindrical shell with a four lobed cross section, J. Vib. Control, Volume 17 (2010) no. 8, pp. 1158-1172
[19] On vibrations of heterogeneous orthotropic cylindrical shells, J. Sound Vib., Volume 15 (1971), pp. 235-256
[20] Natural transverse vibrations of cantilever orthotropic cylindrical shells, Prikl. Mekh., Volume 13 (1977) no. 4, pp. 38-44
[21] Natural vibrations of orthotropic cylindrical shells under initial stress, J. Sound Vib., Volume 60 (1978)
[22] Simplified equations and solutions for the vibration of orthotropic cylindrical shells, J. Sound Vib., Volume 87 (1983) no. 4, pp. 555-566
[23] Vibration and stability of orthotropic circular cylindrical shells subjected to axial load, J. Acoust. Soc. Am., Volume 75 (1984) no. 3, pp. 842-848
[24] Calculations of natural frequencies vibration of thin orthotropic composite shells by energy method, J. Composite Materials, Volume 22 (1988) no. 12, pp. 1102-1115
[25] Vibration analysis of orthotropic shells with variable thickness, Comput. Struct., Volume 35 (1990), pp. 239-248
[26] Deformation of orthotropic cylindrical shells with discontinuity in thickness subjected to asymmetric loading, Composite Struct., Volume 30 (1995) no. 1, pp. 69-83
[27] Transfer Matrix Method, Kluwer Academic, Dordrecht, 1988
[28] Stress in Shells, Springer-Verlag, New York, 1973
[29] The Theory of Thin Elastic Shells, P. Noordhoff Ltd., Groningen, The Netherlands, 1964
[30] Elastostatik und Elastokinetikin Matrizenschreibweise, Springer, Berlin, 1973
[31] Vibration of cylindrical shells with intermediate supports, J. Sound Vib., Volume 187 (1995) no. 1, pp. 69-93
[32] Exact solutions for vibration of cylindrical shells with intermediate ring supports, Int. J. Mech. Sci., Volume 44 (2002), pp. 1907-1924
Cité par Sources :
Commentaires - Politique
Ahmed Mousa Khalifa
C. R. Méca (2015)