Axisymmetric Vibrations of Layered Cylindrical Shells with Cracks
Vibrations of circular cylindrical shells made of
layered composite materials are considered. The shells are weakened
by circumferential cracks. The influence of circumferential cracks
with constant depth on the vibration of the shell is prescribed with the
aid of a matrix of local flexibility coupled with the coefficient of the
stress intensity known in the linear elastic fracture mechanics.
Numerical results are presented for the case of the shell with one
circular crack.
<p>[1] Dimarogonas A.D., Vibration of cracked structures: a state of the art
review, Eng. Fracture Mech.,Vol.55, 1996, pp. 831-857.
[2] Chondros T.G., Dimarogonas A.D., Yao J., A continuous cracked beam
vibration theory,Journal of Sound and Vibration, Vol.215, No.1, 1998,
pp.17-34.
[3] Chondros T.G., Dimarogonas A.D. Vibration of a cracked cantilever
beam,Trans. ASME, J. Vibr. Acoust,Vol. 120, 1998, pp.742-746.
[4] Rizos P.F., Aspragathos N., Dimarogonas A.D., Identification of crack
location and magnitude in a cantilever beam from the vibration
modes,Journal of Sound and Vibration,Vol.138, No.3, 1990, pp. 381-
388.
[5] Liang R.Y., Choy F.K., Hu J., Detection of cracks in beam structures
using measurements of natural frequencies, J. Franklin Inst., Vol.328,
No.4, 1991, pp. 505-518.
[6] Kisa M., Brandon J., Topcu M., Free vibration analysis of cracked
beams by a combination of finite elements and component mode
synthesismethods,Computers and Structures,Vol. 67, 1998, pp. 215-223.
[7] Lellep J., Sakkov E., Bucklingof stepped composite columns,Mechanics
of Composite Meterials,Vol.42, No.1, 2006, pp. 63-72.
[8] Krawczuk M., Ostachowicz W., Damage indicators for diagnostic of
fatigue cracks in structures by vibration measurements – a
Survey,Journalof Theoretical and Applied Mechanics, Vol. 34, No. 2,
1996, pp.307—326.
[9] Ostachowicz W., Krawczuk M., Analysis of the effect of cracks on the
natural frequencies of a cantilever beam, Journal of Sound and
Vibration,Vol.150, No.2, 1991, pp. 191—201.
[10] NikpourK.,Diagnosis of axisymmetric cracks in orthotropic cylindrical
shells by vibration measurement, Compos. Science and Technol.,Vol.
39, pp. 45—61.
[11] Nikpour K., Dimarogonas A., Local compliance of composite cracked
bodies, Composites Sci. and Technology, Vol. 38, 1988, pp. 209-223.
[12] Lellep, J., Roots, L., Vibrations of cylindrical shells with circumferential
cracks, WSEAS Transactions on Mathematics, Vol.9, No.9, 2010, pp.
689 - 699.
[13] L. H. Donnell, Beams, Plates and Shells ,McGraw Hill, 1976.</p>
<p>[1] Dimarogonas A.D., Vibration of cracked structures: a state of the art
review, Eng. Fracture Mech.,Vol.55, 1996, pp. 831-857.
[2] Chondros T.G., Dimarogonas A.D., Yao J., A continuous cracked beam
vibration theory,Journal of Sound and Vibration, Vol.215, No.1, 1998,
pp.17-34.
[3] Chondros T.G., Dimarogonas A.D. Vibration of a cracked cantilever
beam,Trans. ASME, J. Vibr. Acoust,Vol. 120, 1998, pp.742-746.
[4] Rizos P.F., Aspragathos N., Dimarogonas A.D., Identification of crack
location and magnitude in a cantilever beam from the vibration
modes,Journal of Sound and Vibration,Vol.138, No.3, 1990, pp. 381-
388.
[5] Liang R.Y., Choy F.K., Hu J., Detection of cracks in beam structures
using measurements of natural frequencies, J. Franklin Inst., Vol.328,
No.4, 1991, pp. 505-518.
[6] Kisa M., Brandon J., Topcu M., Free vibration analysis of cracked
beams by a combination of finite elements and component mode
synthesismethods,Computers and Structures,Vol. 67, 1998, pp. 215-223.
[7] Lellep J., Sakkov E., Bucklingof stepped composite columns,Mechanics
of Composite Meterials,Vol.42, No.1, 2006, pp. 63-72.
[8] Krawczuk M., Ostachowicz W., Damage indicators for diagnostic of
fatigue cracks in structures by vibration measurements – a
Survey,Journalof Theoretical and Applied Mechanics, Vol. 34, No. 2,
1996, pp.307—326.
[9] Ostachowicz W., Krawczuk M., Analysis of the effect of cracks on the
natural frequencies of a cantilever beam, Journal of Sound and
Vibration,Vol.150, No.2, 1991, pp. 191—201.
[10] NikpourK.,Diagnosis of axisymmetric cracks in orthotropic cylindrical
shells by vibration measurement, Compos. Science and Technol.,Vol.
39, pp. 45—61.
[11] Nikpour K., Dimarogonas A., Local compliance of composite cracked
bodies, Composites Sci. and Technology, Vol. 38, 1988, pp. 209-223.
[12] Lellep, J., Roots, L., Vibrations of cylindrical shells with circumferential
cracks, WSEAS Transactions on Mathematics, Vol.9, No.9, 2010, pp.
689 - 699.
[13] L. H. Donnell, Beams, Plates and Shells ,McGraw Hill, 1976.</p>
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:56560", author = "Larissa Roots", title = "Axisymmetric Vibrations of Layered Cylindrical Shells with Cracks", abstract = "Vibrations of circular cylindrical shells made of
layered composite materials are considered. The shells are weakened
by circumferential cracks. The influence of circumferential cracks
with constant depth on the vibration of the shell is prescribed with the
aid of a matrix of local flexibility coupled with the coefficient of the
stress intensity known in the linear elastic fracture mechanics.
Numerical results are presented for the case of the shell with one
circular crack.
", keywords = "Layered shell, axisymmetric vibration, crack.", volume = "7", number = "7", pages = "1574-4", }
