Clamped-clamped Boundary Conditions for Analysis Free Vibration of Functionally Graded Cylindrical Shell with a Ring based on Third Order Shear Deformation Theory
In this paper a study on the vibration of thin
cylindrical shells with ring supports and made of functionally graded
materials (FGMs) composed of stainless steel and nickel is presented.
Material properties vary along the thickness direction of the shell
according to volume fraction power law. The cylindrical shells have
ring supports which are arbitrarily placed along the shell and impose
zero lateral deflections. The study is carried out based on third order
shear deformation shell theory (T.S.D.T). The analysis is carried out
using Hamilton-s principle. The governing equations of motion of
FGM cylindrical shells are derived based on shear deformation
theory. Results are presented on the frequency characteristics,
influence of ring support position and the influence of boundary
conditions. The present analysis is validated by comparing results
with those available in the literature.
[1] Arnold, R.N., Warburton, G.B., 1948. Flexural vibrations of the walls of
thin cylindrical shells. Proceedings of the Royal Society of London A;
197:238-256.
[2] Ludwig, A., Krieg, R., 1981.An analysis quasi-exact method for
calculating eigen vibrations of thin circular shells. J. Sound vibration;
74,155-174.
[3] Chung, H., 1981. Free vibration analysis of circular cylindrical shells. J.
Sound vibration; 74, 331-359.
[4] Soedel, W., 1980.A new frequency formula for closed circular
cylindrical shells for a large variety of boundary conditions. J. Sound
vibration; 70,309-317.
[5] Forsberg, K., 1964. Influence of boundary conditions on modal
characteristics of cylindrical shells. AIAA J; 2, 182- 189.
[6] Lam, K.L., Loy, C.T., 1995. Effects of boundary conditions on
frequencies characteristics for a multi- layered cylindrical shell. J. Sound
vibration; 188, 363-384.
[7] Loy, C.T., Lam, K.Y., 1996.Vibration of cylindrical shells with ring
support. I.Joumal of Impact Engineering; 1996; 35:455.
[8] Koizumi, M., 1993. The concept of FGM Ceramic Transactions,
Functionally Gradient Materials.
[9] Makino A, Araki N, Kitajima H, Ohashi K. Transient temperature
response of functionally gradient material subjected to partial, stepwise
heating. Transactions of the Japan Society of Mechanical Engineers, Part
B 1994; 60:4200-6(1994).
[10] Anon, 1996.FGM components: PM meets the challenge. Metal powder
Report. 51:28-32.
[11] Zhang, X.D., Liu, D.Q., Ge, C.C., 1994. Thermal stress analysis of axial
symmetry functionally gradient materials under steady temperature field.
Journal of Functional Materials; 25:452-5.
[12] Wetherhold, R.C., Seelman, S., Wang, J.Z., 1996. Use of functionally
graded materials to eliminate or control thermal deformation.
Composites Science and Technology; 56:1099-104.
[13] Najafizadeh, M.M., Hedayati, B. Refined Theory for Thermoelastic
Stability of Functionally Graded Circular Plates. Journal of thermal
stresses; 27:857-880.
[14] Soedel, W., 1981. Vibration of shells and plates. MARCEL DEKKER,
INC, New York.
[15] Loy, C.T., Lam, K.Y., Reddy, J.N., 1999.Vibration of functionally
graded cylindrical shells; 41:309-324.
[16] Najafizadeh, M.M., Isvandzibaei, M.R., 2007. Vibration of functionally
graded cylindrical shells based on higher order shear deformation plate
theory with ring support. Acta Mechanica; 191:75-91.
[1] Arnold, R.N., Warburton, G.B., 1948. Flexural vibrations of the walls of
thin cylindrical shells. Proceedings of the Royal Society of London A;
197:238-256.
[2] Ludwig, A., Krieg, R., 1981.An analysis quasi-exact method for
calculating eigen vibrations of thin circular shells. J. Sound vibration;
74,155-174.
[3] Chung, H., 1981. Free vibration analysis of circular cylindrical shells. J.
Sound vibration; 74, 331-359.
[4] Soedel, W., 1980.A new frequency formula for closed circular
cylindrical shells for a large variety of boundary conditions. J. Sound
vibration; 70,309-317.
[5] Forsberg, K., 1964. Influence of boundary conditions on modal
characteristics of cylindrical shells. AIAA J; 2, 182- 189.
[6] Lam, K.L., Loy, C.T., 1995. Effects of boundary conditions on
frequencies characteristics for a multi- layered cylindrical shell. J. Sound
vibration; 188, 363-384.
[7] Loy, C.T., Lam, K.Y., 1996.Vibration of cylindrical shells with ring
support. I.Joumal of Impact Engineering; 1996; 35:455.
[8] Koizumi, M., 1993. The concept of FGM Ceramic Transactions,
Functionally Gradient Materials.
[9] Makino A, Araki N, Kitajima H, Ohashi K. Transient temperature
response of functionally gradient material subjected to partial, stepwise
heating. Transactions of the Japan Society of Mechanical Engineers, Part
B 1994; 60:4200-6(1994).
[10] Anon, 1996.FGM components: PM meets the challenge. Metal powder
Report. 51:28-32.
[11] Zhang, X.D., Liu, D.Q., Ge, C.C., 1994. Thermal stress analysis of axial
symmetry functionally gradient materials under steady temperature field.
Journal of Functional Materials; 25:452-5.
[12] Wetherhold, R.C., Seelman, S., Wang, J.Z., 1996. Use of functionally
graded materials to eliminate or control thermal deformation.
Composites Science and Technology; 56:1099-104.
[13] Najafizadeh, M.M., Hedayati, B. Refined Theory for Thermoelastic
Stability of Functionally Graded Circular Plates. Journal of thermal
stresses; 27:857-880.
[14] Soedel, W., 1981. Vibration of shells and plates. MARCEL DEKKER,
INC, New York.
[15] Loy, C.T., Lam, K.Y., Reddy, J.N., 1999.Vibration of functionally
graded cylindrical shells; 41:309-324.
[16] Najafizadeh, M.M., Isvandzibaei, M.R., 2007. Vibration of functionally
graded cylindrical shells based on higher order shear deformation plate
theory with ring support. Acta Mechanica; 191:75-91.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:56738", author = "M.Pourmahmoud and M.Salmanzadeh and M.Mehrani and M.R.Isvandzibaei", title = "Clamped-clamped Boundary Conditions for Analysis Free Vibration of Functionally Graded Cylindrical Shell with a Ring based on Third Order Shear Deformation Theory", abstract = "In this paper a study on the vibration of thin
cylindrical shells with ring supports and made of functionally graded
materials (FGMs) composed of stainless steel and nickel is presented.
Material properties vary along the thickness direction of the shell
according to volume fraction power law. The cylindrical shells have
ring supports which are arbitrarily placed along the shell and impose
zero lateral deflections. The study is carried out based on third order
shear deformation shell theory (T.S.D.T). The analysis is carried out
using Hamilton-s principle. The governing equations of motion of
FGM cylindrical shells are derived based on shear deformation
theory. Results are presented on the frequency characteristics,
influence of ring support position and the influence of boundary
conditions. The present analysis is validated by comparing results
with those available in the literature.", keywords = "Vibration, FGM, Cylindrical shell, Hamilton'sprinciple, Ring support.", volume = "4", number = "5", pages = "437-6", }