Natural Vibrations of Open-Variable Thickness Circular Cylindrical Shells in High Temperature Field
Publication: Journal of Aerospace Engineering
Volume 23, Issue 3
Abstract
The feasibility of using the transfer matrix method (TMM) to analyze open-variable thickness circular cylindrical shells exposed to a high-temperature field is explored theoretically. In the approach to the problem, the thermal degradation (TG) of thermoelastic characteristics of the material is considered. Natural frequencies and mode shapes for the cylindrical shells are investigated in detail by combining the vibration theory with the TMM. The governing equations of vibration for this system are expressed by the matrix differential equations, and the coefficient matrices are derived. After the relationship between the transfer matrix and the coefficient matrix is established, the fourth-order Runge-Kutta method is used numerically to solve the matrix equation. Once the transfer matrix of single component has been obtained, the product of each component matrix can compose the matrix of the entire structure. The frequency equations and mode shape are formulated in terms of the elements of the structural matrices. Finite-element numerical simulation has validated the present formulas of natural frequencies. Numerical illustrations, supplying pertinent information on the implications of the TG, are presented for various curvatures, aspect ratios, boundary conditions, and thickness ratios, and the pertinent conclusions are outlined.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The support in this research by the China Postdoctor National Fund through Grant No. UNSPECIFIEDAD4122 awarded in 2008 and Natural Science Foundation of Jiangsu Province through Grant No. UNSPECIFIEDBK2008046 awarded in 2008 to 2011 is deeply acknowledged.
References
Bardell, N. S., and Mead, D. J. (1989). “Free vibration of an orthogonally stiffened cylindrical shell. Part 1: Discrete line simple supports.” J. Sound Vib., 134(1), 29–54.
Bhutani, N., and Loewy, R. G. (1999). “Combined finite-element-transfer matrix method.” J. Sound Vib., 226(5), 1048–1052.
Bogner, F. K., Fox, R. L., and Schmit, L. A. (1967). “A cylindrical shell discrete element.” AIAA J., 5(4), 745–750.
Boyd, D. E. (1969). “Analysis of open noncircular cylindrical shells.” AIAA J., 7(3), 563–565.
Cheung, Y. K., and Cheung, M. S. (1972). “Vibration analysis of cylindrical panels.” J. Sound Vib., 22(1), 59–73.
Dokanish, M. A. (1972). “A new approach for plate vibration: Combination of transfer matrix and finite-element technique.” J. Mech. Des., 94, 526–530.
Gontkevitch, V. S. (1962). “Free vibration of shallow shells.” Transactions Akademii Nauk USSR, 10, 27–27.
Henderson, J. P., and McDaniel, T. J. (1971). “The analysis of curved multi-span structures.” J. Sound Vib., 18(2), 203–219.
Hoff, N. (1958). High temperature effects in aircraft structures, Pergamon Press, New York.
Holzer, H. (1921). Die Berechnung der Drehsenwingungen, Springer, Berlin.
Huiyn, X. (1994). “A combined dynamic finite-element Riccati transfer matrix method for solving nonlinear eigenproblems of vibrations.” Comput. Struct., 53(6), 1257–1261.
Kurt, C. T., and Boyd, D. E. (1971). “Free vibrations of noncircular cylindrical shell segments.” AIAA J., 9(2), 239–244.
Leissa, A. W. (1973). “Vibration of shells.” NASA SP-288, NASA, Washington, D.C.
Librescu, L., Marzocca, P., and Silva, W. A. (2004). “Linear/nonlinear supersonic panel flutter in a high-temperature field.” J. Aircr., 41(4), 918–924.
Lin, Y. K. (1967). Probabilistic theory of structure dynamics, McGraw-Hill, New York.
Lin, Y. K., and McDaniel, T. J. (1969). “Dynamics of beam-type periodic structures.” J. Eng. Mater. Technol., 91, 1133–1141.
Loewy, R. G., Degen, E. E., and Shephard, M. S. (1985). “Combined finite-element-transfer matrix method based on a mixed formulation.” Comput. Struct., 20(1–3), 173–180.
McDaniel, T. J. (1971). “Dynamics of circular periodic structures.” J. Aircr., 8(3), 143–149.
McDaniel, T. J., and Logan, J. D. (1971). “Dynamics of cylindrical shells with variable curvature.” J. Sound Vib., 19(1), 39–48.
McDaniel, T. J., and Murthy, V. R. (1976). “Solution bounds for varying geometry beams.” J. Sound Vib., 44(3), 431–448.
Mead, D. J. (1971). “Vibration response and wave propagation in periodic structures.” J. Eng. Mater. Technol., 93, 783–792.
Mead, D. J., and Gupta, G. S. (1970). “Propagation of flexural waves in infinite, damped rib-skin structures.” AFML TR-70-l3, United States Air Force Report.
Mercer, C. A., and Seavey, C. (1967). “Prediction of natural frequencies and normal modes of skin stringer panel rows.” J. Sound Vib., 6(1), 149–162.
Murthy, V. R., and McDaniel, T. J. (1976). “Solution bounds to structural systems.” AIAA J., 14(1), 111–113.
Murthy, V. R., and Nigam, N. C. (1975). “Dynamics characteristics of stiffened rings by transfer matrix approach.” J. Sound Vib., 39(2), 237–245.
Mustafa, B. A. J., and Ali, R. (1987). “Prediction of natural frequency of vibration of stiffened cylindrical shells and orthogonally stiffened curved panels.” J. Sound Vib., 113(2), 317–327.
Myklestad, N. O. (1945). “New method of calculating natural modes of coupled bending-torsion vibration of beams.” Trans. ASME, 67, 61–67.
Ohga, M., and Shigematus, T. (1987). “Transient analysis of plates by a combined finite-element transfer matrix method.” Comput. Struct., 26(4), 543–549.
Ohga, M., and Takao, H. (1995). “Natural frequency and modes of open cylindrical shells with a circumferential thickness taper.” J. Sound Vib., 183(1), 143–156.
Olson, M. D., and Lindberg, G. M. (1971). “Dynamic analysis of shallow shells with a doubly-curved triangular finite element.” J. Sound Vib., 19(3), 299–318.
Pestel, E. C., and Leckie, F. A. (1963). Matrix methods in elastomechanics, McGraw-Hill, New York.
Petyt, M. (1971). “Vibration of curved plates.” J. Sound Vib., 15(3), 381–395.
Rubin, S. (1964). “Transmission matrices for vibrators and their relation to admittance and impedance.” J. Eng. Mater. Technol., 86, 9–21.
Rubin, S. (1967). “Review of mechanical immittance and transmission matrix concepts.” J. Acoust. Soc. Am., 41, 1171–1179.
Rui, X. T., and Lu, Y. Q. (1995). “Transfer matrix method of vibration of multibody system.” Chinese J. Astronautics, 16(3), 41–47.
Rui, X. T., Sui, W. H., and Shao, Y. Z. (1993). “Transfer matrix of rigid body and its application in multibody dynamics.” Chinese J. Astronautics, 14(4), 82–87.
Sankar, S. (1977). “Extend transfer matrix method for free vibration of shells of revolution.” Shock Vibration Bull., 47, 121–133.
Sen, L., and Chen, H. L. (2006). “The natural vibration of a conical shell with an annular end plate.” J. Sound Vib., 294, 928–943.
Sewall, J. L. (1967). “Vibration analysis of cylindrically curved panels with simply supported or clamped edges and comparison with some experiments.” NASA TND-3791, Langley Research Center, Humpton, Va.
Sheinman, I., and Reichman, Y. A. (1992). “Study of buckling and vibration of laminated shallow curved panels.” Int. J. Solids Struct., 29(11), 1329–1338.
Srinivasan, R. S., and Bobby, W. (1976). “Free vibration of noncircular cylindrical shell panels.” J. Sound Vib., 46(1), 43–49.
Targoff, W. P. (1947). “The associated matrices of bending and coupled bending-torsion vibrations.” J. Aeronaut. Sci., 14, 579–582.
Tesar, A., and Fillo, L. (1988). Transfer matrix method, Kluwer Academic, Dordrecht.
Thomson, W. T. (1950). “Matrix solution of vibration of nonuniform beams.” J. Appl. Mech., 17, 337–339.
Uhrig, R. (1973). Elastostatik und elastokinetik in matrizenschreibweise, Springer, Berlin.
Vosteen, L. F. (1958). “Effect of temperature on dynamic modulus of elasticity of some structural alloys.” NASA TN-4348, Langley Aeronautical Laboratory, Langley Field, Va.
Information & Authors
Information
Published In
Copyright
© 2010 ASCE.
History
Received: Mar 31, 2009
Accepted: Oct 7, 2009
Published online: Nov 9, 2009
Published in print: Jul 2010
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.