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On some treatment of the equations of motion for cylindrical shells based on an improved theory

Zur Berechnung der Eigenfrequenzen von Kreiszylinderschalen bei Berücksichtigung von Schubsteifigkeit und Rotationsträgheit

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Summary

The present paper is concerned with a treatment of the equations for the vibration problem of a cylindrical shell including the effects of shear deformation and rotatory inertia. A method is proposed that reduces the equation system for the improved theory to one containing only three unknowns. The frequencies calculated from the proposed equations are compared with the results from the classical theory and other improved theories for frequency ranges from the 1st up to the 5th mode with regards to the parameters such as shell geometry and wave modes. The comparison is found to be satisfactory for most practical applications.

Übersicht

Die Grundgleichungen für die Schwingungen einer Kreiszylinderschale, bei der die Schubverformung und die Rotationsträgheit berücksichtigt werden, lassen sich durch geeignete Vereinfachungen und Umformungen auf ein System von drei Unbekannten reduzieren. Die ersten fünf Frequenzen werden nach dieser Theorie berechnet und mit den Ergebnissen der klassischen und anderer verbesserter Schalentheorien verglichen. Die numerische Übereinstimmung im betrachteten Parameterbereich (Schalengeometrie, Wellenzahlen) ist gut.

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References

  1. Leissa, A. W.: Vibration of Shells. NASA SP-288 (1973)

  2. Arnold, R. N.; Warburton, G. B.: The Flexural Vibrations of Thin Cylinders. Proc. Inst. Mech. Engrs. 167 (1953) 62–74

    Google Scholar 

  3. Forsberg, K.: Influence of Boundary Conditions on Modal Characteristics of Thin Cylindrical Shells. AIAA J. 2 (1964) 2150–2157

    Google Scholar 

  4. Weingarten, I. V.: Free Vibration of a Thin Walled Cylindrical Shell Subjected to a Bending Moment. AIAA J. 3 (1965) 40–44

    Google Scholar 

  5. Schnell, W.; Hammel, J.: Schwingungen einer Zylinderschale mit freien Rändern. Z. Flugwiss. 21 (1973) 265–268

    Google Scholar 

  6. Naghdi, P. M.; Cooper, R. M.: Propagation of Elastic Waves in Cylindrical Shells, Including the Effects of Transverse Shear and Rotatory Inertia. J. Acoust. Soc. Am. 28 (1956) 56–63

    Google Scholar 

  7. Cooper, R. M.; Naghdi, P. M.: Propagation of Nonaxially Symmetric Waves in Elastic Cylindrical Shells. J. Acoust. Soc. Am. 29 (1957) 1365–1373

    Google Scholar 

  8. Mirsky, I.; Herrmann, G.: Nonaxially Symmetric Motions of Cylindrical Shells. J. Acoust. Soc. Am. 29 (1957) 1116–1123

    Google Scholar 

  9. Greenspon, J. E.: Vibrations of a Thick-Walled Cylindrical Shells-Comparison of the Exact Theory with Approximate Theories. J. Acoust. Soc. Am. 32 (1960) 571–578

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Osaka Prefecture, Mozu-Umemachi, Sakai, 591, Osaka, Japan

    K. Shirakawa

  2. Institut für Mechanik Technische Hochschule Darmstadt, Hochschulstr. 1, D-6100, Darmstadt, Bundesrepublik Deutschland

    W. Schnell

Authors
  1. K. Shirakawa
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  2. W. Schnell
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Shirakawa, K., Schnell, W. On some treatment of the equations of motion for cylindrical shells based on an improved theory. Ing. arch 53, 257–263 (1983). https://doi.org/10.1007/BF00532245

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  • DOI: https://doi.org/10.1007/BF00532245

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