Conclusions
A truncated conical shell with free edges can vibrate at resonance both without and with one half-wave along the generatrix. For m=0, the amplitude decreases from the large end faces of the shell toward the small end faces. For m=1, the vibration amplitude decreases from the end faces toward the central portion of the shell. Overlapping of the natural frequencies of various mode shapes of vibration leads to a complex pattern of the node distribution over the shell surface.
The author agrees with Watkins and Clary's [5] remarks concerning the need for a new analytical method of solving dynamic problems for cylindrical and conical shells with allowance for the peculiar features of vibrations for various boundary conditions.
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Literature Cited
D. D. Ul'yanitskii, “Experimental determination of the frequencies and mode shapes of the natural vibrations of the blades of a Kaplan water turbine,” in: Vibrations in Turbines [in Russian], Izd-vo AN SSSR, Moscow (1956).
W. C. L. Hu. “Comments on vibrational characteristics of thin-walled conical frustum shells, AIAA Journal,3, No. 6 (1965).
L. R. Koval, “About vibrational characteristics of thin-walled shells,” AIAA Journal,4, No. 3 (1966).
S. A. Tobias, “A theory of imperfection for the vibration of elastic bodies of revolution,” Engineering,179 (1951).
J. D. Watkins, R. R. Clary, “Vibrational characteristics of thin-walled conical frustum shells,” AIAA Journal,2, 10 (1964).
J. D. Watkins, R. R. Clary, “Reply by authors to W. C. L. Hu,” AIAA Journal,3, No. 6 (1965).
Additional information
Kazan Aviation Institute. Translated from Prikladnaya Mekhanika, Vol. 5, No. 1, pp. 113–117, January, 1969.
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Sal'nikov, G.M. Natural vibrations of truncated conical shells with free edges. Soviet Applied Mechanics 5, 89–92 (1969). https://doi.org/10.1007/BF00886919
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DOI: https://doi.org/10.1007/BF00886919