Abstract
Natural vibrations of shallow cylindrical shells with rectangular plan and varying thickness are studied using a spline-approximation method developed previously. Computation is carried out for different types of boundary conditions. The effect of the curvature of the midsurface on the natural frequencies is examined. The natural frequencies of shells with constant and varying thickness are compared
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References
A. Ya. Grigorenko, “Calculation of natural vibrations of rectangular plates of varying thickness a method a spline-collocation,” Int. Appl. Mech., 26, No. 12, 116–119 (1990).
Ya. M. Grigorenko, E. I. Bespalova, A. B. Kitaigorodskii, and A. I. Shinkar’, Free Vibrations of Members of Shell Structures [in Russian], Naukova Dumka, Kyiv (1986).
Ya. M. Grigorenko and A. T. Vasilenko, Theory of Shells of Variable Stiffness, Vol. 4 of the five-volume series Methods of Shell Design [in Russian], Naukova Dumka, Kyiv (1981).
L. V. Kurpa and A. V. Chistilina, “Investigation of free vibrations of multilayer shallow shells and plates of complex shape in plan,” Strength of Materials, 35, No. 2, 183–191 (2003).
I. A. Birger and Ya. G. Panovko (ed.), Strength. Stability. Vibrations: A Handbook [in Russian], Vol. 3, Mashinostroenie, Moscow (1968).
P. M. Varvakai and A. F. Ryabov (ed.), A Handbook on the Theory of Elasticity [in Russian], Budivel’nyk, Kyiv (1971).
Ya. M. Grigorenko, A. Ya. Grigorenko, and L. I. Zakhariichehko, “Stress-strain analysis of orthotropic closed and open noncircular cylindrical shells,” Int. Appl. Mech., 41, No. 7, 778–785 (2005).
A. Ya. Grigorenko and T. L. Efimova, “Spline-approximation method applied to solve natural-vibration-problems for rectangular plates of varying thickness,” Int. Appl. Mech., 41, No. 10, 1161–1169 (2005).
Ya. M. Grigorenko, A. Ya. Grigorenko, and L. I. Zakhariichehko, “Stress analysis of noncircular cylindrical shells with cross-section in the form of connected convex half-corrugations,” Int. Appl. Mech., 42, No. 4, 431–438 (2006).
Ya. M. Grigorenko, A. Ya. Grigorenko, and L. I. Zakhariichehko, “Stress—strain solutions for circumferentially corrugated elliptic cylindrical shells,” Int. Appl. Mech., 42, No. 9, 1021–1028 (2006).
J. K. Lee, A. V. Leissa, and A. J. Wang, “Vibrations of blades with variable thickness and curvature by shell theory,” Trans ASME, J. Eng. Gas Turb. Power, 106, 11–16 (1984).
K. M. Liew, C. W. Lim, and S. Kitipornchai, “Vibration of shallow shells: A review with bibliography,” Appl. Mech. Rev., 50, No. 8, 431–444 (1997).
K. M. Liew and C. W. Lim, “Vibratory characteristics of cantilevered rectangular shallow shells of variable thickness,” Inst. Aerounaut. Astronaut. J., 32(2), 387–396 (1998).
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 89–98, April 2007.
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Budak, V.D., Grigorenko, A.Y. & Puzyrev, S.V. Solution describing the natural vibrations of rectangular shallow shells with varying thickness. Int Appl Mech 43, 432–441 (2007). https://doi.org/10.1007/s10778-007-0040-8
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DOI: https://doi.org/10.1007/s10778-007-0040-8