We propose an algorithm for the evaluation of frequencies and forms of natural vibrations of a thin-walled circular cylindrical shell reinforced by a transverse annular elastic rib of small width with regard for the presence of discontinuities of the first kind in the force factors acting on the line of contact of the rib with the shell. To construct approximate solutions of the analyzed spectral problem, we use the variational method in combination with the partition of the domain of definition of the required functions into regular subdomains in each of which the displacements, forces, and moments have the properties of continuity and differentiability. The Ritz method proposed for the solution of the analyzed problem guarantees convergence in the uniform metric for displacements and the force factors of elastic shell.
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References
V. A. Zarutskii, “Theory and methods for the determination of the stress-stain state of ribbed shells,” Prikl. Mekh., 36, No. 10, 3–24 (2000).
A. M. J. Al-Najafi and G. B. Warburton, “Free vibration of ring stiffened cylindrical shells,” J. Sound Vibrat., 13, 9–25 (1970).
C. M. Wang, S. Swaddiwudhipong, and J. Tian, “Ritz method for vibration analysis of cylindrical shells with ring stiffeners,” J. Eng. Mech., 123, 134–142 (1997).
X. Qu, X. Chen, X. Long, H. Hua, and G. Meng, “A modified variational approach for vibration analysis of ring-stiffened conicalcylindrical shell combinations,” Europ. J. Mech. A Solids, 37, 200–215 (2013).
Yu. Yu. Shveiko and A. D. Brusilovskii, “On the natural vibrations of cylindrical shells reinforced by transverse ribs,” Raschet. Prochn., Issue 15, 312–327 (1971).
V. Z. Vlasov, General Theory of Shells and Its Applications in Engineering [in Russian], Gostekhizdat, Moscow (1949).
V. V. Novozhilov, Theory of Thin Shells [in Russian], Sudpromgiz, Leningrad (1962).
G. D. Galletly, “On the in-vacuo vibrations of simply reinforced, ring-stiffened cylindrical shells,” U.S. Nat. Congr. Appl. Mech., No. 2, 225–231 (1965).
Yu. V. Trotsenko, “Determination of the frequencies and modes of natural oscillations of liquids in composed vessels,” Nelin. Kolyv., 18, No. 1, 120–132 (2015); English translation: J. Math. Sci., 215, No. 3, 395–407 (2016).
Yu. V. Trotsenko, “Vibrations of elastic shells of revolution partially filled with ideal liquid,” Nelin. Kolyv., 20, No. 1, 127–144 (2017); English translation: J. Math. Sci., 229, No. 4, 470–486 (2018).
V. A. Trotsenko and Yu. V. Trotsenko, “Solution of a problem of free vibrations of a nonclosed shell of revolution under conditions of its singular perturbation,” Nelin. Kolyv., 8, No. 3, 415–432 (2005); English translation: Nonlin. Oscillat., 8, No. 3, 414–429 (2005).
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Translated from Neliniini Kolyvannya, Vol. 25, No. 1, pp. 89–107, January–March, 2022.
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Trotsenko, V.A., Trotsenko, Y.V. Free Vibrations of a Cylindrical Shell Reinforced by an Elastic Annular Rib. J Math Sci 274, 94–113 (2023). https://doi.org/10.1007/s10958-023-06573-0
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DOI: https://doi.org/10.1007/s10958-023-06573-0