The method of calculating the nonlinear vibrations of shallow shells in fluid is proposed. Normal modes and natural frequencies of linear vibrations in fluid are specified, then the nonlinear vibrations of a shell are expanded in terms of the normal modes of the system. The Shaw–Pierre normal nonlinear modes are determined to get the shell model with the finite number of degrees of freedom.
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V. D. Kubenko and P. S. Koval’chuk, “Nonlinear problems of dynamics of elastic shells partially filled with fluid,” Prikl. Mekh., 36, No. 4, 3–34 (2000).
M. Amabili, F. Pellicano, and M. P. Paidoussis, “Nonlinear vibrations of simply supported, circular cylindrical shells, coupled to quiescent fluid,” J. Fluids Struct., No. 12, 883–918 (1998).
B. Ya. Kantor, V. V. Naumenko, and E. A. Strel’nikova, “Determination of free vibration frequencies and modes of cantilever plates in fluid by the method of integral equations,” in: Proc. of Institute of Applied Mathematics and Mechanics [in Russian] (2001), No. 6, pp. 44–49.
X. X. Hu and T. Tsuiji, “Free vibration analysis of curved and twisted cylindrical thin panels,” J. Sound Vibr., 219, No. 1, 63–68 (1999).
T. Sakiyama, X. X. Hu, H. Matsuda, and C. Morita, “Vibration of twisted and curved cylindrical panels with variable thickness,” J. Sound Vibr., 254, No. 3, 481–502 (2002).
S. Moffatt and L. He, “On decoupled and fully-coupled methods for blade forced response prediction,” J. Fluids Struct., No. 20, 217–234 (2005).
A. Ergin and B. Ugurlu, “Linear vibration analysis of cantilever plates partially submerged in fluid,” J. Fluids Struct., No. 17, 927–939 (2003).
B. Ya. Kantor and E. A. Strel’nikova, Hypersingular Integral Equations in the Continuum Mechanics Problems [in Russian], Novoe Slovo, Kharkov (2005).
V. V. Golubev, Lectures oh the Wing Theory [in Russian], Gostekhteoretizdat, Moscow, Leningrad (1949).
N. M. Gyunter, Potential Theory and Its Application to the Basic Problems of Mathematical Physics [in Russian], Gostekhteoretizdat, Moscow (1953).
A. P. Filippov, Vibrations of Deformable Systems [in Russian], Mashinostroenie, Moscow (1970).
S. N. Yavits, “Investigation of frequency characteristics of impeller blades of PL hydraulic turbines,” Énergomashinostroenie, No. 8, 25–28 (1970).
É. I. Grigolyuk and V. V. Kabanov, Stability of Shells [in Russian], Nauka, Moscow (1978).
N. E. Kochin, I. A. Kibel’, and N. V. Rose, Theoretical Hydromechanics [in Russian], Gosnauchtekhizdat, Moscow, Leningrad (1948).
S. W. Shaw and C. Pierre, “Normal modes for nonlinear vibratory systems,” J. Sound Vibr., 164, 58–124 (1993).
V. A. Yakubovich and V. M. Starzhinskii, Linear Differential Equations with Periodic Coefficients and Their Applications [in Russian], Nauka, Moscow (1972).
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Translated from Problemy Prochnosti, No. 1, pp. 40 – 50, January – February, 2011.
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Breslavskii, I.D., Strel’nikova, E.A. & Avramov, K.V. Free vibrations of a shallow shell in fluid under geometrically nonlinear deformation. Strength Mater 43, 25–32 (2011). https://doi.org/10.1007/s11223-011-9264-2
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DOI: https://doi.org/10.1007/s11223-011-9264-2