LOCALIZED FORMS OF PARAMETRIC VIBRATIONS OF A CYLINDRICAL SHELL LAYING ON A NON-HOMOGENEOUS ELASTIC FOUNDATION

Mihasev G.I., Vitebsk State University, Vitebsk, Belarus, This email address is being protected from spambots. You need JavaScript enabled to view it.

The problem on the parametric vibrations of a thin, long cylindrical shell lying on an elastic foundation under action of compressive static axial forces and pulsing pressure is considered. Under an assumption that a thickness and physical characteristics of the shell as well as a foundation factor of an elastic basis are functions of a longitudinal coordinate, solutions of the Flugge type equations are constructed in the form of functions decaying far from some parallel on the shell surface.

Parametric vibrations, cylindrical shell, elastic foundation, static axial forces

• Yao John C. Dynamic stability of cylindrical shells under static and periodic axial and radial loads. AIAA Journal, 1963, Vol. 1, no. 6, pp. 1391-1396.
• Vijayaraghavan A., Evan-Iwanowski Parametric instability of circular cylindrical shells. Trans. ASME, 1967, Ed. 34, no. 4, pp. 985-990.
• Mikhasev G.I. Free and parametric vibrations of cylindrical shells under static and periodic axial loads. Technische Mechanik [Technical mechanics], 1997, Vol.17, Part 3, pp. 209-216.
• Kuntsevich S.P., Mikhasev G.I. Parametric Vibrations of Viscoelastic Cylindrical Shell under Static and Periodic Axial Loads. Technische Mechanik [Technical mechanics], 1999, Vol. 19, Part 3, pp. 187-195.
• Kuntsevich S.P., Mikhasev G.I Lokal'nye parametricheskie kolebanija nekrugovoj konicheskoj obolochki pod dejstviem neodnorodnogo pul'sirujushhego davlenija [Local parametric vibrations of a non-circular conical shell under uniform pulsating pressure]. Izv. RAN. Mehanika tverdogo tela [Bulletin of the Academy of Sciences. Mechanics of solid body], 2002, no. 3. pp. 156-163.
• Tovstik P.E. Dvumernye zadachi ustojchivosti i kolebanij obolochek nulevoj gaussovoj krivizny [Two-dimensional problems of stability and vibrations of shells of zero Gaussian curvature]. Dokl. AN SSSR [Report of the Academy of Sciences of the USSR], 1983, Vol. 271, no. 1, pp. 69-71.
• Mihasev G.I. O vozmozhnyh lokalizovannyh formah sobstvennyh kolebanij dlinnyh predvaritel'no naprjazhennyh neodnorodnyh cilindricheskih obolochek [On the possible localized forms of natural oscillations of long prestressed nonuniform cylindrical shells]. Mezhved. sb. nauch.-metod. st. Bel. nac. tehn. un-t. [Interdepartmental collection of scientific and methodological articles. BNTU]. Minsk, 2006, Ed. 21, pp. 117-122.
• Mihasev G.I. K issledovaniju izgibnyh voln v beskonechnoj obolochke vrashhenija [On the study of flexural waves in the endless rotation of the shell]. Prikl. mat. i meh. [Applied mathematics and mechanics], 1966, Vol. 32, no. 7. pp. 60-64.
• Yao John C. Nonlinear elastic buckling and parametric excitation of a cylinder under axial loads. Trans. ASME, 1965, Ed. 32, no. 1, pp. 109-115.