Parametric instability of glass-plastic cylindrical shells

Dynamic stability of a thin cylindrical shell with top mass subjected to harmonic base-acceleration

“…According to Donnell's assumptions, the nonlinear strain-displacement relations read (Brush and Almroth, 1975;Donnell, 1976)…”

“…(1), the radial displacement field w and the radial imperfection shape w 0 are measured positively inwards. Considering isotropic material properties with elasticity modulus E and Poisson ratio m, the stress resultants and stress couples per unit length are defined by Brush and Almroth (1975) …”

“…Experimental results regarding parametric instabilities of a base excited cylindrical shell with a free top edge (i.e. no top mass) are reported in Bondarenko and Galaka (1977). Results for a base-excited thin beam with top mass can be found in Mallon et al (2006).…”

“…It is well known that under compressive loading, such structures may loose their stability, that is they buckle. The classical static buckling analyses of axially compressed perfect cylindrical shells (based on linearized small deflection theory, see Brush and Almroth, 1975;Yamaki, 1987) predict many closely spaced buckling loads with buckling modes being sinusoidal both in axial direction and in circumferential direction. Experiments on the static buckling of axially compressed cylindrical shells reveal a large scatter in the obtained buckling loads and notorious discrepancies with the results obtained from the classical static buckling analyses (Brush and Almroth, 1975;Arbocz and Starnes, 2002).…”

“…The classical static buckling analyses of axially compressed perfect cylindrical shells (based on linearized small deflection theory, see Brush and Almroth, 1975;Yamaki, 1987) predict many closely spaced buckling loads with buckling modes being sinusoidal both in axial direction and in circumferential direction. Experiments on the static buckling of axially compressed cylindrical shells reveal a large scatter in the obtained buckling loads and notorious discrepancies with the results obtained from the classical static buckling analyses (Brush and Almroth, 1975;Arbocz and Starnes, 2002). Both the inevitable small deviations from the nominal cylindrical shape (geometric imperfections) and the boundary conditions have been widely accepted as contributing to the poor correlation between the experimental results and the classical static buckling results.…”