Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Large-amplitude vibrations of doubly-curved shallow shells

M. Amabili*
Dipartimento di Ingegneria Industriale, Università di Parma, 43100 Parma, Italy

  Full Text
Large-amplitude (geometrically non-linear) vibrations of doubly curved shallow shells with rectangular boundary, simply supported at the four edges and subjected to harmonic excitation normal to the surface are investigated. Both Donnell's and Novozhilov's shell theories are used to calculate the elastic strain energy. In-plane inertia and geometric imperfections are taken into account. The solution is obtained by Lagrangian approach. Numerical results are compared to those available in the literature and convergence of the solution is shown. Internal resonances are also studied. Shell stability under dynamic load is also investigated by using continuation method, bifurcation diagram from direct time integration and calculation of the Lyapunov exponents. Interesting phenomena, such as (i) snap-through instability, (ii) subharmonic response, (iii) period doubling bifurcations, and (iv) chaotic behavior with up to four positive Lyapunov exponents, have been observed.

Keywords:  Shells; Curved panels; Double curvature; Nonlinear vibrations; Large-amplitude vibrations; Chaos; Lyapunov exponents

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