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A Qualitative Analysis of the Nonlinear Dynamic Characteristics of Curved Orthotropic Panels

R. Raouf
Journal / Anthology

Composites Engineering
Year: 1993
Volume: 3
Issue: 12
Page range: 1101-1110

This paper presents a qualitative study of the nonlinear free vibration characteristics of curved, simply supported othotropic panels. The panels are modeled using the Donnell-Mushtari-Vlasov shell relationships. An approximate solution to the resulting nonlinear equations is constructed using the Galerkin procedure in the spatial domain and the Lindstedt-Poincaré perturbation technique in the temporal domain. The combination of these procedures is implemented using the symbolic manipulator Mathematica. The analysis shows that although the transverse displacement may be assumed to have a single mode, the compatibility condition forces the in-plane stress resultants to be multi-modal. It is shown that the type of nonlinearity that the panel exhibits is strictly cubic if either of the axial or circumferential modes is asymmetric. On the other hand, the nonlinearity is both quadratic and cubic for axisymmetric modes. Numerical simulations using various geometric and material properties show that the response of the first modes of the panel could be either hardening or softening depending on the geometric and material properties of the panel. On the other hand, the response of the higher modes for the studies cases is always hardening. Numerical results also suggest that it is possible to tailor the dynamic response of some panels to produce softening or hardening behaviors.

*Engineering > Mechanical and Structural Engineering