Reduced-order models for nonlinear vibrations, based on natural modes: the case of the circular cylindrical shell. (English) Zbl 1327.74073
Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 371, No. 1993, Article ID 20120474, 17 p. (2013).
Summary: Reduced-order models are essential to study nonlinear vibrations of structures and structural components. The natural mode discretization is based on a two-step analysis. In the first step, the natural modes of the structure are obtained. Because this is a linear analysis, the structure can be discretized with a very large number of degrees of freedom. Then, in the second step, a small number of these natural modes are used to discretize the nonlinear vibration problem with a huge reduction in the number of degrees of freedom. This study finds a recipe to select the natural modes that must be retained to study nonlinear vibrations of an angle-ply laminated circular cylindrical shell that the author has previously studied by using admissible functions defined on the whole structure, so that an accuracy analysis is performed. The higher-order shear deformation theory developed by Amabili and Reddy is used to model the shell.
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