Geometrically nonlinear random vibrations of structures
Abstract
A finite element formulation combined with stochastic linearization and normal mode methods, including geometrical nonlinearity, have been presented for the study of the random vibration responses of beam, frame, plate (isotropic as well as composite), and shell structures subjected to simultaneously spatial and temporal Gaussian stationary nonwhite and nonzero mean random excitations. Six degrees-of-freedom beam and frame elements and Forty-eight degrees-of-freedom quadrilateral thin shell element (including the plate version) are used in this study. Examples include dynamic random responses of simply supported beams, clamped-clamped beams, a simply supported beam on an elastic foundation, a fixed-end portal frame, simply supported square plate, clamped square plate, cylindrical panel with all edges supported by rigid diaphragms, clamped spherical cap, double-curved panel, simply supported specially orthotropic laminated square plate, simply supported (0$\sp\circ$/90$\sp\circ$) s laminated square plate, simply supported anti-symmetric angle-ply ($\theta$/$-\theta$) laminated square plate, simply supported ($\pm$45$\sp\circ$/90$\sp\circ$/0$\sp\circ$) s laminated anisotropic square plate, and simply supported (45$\sp\circ\sb2$/0$\sp\circ$) s laminated anisotropic square plate subjected to different random loadings. To compare and validate the present solutions and formulation, results are compared with alternative analytical solutions whenever available. Monte Carlo simulation method is also used to generate solutions to compare with some of the present results when alternative solutions are not available. Some linear analytical solutions of simply supported beam and plate under nonwhite and nonzero mean loadings are also derived for comparison. Some linear and nonlinear analytical solutions of simply supported laminated composite plate are also obtained for comparison based on the formulation of isotropic plate.
Degree
Ph.D.
Advisors
Yang, Purdue University.
Subject Area
Aerospace materials
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