The natural frequencies and mode shapes of thin-walled beams constructed of walls, or panels, of advanced composite materials depend upon both the geometry of the cross-section and the mechanical properties of the materials used in the panels. A shear deformation beam theory having the form of a Timoshenko beam theory is used to investigate the influence of these design variables. It is found that the maximum stiffness of a particular beam configuration is obtained when the contributions from the bending and shearing modes of deformation are optimized. Results show the influence of shear deformation even in the fundamental mode of vibration. Simply-supported, cantilever and free-free beams of various cross-sectional shapes and materials are analyzed.
The Influence of Geometric and Material Design Variables on the Free Vibration of Thin-Walled Composite Material Beams
Bank, L. C., and Kao, C. H. (July 1, 1989). "The Influence of Geometric and Material Design Variables on the Free Vibration of Thin-Walled Composite Material Beams." ASME. J. Vib., Acoust., Stress, and Reliab. July 1989; 111(3): 290–297. https://doi.org/10.1115/1.3269855
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