This paper considers the optimum structural design of vibrating beams in which the inertial axes and the elastic axes are noncollinear. The condition of noncollinear axes exists in structures having unsymmetric cross-sections. For unsymmetric cross-sections the centroid and the shear center do not coincide. This results in coupling between some of the bending and torsional modes. This paper presents results for the simply supported and cantilever beams with a thin-walled channel cross-section. The minimization of the structural volume subject to multiple frequency constraints and its dual problem of maximization of the fundamental frequency subject to a volume constraint are considered. A quadratic extended interior penalty function with Newton’s method of unconstrained minimization is used in structural optimization. The structures considered have nonstructural masses besides their own mass.
Optimum Synthesis of Thin-Walled Vibrating Beams With Coupled Bending and Torsion
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Grandhi, R. V., and Moradmand, J. K. (December 1, 1989). "Optimum Synthesis of Thin-Walled Vibrating Beams With Coupled Bending and Torsion." ASME. J. Mech., Trans., and Automation. December 1989; 111(4): 555–560. https://doi.org/10.1115/1.3259037
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