Abstract
The present paper discusses the minimum weight design problem for Timoshenko and Euler beams subjected to multi-frequency constraints. Taking the simply-supported symmetric beam as an example, we reveal the abnormal characteristics of optimal Timoshenko beams, i.e., the frequency corresponding to the first symmetric vibration mode could be higher than the frequency of antisymmetric vibration mode if a very thin and high strip is suitably formed at the middle of the beam, and, optimal Timoshenko beams subjected to two different sets of frequency constraints could have the same minimum weight. The above abnormal characteristics demonstrate the need for including maximum cross sectional area constraint in the problem formulation in order to have a well-posed problem.
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Keng-tung, C., Hua, D. On dynamic optimization of Timoshenko beam. Appl Math Mech 4, 69–77 (1983). https://doi.org/10.1007/BF01896714
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DOI: https://doi.org/10.1007/BF01896714