| 摘 要： | The present paper discusses the minimum weight design pro-blem for Timoshenko and Euler beams subjected to multi-frequ-ency constraints.Taking the simply-supported symmetric beamas an example,we reveal the abnormal characteristics of op-timal Timoshenko beams,i.e.,the frequency corresponding tothe first symmetric vibration mode could be higher than thefrequency of antisymmetric vibration mode if a very thin andhigh strip is suitably formed at the middle of the beam.and,optimal Timoshenko beams subjected to two different sets offrequency constraints could have the same minimum weight.Theabove abnormal characteristics demonstrate the need for in-cluding maximum cross sectional area constraint in the problemformulation in order to have a well-posed problem.
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