关于铁木森柯梁动力优化的讨论

On Dynamic Optimization of Timoshenko Beam

Research Institute of Engineering Mechanics, Dalian Institute of Technology, Dalian

摘要: 本文讨论受到多频率约束的铁木森柯梁和尤拉梁的最小重量设计问题.以对称的简支梁为例,本文揭示了铁木森柯梁的异常特征:如果在梁的中部适当地构造很高的一个薄条,相应于第一对称振形的频率可以高于反对称振型的频率;受到二组不同频率约束的铁木森柯梁很可能有同样的最小重量.这些异常特征说明,为了得到一个良态的问题,有必要将最大横断面积约束包括到问题提法中.

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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