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给出桁架在给定固频约束时 ,动力学优化解存在性的基本理论。指出 :桁架固频约束通常是决定其动力学优化解是否存在的“关键约束”。基此 ,给出了一种工程算法 ,只用到固频对设计变量的一阶导数 ,就可很快确定约束是否可能满足。反之 ,当提出的方法判定给定固频约束不能满足时 ,可以求出一个解存在的极限频率的狭窄范围及相应的设计变量范围 ,以供设计人员重新设计时参考。三个由简到繁的算例说明了所提出方法实用、有效。
The basic theory of the existence of optimal dynamic solution for a truss given a fixed frequency constraint is given. It is pointed out that the truss fixed frequency constraint is usually the “key constraint” that determines the existence of its optimal dynamic solution. Based on this, an engineering algorithm is given, which can quickly determine whether a constraint is likely to be satisfied by using only the first derivative of the fixed frequency for the design variable. Conversely, when the proposed method determines that a given fixed-frequency constraint can not be satisfied, a narrow range of the ultimate frequency of the solution and the corresponding design variable range can be found for reference by the designer when redesigning. Three simple to complex examples illustrate the proposed method is practical and effective.