结构振动的鲁棒可靠性

以传统的结构振动概率设计方法为基础,用区间集(超长方体)将不确定变量定量化,降低了传统的概率统计方法对统计特性的过分要求,通过区间参数摄动法得到固有频率所在的区间集,建立了激振力频率与结构固有频率干涉的非概率模型,给出了结构振动鲁棒可靠性准则.振动鲁棒可靠性的度量是通过结构避免发生共振所允许的不确定量的大小来体现的.结构所能承受的不确定度越大就越可靠,反之就不可靠,在数学模型上表现为激振力频率区间集与结构固有频率区间集的偏序关系.通过数值算例表明了所提出的结构振动非概率鲁棒可靠性准则的可行性. 

Robust reliability of structural vibration

Based on the conventional probabilistic design methods of structural vibration, modeling uncertain variables as interval (hyper-rectangle), a non-probabilistic interference model between the exciting frequencies and the natural frequencies of a structure was established and a non-probabilistic method of reliability analysis was presented, called robust criterion of reliability of structural vibration. A measure of reliability developed here is the amount of the uncertainty structure can tolerate before occurring resonance. The larger the structure can tolerate the amount of uncertainty, the more reliable, vice versa. It can be described as the partial order relation between the hype-rectangles in mathematics. Numerical example illustrates the feasibility of the presented non-probabilistic robust reliability criterion.