【摘要】 利用区间数学研究了具有有界不确定结构参数的复合材料层合梁自由振动问题.将不确定结构参数用区间向量进行定量化,结合区间数学与Taylor级数,提出了求解具有不确定结构参数的复合材料层合梁自由振动问题的区间分析法.与传统的概率分析方法相比,它只需不确定参数所在范围的界限,而不需要其它任何概率统计信息来确定结构振动固有频率的变化区间.通过数值算例,将非概率区间分析法和概率分析方法进行了比较,可看出由区间分析方法得到的固有频率区间包含由概率方法得到的固有频率区间,即概率方法得到的区间宽度比区间分析方法得到的区间宽度要“紧”,表明了区间分析方法的可行性和有效性.更多还原

【Abstract】 A new method named interval analysis method,which solves the free vibration of composite laminated beams with uncertain parameters,was presented.Based on interval mathematics and Taylor series expansion,uncertain parameters were described by interval numbers.Instead of conventional probabilistic approach,interval analysis method could get the variation intervals of the natural frequencies of structure,in which the bounds on the magnitude of uncertain parameters were only required,not necessarily knowing other information of statistics.From the comparison between the non-probabilistic interval analysis method and the probabilistic approach in the numerical examples,it could be seen that the region of the natural frequency of structures with uncertain parameters obtained by the interval analysis method contained that produced by the probabilistic approach.In other words,the width of the maximum or upper and minimum or lower bounds on the natural frequency yielded by the probabilistic approach was tighter than that produced by the interval analysis method.The result illustrates the feasibility and the efficiency of the interval analysis method.更多还原