含不确定参数的复合材料板振动的区间分析法  

Interval analysis method for vibration of composite laminatewith uncertain parameters

作　　者：邱志平[1] 马一[1] 王晓军[1] 

机构地区：[1]北京航空航天大学航空科学与工程学院,北京100083

出　　处：《北京航空航天大学学报》2004年第7期682-685,共4页Journal of Beijing University of Aeronautics and Astronautics

基　　金：国家自然科学基金资助项目(10172013);航空基金资助项目(01B51046)

摘　　要：提出了求解具有不确定参数的复合材料板的振动固有频率区间分析法 .区间分析法利用区间数学和泰勒定理 ,把不确定变量简化为区间向量 .这样可以在较少的结构信息的情况下确定结构响应的变化区间 .在样本比较小 ,概率统计特性缺乏 ,从而通常的概率统计方法不能有效应用时 ,区间分析仍然有效 .对复合材料板的振动固有频率的区间法公式进行了推导 ,并用 2个数值例子与凸模型方法的解进行比较 .A method named interval analysis method, which solves the natural frequencies of composite laminate with uncertain parameters, was presented. Based on interval mathematics and Taylor series expansion, interval analytical method simplifies the uncertain parameters to interval vectors so that it can get the intervals within which the response of structure varies when less information of structure is known. The interval analytical method is efficient under the condition that probability approach can not work because of small samples and spare statistics characteristics. The formulation of natural frequencies of composite laminate using interval analytical method was formulated. Two numerical examples of comparison between interval analytical method and convex model were given. The results show that the solutions of interval analytical method are sharper than that of convex model.

关 键 词：复合材料 振动 区间数学 不确定参数 

分 类 号：O324[理学—一般力学与力学基础]