未确知信息板梁组合结构的动力特性分析

 为了克服随机方法难以处理小样本的缺陷,文中充分利用客观的不确定性信息,构建了物理参数(弹性模量、质量密度)同时具有未确知性的空间板梁组合结构动力特性分析模型,提出了基于未确知因子法的板梁组合结构动力特性分析方法.首先利用未确知因子的数学表述,构建结构的刚度矩阵和质量矩阵,然后从结构振动理论中的Rayliegh商出发,根据未确知有理数的运算规则,推导出板梁组合结构特征值的计算表达式.得出结构特征值取某值的可信度与各参数取值可信度的趋势一致的结论.在缺乏足够数据或者信息不完整的情况下,用未确知信息表述结构模型参数的不确定性,比用成熟的随机方法具有更高的可信度且方法简易可行.算例给出了某未确知性板梁组合结构的固有频率可能值及其可信度的计算结果,表明该方法的可行性和有效性.

Dynamic Characteristic Analysis on Beam-plate Composite Structures with Unascertained Information

To overcome the limitation of random method that is not suitable for the case of small sample, the objective unascertained information is fully used, and the dynamic characteristics analysis model of space beam-plate composite structures is built, in which structural elastic module and mass density are all considered as unascertained variables. And a structure analysis method based on the unascertained factor method is given. Firstly, the structural element stiffness and mass matrices are built based on the mathematics expression of unascertained factor. Then by using the arithmetic operation rules of unascertained rational numbers, the computational expressions of dynamic eigenvalue for the beam-plate structures are derived from the Rayleigh's quotient. It is concluded that the confidence level of structural responses are in direct proportion to the confidence level of each parameter. Comparing with the mature random method, the proposed method is able to obtain reliability result of safer and higher faith degree in the case of inadequate data or insufficient information; moreover, it is simple and easy to apply. At last, an example is given, in which the possible values and confidence levels of natural frequencies for the unascertained beam-plate composite structures are obtained. The rationality and validity of presented method are demonstrated.