基于区间分析的不确定性结构动力学模型修正方法

提出了一种基于区间分析的不确定性有限元模型修正方法。在区间参数结构特征值分析理论和确定性有限元模型修正方法基础上，假设不确定性与初始有限元模型误差均较小，采用灵敏度方法推导了待修正参数区间中点值和不确定区间的迭代格式。以三自由度弹簧-质量系统和复合材料板为例，采用拉丁超立方抽样构造仿真试验模态参数样本，开展仿真研究。结果表明，当仿真试验样本能准确反映结构模态参数的区间特性时，方法的收敛精度和效率均较高；修正后计算模态参数能准确反映试验数据的区间特性。所提出方法适用于解决试验样本较少，仅能得到试验模态参数区间的有限元模型修正问题。

Model updating of structural dynamics model with uncertainty based on interval analysis

A finite element model updating method in structural dynamics considering the effects of uncertainty is proposed using interval analysis. Based on the theory of eigen-frequency analysis of structures with interval parameters and the deterministic finite element model updating technologies, an interval model updating formulation are developed by applying the sensitivity method, under the assumption that the variability in measurements and structural parameters as well as the error in the initial finite element model are small. In the iterative formulation, each variable is presented in an interval form which consists of an interval mid-point and an interval radius. Simulation study is conducted by employing a three degrees of freedom mass-spring system and a composite panel, the simulated experimental samples are generated by adopting Latin Hypercube sampling methods. Results show that when the testing samples can accurately reflect the interval characteristics of the experimental modal data, the high convergence accuracy and high efficiency can both be achieved. The presented method provides a solution to the problem that the measured sample is small in finite element model updating of structures with uncertainties.