测量模态不确定的梁式结构随机有限元模型修正

Stochastic finite element model updating of beam structure based on uncertain measurement modes

针对测量模态不确定导致的结构修正参数随机的实际情况,提出了一个随机模型修正方法.该方法以随机有限元法为基础,将结构修正参数表示为多变量非正交多项式展开式,建立了表达随机响应和待修正参数之间精确关系的随机模型修正方程.采用混合摄动-伽辽金方法对该方程进行求解,得到了修正参数的统计特征.数值算例表明,采用测量的前三阶竖向位移模态信息对结构参数进行修正,所提方法的修正结果与蒙特卡洛方法模拟结果一致,但耗时较少.采用修正参数计算得到的随机响应和测量结果吻合很好,验证了本文方法的有效性.

A stochastic model updating method is proposed for the situation where the randomness of structural update parame-ters is caused by the uncertainty of measurement modes. Based on the stochastic finite element method,the structural update parameters are expressed as multivariate non-orthogonal polynomial expansions,and a stochastic model updating equation is es-tablished, which expresses the exact relationship between the random responses and the update parameters. The stochastic up-dating equation is solved by the mixed perturbation-Galerkin methods and the statistical characteristics of the updated parame-ters are obtained. Numerical examples show that by using the first three orders of measured vertical modal displacements, the updating results of the proposed method are consistent with the results of the Monte Carlo simulation method,but the proposed method spends less computational time than the Monte Carlo simulation method.The random responses obtained by the update parameters are in a very well agreement with the measured results,which verifies the effectiveness of the proposed method.