【作者】 毛利军； 陈少林；

【Author】 MAO Li-jun, CHEN Shao-lin (Civil Engineering Department, Nanjing University of Aeronuautics and Astronutics, Nanjing 210016, China;)

【机构】 南京航空航天大学土木工程系；

【摘要】 本文提出了一种时域内基于假设模态法的结构模态识别方法。首先,建立结构无阻尼有限元模型,假定有限元模型所得结构质量矩阵为实际结构质量矩阵,仅所得刚度矩阵与实际结构存在误差;获得关于质量矩阵归一化的有限元模态振型,并以此作为结构假设模态;选择与测点数目相同的低阶假设模态拟合测点数据,可得假设模态基下的模态坐标;根据结构输入,建立基于假设模态基的动力方程;将动力方程重新整理,形成以模态阻尼和模态刚度为未知量的超定方程组;对未知参数较多、系数矩阵条件数较大的超定方程组,利用截断总体最小二乘法(TTLS)进行求解,降低问题的不适定性,改善方法的抗噪性能;结合已知模态质量,最终得到结构的试验模态参数。数值试验表明,与常规最小二乘法(LS)相比,TTLS法有良好的适定性和抗噪声性能。更多还原

【Abstract】 A modal-parameter-identification method in time domain based on assumed modes method is proposed in this paper. First, the undamped finite element model is established, assume that its mass matrix is consistent with real structure, only error lie in its stiffness matrix; then the unitary modal shapes corresponding with the mass matrix derived from finite element model are taken as the assumed modes; the modes coordinates based on the assumed modes is derived from the responses with the same numbers as the assumed modes. The dynamics equation systems based the assumed modes is established, and adjust the equation to form the undecided equation systems with the modal damping and stiffness elements as unknown quantity. For large number of unknown quantity, and ill-posed equation systems with large condition coefficient matrix, the truncated total least squares (TTLS) method is used to alleviate its ill-posedness and improve its noise imunity. Combining the known modal mass, the structure modal parameters are identified. Numerical simulation show that TTLS method have well-posedness and noise imunity than traditional least squares (LS) method.更多还原