一种运用不完全模态试验数据的无溢出模型修正方法

NO SPILLOVER METHOD FOR STRUCTURAL DYNAMICS MODEL UPDATING WITH INCOMPLETE MODAL EXPERIMENTAL DATA

模型修正即为利用结构现场实测的振动信息修正不精确的有限元结构动力模型。鉴于测量的模态数据一般是不完整的,因此在进行模型修正时,希望测量的低阶模态数据融于修正模型而不改变原模型的高阶模态数据。这样的一种修正,如果可能,称为无溢出模型修正。在假定有限元模型的质量矩阵与刚度矩阵均为对称非负定矩阵,并且质量矩阵是精确的情况下,提出了一种无溢出有限元模型修正方法。该方法可使得修正模型仍为对称非负定、测试模态与测试频率融于修正模型、并且修正模型的剩余模态和频率与原模型一致。最后数值例子验证了该方法的有效性。

In conducting the model updating, it is often desirable to match only the part of observed data without tampering with the other part of unmeasured or unknown eigenstructure inherent in the original model. Such an updating, if possible, is said to have no spillover. In the paper, a no spillover model updating method is established under the assumption that the mass matrix and the stiffness matrix of a finite element model are symmetric positive semi-definite and the mass matrix is exact. By the method, the updated model remains also symmetric positive semi-definite, a set of natural frequencies and corresponding mode shapes, measured from a real-life structure, are embodied in the updated model, and the remaining natural frequencies and corresponding mode shapes of the updated model are the same as those of the original model. The proposed method is demonstrated by a numerical example.