Finite element (FE) models are useful for many applications in engineering practice such as structural analysis, dynamic behaviour predication, structural condition assessment, and damage detection. In reality, the FE models often differ with the real structures due to significant discrepancies between test measurements and model predictions. This study is intended to propose an iterative model updating method to adjust the mass and stiffness matrices of the FE models by improving model updating formulations. Under dynamic discrepancy theory, mass and stiffness orthogonality conditions are independently expanded to establish two model updating formulations consistent with the incomplete modal data. In the proposed iterative method, each of the improved equations is solved by an efficient iterative method named as least squares minimal residual (LSMR) to compute structural discrepancy matrices after transforming linear matrix systems of the updating equations to linear vector systems. In the following, the mass and stiffness matrices of the FE models are iteratively updated in the algorithm of the proposed iterative method using the structural discrepancy matrices obtained from LSMR technique. The efficiency and accuracy of the proposed methods are numerically verified by a simple planner truss and two shear building models. Results demonstrate that the proposed methods provide reliable estimates of finite element model updating using the measured incomplete modal data.

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