Model Updating Using Frequency Response Functions Based on Sherman–Morrison Formula

Model updating plays an important role in dynamics modeling with high accuracy, which is widely used in mechanical engineering. In this paper, a model updating method using frequency response function (FRF) is proposed based on Sherman–Morrison formula, in which only the initial FRFs and parameter perturbations are employed to calculate the sensitivity avoiding repeated finite element (FE) analyses and improving the computational efficiency. Firstly, the sensitivity of FRFs to the design parameters is calculated by Sherman–Morrison formula based on the QR decomposition of the system dynamic stiffness matrix variation after parameter perturbations, then the influence of damping on the amplitude of FRFs is considered to select an appropriate frequency range, and finally conduct the model updating according to the sensitivity of the FRFs. By employing simulation examples of a truss and a solar wing and the experiment of an aluminum frame, the updating error is still within ±1.00% in the condition of 5% random white noise, which shows the proposed method has high accuracy and a certain anti-noise capability. When only a few numbers of frequency points are selected near the resonance peak of the FRFs, the result shows that selecting the appropriate frequency range and points can reduce the computational cost. The results of the experiment study show that the proposed method can effectively identify the structural parameters. The above results verify the feasibility and effectiveness of proposed model updating method using FRFs.