Model Updating of Dynamic Structures with Strong Nonlinearities using Fixed Frequency Continuation Tests

TX Zhu, GB Zhang, CP Zang, HT Cui (Nanjing University of Aeronautics and Astronautics, China) & MI Friswell (Swansea University)

Mechanical Systems and Signal Processing, Vol. 193, 15 June 2023, paper 110209


Model updating using multivalued responses is an important approach to construct strongly nonlinear models. During updating, swept frequency tests are usually used to measure the multivalued responses, but the measured responses only contain the stable branches. Accordingly, updating mainly uses these stable responses for the nonlinear model construction. Unstable responses are rarely tested or participate in the updating process, which may lead to errors in the constructed model with strong nonlinearities. Recently, fixed frequency tests using a continuation scheme have been used to measure fully multivalued responses, including both the stable and unstable branches, for structures with the strong nonlinearity. However, the measured responses were then transformed to equivalent swept frequency tests for the existing updating schemes, where this transformation may induce errors in the updating process. In this paper, a novel method for strong nonlinear model updating using the results of the fixed frequency test is proposed. Such updating is based on the directly measured data of the fixed frequency tests and can handle both the stable and unstable responses. Fixed frequency continuation using the Multi-Harmonic Balance Method (MHBM) is developed to predict the multivalued responses and their sensitivities. The multivalued responses of the prediction and measurement are directly matched in sensitivity-based updating. The proposed method is numerically verified on a 2 DOF nonlinear model. Using the proposed method, the nonlinear model is updated from linear to strongly nonlinear and the updated parameters all converge to the simulated values after 7 iterations. The proposed method is then experimentally validated on a 3 DOF nonlinear system with a non-smooth nonlinearity. A nonlinear model with a 7th order polynomial stiffness represents the equivalent system and is directly updated based on the fixed frequency test results. The updated responses are generally a good fit to the tested responses. Compared with updating using only the stable responses, the proposed updating method achieves higher precision and its updated responses are closer to the tested responses. These results show the validity and superiority of the proposed method.

Paper Availability

This material has been published in Mechanical Systems and Signal Processing, Vol. 193, 15 June 2023, paper 110209. Unfortunately the copyright agreement with Elsevier does not allow for the PDF file of the paper to be available on this website. However the paper is available from ScienceDirect - see the link below.

Link to paper using doi: 10.1016/j.ymssp.2023.110209

Mechanical Systems and Signal Processing on ScienceDirect