Arclength-based response matching of multivalued frequency responses to update models with strong nonlinearities

Abstract

Model updating of strongly nonlinear systems is a vital tool to establish the precise nonlinear model from the multivalued responses and one major step in the updating process is the matching of the predicted and measured multivalued responses. However, when the multivalued behavior of the predicted and measured responses varies widely, the traditional multivalued response matching methods perform poorly. In this paper, a novel arclength-based multivalued response matching technique is proposed, which can help to update the model from linear to strongly nonlinear and handle both stable and unstable responses. The arclength is obtained from the continuation and the multivalued response is parameterized and transferred from the frequency domain to the arclength domain. The Arclength-Response curve is single-valued and can be easily separated into several parts based on feature points. Transferring the separation results back to the frequency domain, the full multivalued response is divided to single-valued Frequency-Response curves, where single-valued predicted and tested responses may be directly matched. A 2 DOF strong nonlinear model is first updated for verification. Using the proposed method, the linear response is directly updated based on the multivalued response with both softening and hardening regions. The error in the final updated parameters is below 1% and the proposed updating method performs better than two traditional methods. A real 3 DOF nonlinear model with a non-smooth strong nonlinearity with the hardening region is then used for validation. The stable and unstable responses of the system are measured from a shaker voltage-based constant frequency test and model updating is then conducted from linear to strongly nonlinear. During the updating process, the complex nonlinear behavior has six bifurcation points on one predicted response curve, but the updated responses fit the real ones well after 18 iterations. These results show the validity and superiority of the proposed method.