Abstract
The existence of nonlinearity is an inevitable frequent occurrence that should be considered to accurately identify the modal parameters of a vibration system using operational modal analysis. A problem is that the traditional operational modal analysis method based on the linear modal theory is not applicable to modal parameter identification of vibration systems with nonlinearity. A solution is as follows: this paper is aimed at solving the problem by proposing a new operational modal analysis method to carry out modal parameter identification for a nonlinear vibration system. The new operational modal analysis method, based on the forced response and symbolic regression method without assuming any pre-existing information and only using mathematical symbols, is introduced to solve the problem by automatically searching for the expression structure and modal parameters of a system in nonlinear normal modes. The simulation result of a three-degrees-of-freedom nonlinear system reveals the high accuracy of the proposed operational modal analysis method in extracting the modal parameters. Then, a rod fastening rotor model is considered, and the capability of the proposed operational modal analysis method to precisely extract its modal parameters is further evaluated.
Highlights
System identification is aimed at the improvement of structural models built from input and output measurements for a real structure with vibration sensing devices
Based on forced responses x1,2 and y1,2, symbolic regression is adopted to optimize the estimation of the nonlinear normal modes (NNMs) for the extraction of modal parameters by operational modal analysis (OMA)
The phase diagrams show that the estimated curves from the OMA method with symbolic regression method (SR) are in good agreement with the theoretical reference
Summary
System identification is aimed at the improvement of structural models built from input and output measurements for a real structure with vibration sensing devices. The modal parameters (namely, the natural frequencies, damping ratios, and mode shapes) are the basis of the model of the system to be expressed. In the past several decades, nonlinear normal modes (NNMs), which are a natural property of structural and mechanical systems, have been researched by many scholars. NNMs are a good tool for performing modal analysis of nonlinear mechanical systems. The meaning of the NNM can be extended from the concept of the linear normal mode (LNM) for linear systems, but the NNM of structural and mechanical systems cannot be reflected in the decoupling of equations of motion. Similar to the LNM for a linear system, the NNM for a nonlinear system is defined as any periodic motion of any undamped and autonomous system, but its principles and mechanisms are more complicated. A detailed description and explanation of NNMs can be found in the literature reviews.[1,2] To date, a few methods have been introduced to solve this problem
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