Variable Modal Parameter Identification Based On Time-varying Prony Method In The Mexican Hat Wavelet Basis

Vibration modal parameters are the main parameters that determine the dynamic characteristics of structures, which can offer important reference to structure modeling, model updating, sensitivity analysis, vibration control and damage detection. However, so far studies on modal parameter identification have been mainly limited to linear time-invariant structures. Modal parameter identification for a linear time-varying structure is so difficult that many problems to it are not to be solved. This paper applies Mexican-hat wavelet base to basis function of time-varying Prony method, and the focus is on the study in modal parameter identification of time-varying structural by time-varying Prony method based on Mexican-hat wavelet base. The major work and research contents are as following:1. Time series model is stated simply. The theoretical basis, the establishment of the model and the estimation of model parameter are introduced.2. According to the good time-frequency localization ability of Mexican-hat wavelet base, the time-varying Prony method based on Mexican-hat wavelet base, which has a better ability of modal parameter identification of dispersion-decreasing signal, fast variation signal and mutation signal, is proposed.3. The method proposed in this paper is used to identify the modal parameters of time-varying single degree of freedom (SDOF) structure and multi-degree of freedom (MDOF) structure. Results of numerical simulations show that the proposed method is feasible and has better precisions than the methods based on traditional basis functions for fast variation signal and mutation signal.4. Based on the Mexican-hat wavelet base, the frequency resolution and the anti-noise performance of the proposed method are researched. The proposed method can separate two frequencies accurately without noise and still identify the frequency of signal in the case of very low signal-to-noise ratio.5. Taking a cantilever beam and the adjustable additive mass and stiffness as the experimental object, based on the presented method, modal parameters of the beam are identified from the free vibration responses with continuous mass change, continuous stiffness change and mutational stiffness change. The identified results are compared with the modal parameters identified under several specified conditions corresponding to the beam and obtained by finite element analysis. The validity of the method proposed in this paper are investigated and verified.