Research On Parameter Identification Method And Application Of Nonlinear Vibration System Based On Dynamic Frequency

With the development of science and technology,more and more nonlinear systems have attracted wide attention of researchers,and the effective establishment of models describing nonlinear systems is the basis for research and control of nonlinear systems.For systems with less influence from nonlinear factors,we can use the identification theory of linear systems to obtain the governing equations of the system.However,as the requirements for system control accuracy are gradually improved,those systems with complex nonlinear behavior cannot be analyzed simply by linearization models,and the necessary nonlinear form control equations need to be established.Therefore,the development of data-driven nonlinear system identification methods has important theoretical and practical application value.Based on prior knowledge,we can obtain the estimated form of the dynamic governing equation of the system.By identifying the coefficients of one or more unknowns in the governing equation by some methods,the governing equation of the system can be determined.In general,the parameter identification problem of nonlinear vibration system can be regarded as the inverse process of solving system differential equations.In this paper,the parameter identification problem of nonlinear systems is studied by means of a new quantitative analysis method of differential equations,and the identification of the system is deduced.The equation is validated by numerical simulation.The research contents and main results of this paper are reflected in the following aspectsFirstly,a dynamic frequency method for calculating steady-state asymptotic solutions of strongly nonlinear vibration systems is proposed.This method is based on the energy equation of the system and introduces unknown dynamic frequency components to fully reflect the influence of non-linear factors in the system.It overcomes the shortcoming of harmonic balance method that ignores the influence of high-order harmonic components due to truncation of Fourier Series in the calculation process.It also introduces second-order dynamic frequency method and improved energy method to further improve the calculation of steady-state response and to reduce the difficulty of analysis.Secondly,the problem of parameter identification of nonlinear vibration systems with periodic response is studied.Based on the dynamic frequency,a new parameter identification method for nonlinear systems is proposed.The parameter identification theory is derived for a self-excited vibration system,and the identification equation of the system is obtained.The numerical simulation is used to analyze the validity of the method,and the influence of noise on the identification results is discussed.Finally,taking a kind of vibration energy harvester as the experimental object,the unknown parameters in the system control equation are identified by the experimental data of response.By optimizing the nonlinear term in the control equation,the dynamic control equation of the vibration energy harvester is established and perfected.The validity of the control equation is verified by comparing with the experimental data.