Nonlinear Jump Based Parameter Estimation

Parameter identification,as an "inverse problem" analysis method in vibration analysis,is based on experiments.It uses the combination of theoretical analysis and experimental measurement to deal with vibration problems in engineering.Parameter identification can improve the vibration structure from a more practical point of view,find and make up for the defects of the engineering structure.On the other hand,the parameter identification can supplement and optimize the vibration analysis theory from a more practical point of view.Therefore,the in-depth study of the parameter identification problem is of great significance to the improvement of engineering structures and theoretical methods.The use of non-linear improvements in the design of vibration control structures,especially the design of vibration isolators,has received extensive attention.For such systems,it is necessary to predict the dynamic behavior and system parameters through experiments in order to achieve a deeper understanding of the system characteristics,necessary optimization and model improvement and upgrade.This topic is based on the nonlinear vibration system,studies the external jump phenomena and the internal theoretical mechanism in the nonlinear vibration system,and analyzes the relationship between the phenomena and the theory.Firstly,the general multi-degree-of-freedom nonlinear vibration problem is considered.Based on the jump phenomena,the theoretical framework of multi-degree-of-freedom nonlinear vibration system parameter identification method is established by using harmonic balance method and signal processing means.Then,for a class of single-degree-of-freedom nonlinear vibration systems with quadratic nonlinear damping and cubic nonlinear stiffness,the response curves obtained by two nonlinear jump phenomena,FRC(frequency-response curves)and ARC(frequency-response curves)Amplitude-response curves(excitation amplitude-response curves)can be used to obtain the explicit parameter identification formulas of this type of system,and numerical and experimental verifications are performed.For a class of two-degree-of-freedom nonlinear vibration systems with cubic nonlinear stiffness,the parameters identification process and results of this kind of system are given by general parameter identification method and verified numerically.In this paper,the single-degree-of-freedom nonlinear vibration system and the two-degree-of-freedom nonlinear vibration system are illustrated to prove the correctness and accuracy of the nonlinear parameter identification method based on the jump phenomena.