Studies On Parameter Identification Of Nonlinear Oscillatory System

The complicated dynamical behavior of nonlinear oscillatory systems is one of the forward topics in the field of nonlinear dynamics. However, for some new materials, it is impossible to use only the theoretical methods to constitute dynamical equation of the system because some material parameters and constitutive relations are unknown. Combining theory with experiment is one of the methods for constituting dynamical equation of the system. Therefore, studying and exploring the conversely solution for nonlinear parameters in a vibration system is of important theory significance and application value. This thesis is devoted to exploring, by theoretical analysis and numerical simulation, the stable periodic solutions and parameter identification method in the nonlinear parametrically excited systems.Firstly, the Harmonic Balance Nonlinearity Identification (HBNID) is improved before it is used to identify the parameters of a time-invariant system. The free oscillatory and forced oscillatory system is discussed as a stress. Then, satisfying result is obtained which is that there are more calculation precision and efficiency by the improved method. The condition is that the stable response is periodic in identification. Above is common in the free oscillatory and force oscillatory system. Above all, some identification equations are obtained by applying Fourier series. These equations contain the system parameters and the parameters of Fourier series. Next, some linear equations are obtained by taking the place of the identification parameter using some new parameters. This will bring convenience for using the least squares. Lastly, the normal equations are obtained based on the least squares. The system parameters can be obtained by solving the normal linear equations. The advantage of this method is verified by the numerical analysis of some examples.Secondly, the classical multi-scale method is used to discuss the stable periodic response under resonance of the harmonically -variant parametrically excited system. The conditions for the stable periodic responses and parameter influence on them are discussed. For the more, the periodic motion of harmonically -variant parametrically excited system with the excitation frequency and 1/2 excitation frequency are discussed by numerical simulation. The parameter influences on the stable periodic response of the harmonically -variant parametrically excited system are also discussed by numerical simulation.Finally, the improved HBNID is extended to nonlinear systems with parametrically excitation, firstly. The application of the improved HBNID in the weak nonlinear harmonically -variant parametrically excited system with 1/2 excitation frequency periodic motion is studied. The effective harmonics are extracted to the best in the studying. And the accuracy and reliability of the improved HBNID is proved by numerical simulation. For the more, the parametrically excited system is transformed to a two-DOF oscillatory system. In the experiment, the two-DOF oscillatory experiment system can be used to take the place of the weak nonlinear parametrically excited experiment system when the system response is 1/2 parametrically excitation frequency of periOdic motion. The same identified equation can also be obtained after analyzing the two-DOF oscillatory experiment system when the system response is parametrically excitation frequency of periodic motion. This appears that the parametrically excited system can be ientified using the common oscillatory system (not the parametrically excited system) based on the experiment. Secondly, the conditions are analyzed when multi-scale method is used to identify equations from oscillatory systems. That is using the bifurcation equation of the system as identification and the equation containing all the system parameters. The results appear that the different approximation condition, resonance condition and combination mode need to be discussed for different parametrically excitationoscillatory system. The application of this identifying method is simulated in the parametrical system of a ship with parametrically and force excitation. Thirdly, the improved HBNID is used to identify the strong nonlinear harmonically -variant parametrically excited system with excitation frequency periodic motion. The effective harmonics are extracted to the best in the studying. And the accuracy and reliability of the improved HBNID is proved by numerical simulation in a strong nonlinear oscillatory system with parametrically and force excitation. At the same time, the parametrically excited system can be identified using the common oscillatory system (not the parametrically excited system) based on the experiment by extending the improved HBNID to the two-DOF oscillatory experiment system when the system response is parametrically excitation frequency of periodic motion. Fourthly, the Unitary Average Method is used to identify the strong nonlinear parametrically excited system. And a new frequency field identification method is put forward. The accuracy and reliability of the improved method is proved by numerical simulation in a parametrically and force excited oscillatory system.