Study On Time-Varying Structural Dynamics Numerical Algorithm And Madol Parameter Identification Method

It has been being difficult to study the dynamics of time-varying structure, because theoretically it has not general solution up to now. But there are many thus problems in engineering to solve urgently, for example: the stretching dynamics of large spacecraft flexible structure, varying mass problem of rocket, bridge vibration causing high-speed train, etc. Therefor the numerical methods on dynamics of time-varying structure and application of wavelet theory in structural parameter identification are studied in this dissertation. The main new work of this dissertation is as following: The incompatible time finite element on time-discrete Galerkin method is established, and the numerical algorithm with high order accuracy and unconditional stability and good dissipation is obtained. The characteristic of this algorithm is described by finite difference analysis. A set of formulas on linear high order Lagrange interpolation and Hermite interpolation is shown, then iterative step reduced calculating is proposed. The advantage of the algorithms is shown by numerical simulation for linear time invariant system. Based on Hamilton law, the numerical algorithm of time-varying parameter using Hermite interpolation is discussed, and the algorithm formula is presented. The algorithm is effective on Mathieu equation and two DOF systems with varied stiffness and varied damping. Some kinds of wavelet and its fundamental function are reviewed. The performance and actual characteristic in application are studied carefully. These can provide benefit reference to choice wavelet. The general formula of the signal cycling wavelet decomposition is obtained, and Daubechies wavelet transform matrix is described. The wavelet de-noise algorithms are investigated systematically. For the method of Donoho de-noise, the algorithm is improved to eliminate the Gauss white and impulse noise. The simulation analysis has shown that the algorithm is available. Additionally, the experimentally estimated de-noise method is given. These algorithms are more available than classical windowing method to eliminate the noise in frequency respond function. The average step of extracting system impulse respond function is presented by using wavelet transform method, and the step is popularized to time-varying impulse respond function extracting, then the time-varying modal parameter is identified. Simulating analysis is made for two DOF systems with varied stiffness and varied damping, and results have shown that this method is available for slow-varying parameter. The frequency modulation Gauss wavelet transform of impulse respond function is made to identified modal parameter. The wavelet transform nature of impulse respond function is analyzed, and the application condition and the choice principle of frequency modulating parameter and Gauss parameter pointed qualitatively to improve the identifying accuracy is proposed. The correctness of method and the analysis result are verified by simulating analysis. Since the quantity of sample is not very large, the signal is segmented and processed quantitatively in every segment, then segmented AR model is established to identify the time-varying modal parameter. The experiment facility of cantilever beam with time-varying mass is developed and the test data are analyzed with AR model method, wavelet transform method and short FFT method. The result show that the AR model method and wavelet transform method are convincible for slow time-varying parameters to identify the first two order modal parameters and the short FFT method is not very effect.