时变结构动力学数值方法及其模态参数识别方法研究
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摘要
时变结构动力学问题一直是学术界研究的难点,理论上至今还未有太大的进展,但大型柔性空间结构、高速飞行器和高速列车等实际工程问题又有迫切的需求,为此本文在在系统总结时变结构动力学及相关领域的研究现状的基础上主要研究了时变结构动力学的数值方法以及小波理论在结构系统识别中的应用。主要研究内容和相关结论如下:
参数时变的结构动力响应的数值计算方法研究。通过时间离散的Galerkin方法建立了不协调时间有限元,由此得到了高阶精度、无条件稳定的有好的耗散特性的数值算法。通过有限差分分析说明了算法的特性,并基于线性、高阶拉格朗日插值、埃米特插值给出了一族算法公式。接着又给出了减小计算量的迭代步骤。对线性时不变问题仿真分析验证了所有的算法公式的正确性和算法本身的优良特性,对时变参数、非线性问题仿真分析说明了这些算法公式的有效性。基于Hamilton 定律探讨了对时变参数使用埃米特插值即允许参数在求解的时间区间内是时变的数值算法,给出了算法公式。对Mathieu 方程和一个变刚度变阻尼的两自由度问题的仿真分析验证了算法的有效性。
小波函数性质、应用特点及小波变换方法研究。总结了近年来提出的各类典型的小波及其小波基函数,较详细地研究了它们的几种重要的性质及其实际应用特点。这些工作可以为如何选择小波和小波基提供有益的参考。接着对循环小波变换方法给出了信号的循环小波分解的一般公式,对Daubechies 小波的变换矩阵的构成给出了统一的描述。
小波去除噪音算法研究及其在频率响应函数提取中的应用。较全面地研究了小波去噪音方面已经取得的成果,在此基础上,对Donoho 的去噪方法给出了一个可以有效地同时去除数据中所含的高斯白噪音和脉冲噪音的改进算法,仿真表明算法是有效的。另外,基于Donoho 的去噪原理还给出了一个试验估计去噪方法。将这些算法用于剔除频率响应函数中的噪音比传统的加窗方法更为有效。
小波理论在结构系统模态参数识别上的应用。对用小波变换方法提取系统的脉冲响应函数的思想给出了平均和滤波步骤,并将这个步骤推广到时变的脉冲响应函数的提取,进而识别系统时变的模态参数。对一个变刚度和变阻尼的两自由度问题进行了仿真分析,并考虑了噪音和参数变化的影响,结果表明方
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.
参数时变的结构动力响应的数值计算方法研究。通过时间离散的Galerkin方法建立了不协调时间有限元,由此得到了高阶精度、无条件稳定的有好的耗散特性的数值算法。通过有限差分分析说明了算法的特性,并基于线性、高阶拉格朗日插值、埃米特插值给出了一族算法公式。接着又给出了减小计算量的迭代步骤。对线性时不变问题仿真分析验证了所有的算法公式的正确性和算法本身的优良特性,对时变参数、非线性问题仿真分析说明了这些算法公式的有效性。基于Hamilton 定律探讨了对时变参数使用埃米特插值即允许参数在求解的时间区间内是时变的数值算法,给出了算法公式。对Mathieu 方程和一个变刚度变阻尼的两自由度问题的仿真分析验证了算法的有效性。
小波函数性质、应用特点及小波变换方法研究。总结了近年来提出的各类典型的小波及其小波基函数,较详细地研究了它们的几种重要的性质及其实际应用特点。这些工作可以为如何选择小波和小波基提供有益的参考。接着对循环小波变换方法给出了信号的循环小波分解的一般公式,对Daubechies 小波的变换矩阵的构成给出了统一的描述。
小波去除噪音算法研究及其在频率响应函数提取中的应用。较全面地研究了小波去噪音方面已经取得的成果,在此基础上,对Donoho 的去噪方法给出了一个可以有效地同时去除数据中所含的高斯白噪音和脉冲噪音的改进算法,仿真表明算法是有效的。另外,基于Donoho 的去噪原理还给出了一个试验估计去噪方法。将这些算法用于剔除频率响应函数中的噪音比传统的加窗方法更为有效。
小波理论在结构系统模态参数识别上的应用。对用小波变换方法提取系统的脉冲响应函数的思想给出了平均和滤波步骤,并将这个步骤推广到时变的脉冲响应函数的提取,进而识别系统时变的模态参数。对一个变刚度和变阻尼的两自由度问题进行了仿真分析,并考虑了噪音和参数变化的影响,结果表明方
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.
引文
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