HHT方法在两自由度体系动力响应特征分析中的应用研究
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摘要
本文围绕着希尔伯特-黄变换方法对两自由度体系动力响应特征展开了研究。针对HHT方法中的EMD筛分问题,本文通过大量的数据研究总结了并不是所有的数据都可以正确筛分,试验研究表明存在一个可筛分的数据区域边界。在此基础上,借助于Yang提出的基于Fourier变换的EMD方法,可以实现模态混淆信号的筛分。研究了线性时不变2-DOF体系、以及刚度渐变与刚度突变两种线性时变2-DOF体系在强迫振动下的IMF分量与Hilbert谱所蕴含的物理意义。在简谐波形输入下,HHT以体系动力响应的不同振动模态之间的波间组合机制来描述体系线性的力学行为,利用HHT分解出来的表征稳态反应的IMF分量可以获得有关输入的信息;而利用表征瞬态反应的IMF分量,则可以获得有关体系自振特性方面的信息,识别出体系的自振频率和阻尼参数。对于线性时变体系,能够识别出时变2-DOF体系的自振频率变化情况,从而得到体系刚度参数随时间的变化。如果体系的输入为地震波,HHT谱依然能够如实地描述体系在地震动输入下动力响应的能量在时频平面内的分布,体现出了其独特的优越性。
分析了双线性2-DOF体系动力响应的Hilbert谱及Hilbert边缘谱所蕴含的物理意义,通过体系振动过程中的屈服时程论述了瞬时频率波动所蕴含的物理意义,以及输入单分量简谐波的幅值、频率及体系的阻尼等不同因素对HHT谱的影响。得到体系的屈服时刻比卸载时刻更容易被识别出来;体系的屈服及卸载情况,在本层的输出加速度反应中有明显的反映,而相邻层的刚度变化情况反映不明显。还对地震动输入下体系动力响应的Hilbert谱及Hilbert边缘谱、Fourier谱以及Morlet小波谱的特征进行了探讨与分析。
详细研究了不同的等效线性单自由度(SDOF)体系动力响应的Hilbert谱以及Hilbert边缘谱所蕴含的物理意义,以及输入单分量简谐波的幅值等因素对这两种谱特征的影响,并对不同等效线性化体系的动力响应频谱特征的异同点进行了比较,评价了各种方法的优缺点。此外,还对地震动输入下等效线性单自由度体系动力响应的频谱特征进行了探讨与分析。
This dissertation was devoted to the application of the Hilbert-Huang transform in the field of dynamic response.
Aiming at the sifting range problem in EMD, it was proposed that not all the data can be well sifted and there was range of sifting. An improved method named EMD based on Fourier transform can sift the mode-mixing signal into good mode, which was proposed by Yang. The IMF components and Hilbert spectrum of the excited dynamic responses of linear time-invariant 2-DOF system and two types of linear time-variant 2-DOF systems were studied, such as the 2-DOF system with gradually changing stiffness and the 2-DOF system with suddenly broken stiffness. When the linear 2-DOF system was excited by regular inputs, HHT described the linear mechanical behavior of system by the inter-wave combination mechanism among different intrinsic oscillatory modes of dynamic response of system. By the aide of the IMF components representing the steady-state response and the transient response, the information about the input and the system can be obtained, respectively; and thus the vibration properties of system can be identified. When the system was excited by earthquake ground motion, the aforementioned steady-state response and transient response of vibration cannot be distinguished. However, the study manifested that the Hilbert spectrum can still represent precisely the energy distribution of the dynamic response of system in the time-frequency plane.
The second part was dedicated to the study of the physical meanings embedded in the HHT spectrum of dynamic response of bilinear 2-DOF system, and the study of the influences of different factors, such as the amplitude and the frequency of single-component harmonic input, the damping of system, on the characteristics of these two spectra. The yielding time history of the bilinear 2-DOF system during its vibration gives out the physical meaning of undulation of instantaneous frequency of the corresponding IMF component. This part also studied the characteristics of Fourier spectrum, Morlet wavelet spectrum and its marginal spectrum, and Hilbert spectrum and its marginal spectrum of the dynamic response of system under the inputs of earthquake ground motion.
At last, the physical meanings embedded in the HHT spectrum and Fourier spectrum of dynamic response of different equivalent linear SDOF systems is studied. And the influences of different factors, such as the amplitude of input single-component harmonic, on these two spectra were discussed. The similarities and differences of equivalent linear system were studied. In addition, this part also studied frequency spectrum of the dynamic response of system under the inputs of earthquake ground motion.
分析了双线性2-DOF体系动力响应的Hilbert谱及Hilbert边缘谱所蕴含的物理意义,通过体系振动过程中的屈服时程论述了瞬时频率波动所蕴含的物理意义,以及输入单分量简谐波的幅值、频率及体系的阻尼等不同因素对HHT谱的影响。得到体系的屈服时刻比卸载时刻更容易被识别出来;体系的屈服及卸载情况,在本层的输出加速度反应中有明显的反映,而相邻层的刚度变化情况反映不明显。还对地震动输入下体系动力响应的Hilbert谱及Hilbert边缘谱、Fourier谱以及Morlet小波谱的特征进行了探讨与分析。
详细研究了不同的等效线性单自由度(SDOF)体系动力响应的Hilbert谱以及Hilbert边缘谱所蕴含的物理意义,以及输入单分量简谐波的幅值等因素对这两种谱特征的影响,并对不同等效线性化体系的动力响应频谱特征的异同点进行了比较,评价了各种方法的优缺点。此外,还对地震动输入下等效线性单自由度体系动力响应的频谱特征进行了探讨与分析。
This dissertation was devoted to the application of the Hilbert-Huang transform in the field of dynamic response.
Aiming at the sifting range problem in EMD, it was proposed that not all the data can be well sifted and there was range of sifting. An improved method named EMD based on Fourier transform can sift the mode-mixing signal into good mode, which was proposed by Yang. The IMF components and Hilbert spectrum of the excited dynamic responses of linear time-invariant 2-DOF system and two types of linear time-variant 2-DOF systems were studied, such as the 2-DOF system with gradually changing stiffness and the 2-DOF system with suddenly broken stiffness. When the linear 2-DOF system was excited by regular inputs, HHT described the linear mechanical behavior of system by the inter-wave combination mechanism among different intrinsic oscillatory modes of dynamic response of system. By the aide of the IMF components representing the steady-state response and the transient response, the information about the input and the system can be obtained, respectively; and thus the vibration properties of system can be identified. When the system was excited by earthquake ground motion, the aforementioned steady-state response and transient response of vibration cannot be distinguished. However, the study manifested that the Hilbert spectrum can still represent precisely the energy distribution of the dynamic response of system in the time-frequency plane.
The second part was dedicated to the study of the physical meanings embedded in the HHT spectrum of dynamic response of bilinear 2-DOF system, and the study of the influences of different factors, such as the amplitude and the frequency of single-component harmonic input, the damping of system, on the characteristics of these two spectra. The yielding time history of the bilinear 2-DOF system during its vibration gives out the physical meaning of undulation of instantaneous frequency of the corresponding IMF component. This part also studied the characteristics of Fourier spectrum, Morlet wavelet spectrum and its marginal spectrum, and Hilbert spectrum and its marginal spectrum of the dynamic response of system under the inputs of earthquake ground motion.
At last, the physical meanings embedded in the HHT spectrum and Fourier spectrum of dynamic response of different equivalent linear SDOF systems is studied. And the influences of different factors, such as the amplitude of input single-component harmonic, on these two spectra were discussed. The similarities and differences of equivalent linear system were studied. In addition, this part also studied frequency spectrum of the dynamic response of system under the inputs of earthquake ground motion.
引文
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