A new parameter transformation alpha = alpha (epsilon, n omega (0)/m, omega (l)) was defir2ed for extending the applicable range of the modified Lindstedt-Poincare method. It is suitable for determining subharmonic an...A new parameter transformation alpha = alpha (epsilon, n omega (0)/m, omega (l)) was defir2ed for extending the applicable range of the modified Lindstedt-Poincare method. It is suitable for determining subharmonic and ultraharmonic resonance solutions of strongly nonlinear systems. The 1/3 subharmonic and 3 ultraharmonic resonance solutions of the Duffing equation and the 1/2 subharmonic resonance solution of the Van der Pol-Mathieu equation were studied. These examples show approximate solutions are in good agreement with numerical solutions.展开更多
The slowly-variant-system is defined and analyzed in this paper and the nonlinear relationship between its instantaneous parameters and the instantaneous amplitude and frequency of its free vibration response is estab...The slowly-variant-system is defined and analyzed in this paper and the nonlinear relationship between its instantaneous parameters and the instantaneous amplitude and frequency of its free vibration response is established. By defining the band-pass mapping, a slowly-variant-system which we call the accompanied slowly-variant-system is extracted from the nonlinear system; and the relationship between the two systems is discussed. Also, the skeleton curves that can illustrate the nonlinearity and the main properties of the nonlinear system directly and concisely are defined. Work done in this paper opens a new way for nonlinearity detection and identification for nonlinear systems.展开更多
该文采用Hilbert-Huang变换(HHT)对时变阻尼自由振动系统以及常见的Duffing振动系统和Van der Pol振动系统进行参数识别。首先通过经验模态分解将振动信号分解为自由振动信号和强迫振动信号,通过经验包络法得到分解后信号的振幅包络线...该文采用Hilbert-Huang变换(HHT)对时变阻尼自由振动系统以及常见的Duffing振动系统和Van der Pol振动系统进行参数识别。首先通过经验模态分解将振动信号分解为自由振动信号和强迫振动信号,通过经验包络法得到分解后信号的振幅包络线和瞬时频率。进而使用瞬时振幅及瞬时频率通过最小二乘法估计得到振动方程的各项参数。与小波识别结果进行对比,数值算例表明Hilbert-Huang变换可以有效地识别时变阻尼自由振动以及Duffing振动系统和Van der Pol振动系统的时变参数并且有较高精度。展开更多
文摘A new parameter transformation alpha = alpha (epsilon, n omega (0)/m, omega (l)) was defir2ed for extending the applicable range of the modified Lindstedt-Poincare method. It is suitable for determining subharmonic and ultraharmonic resonance solutions of strongly nonlinear systems. The 1/3 subharmonic and 3 ultraharmonic resonance solutions of the Duffing equation and the 1/2 subharmonic resonance solution of the Van der Pol-Mathieu equation were studied. These examples show approximate solutions are in good agreement with numerical solutions.
文摘The slowly-variant-system is defined and analyzed in this paper and the nonlinear relationship between its instantaneous parameters and the instantaneous amplitude and frequency of its free vibration response is established. By defining the band-pass mapping, a slowly-variant-system which we call the accompanied slowly-variant-system is extracted from the nonlinear system; and the relationship between the two systems is discussed. Also, the skeleton curves that can illustrate the nonlinearity and the main properties of the nonlinear system directly and concisely are defined. Work done in this paper opens a new way for nonlinearity detection and identification for nonlinear systems.
文摘该文采用Hilbert-Huang变换(HHT)对时变阻尼自由振动系统以及常见的Duffing振动系统和Van der Pol振动系统进行参数识别。首先通过经验模态分解将振动信号分解为自由振动信号和强迫振动信号,通过经验包络法得到分解后信号的振幅包络线和瞬时频率。进而使用瞬时振幅及瞬时频率通过最小二乘法估计得到振动方程的各项参数。与小波识别结果进行对比,数值算例表明Hilbert-Huang变换可以有效地识别时变阻尼自由振动以及Duffing振动系统和Van der Pol振动系统的时变参数并且有较高精度。
