参数振动系统响应的频谱成分及其分布规律

SPECTRAL COMPONENTS AND THEIR DISTRIBUTIONS OF THE RESPONSE FOR PARAMETRIC VIBRATION SYSTEM

采用Sylvester理论和Fourier级数展开方法分别研究了参数振动系统自由响应和强迫响应的频谱特性(频谱成分及其分布规律),讨论了系统稳定性和阻尼对于频谱幅值的影响,并给出了系统外激励共振条件.理论研究结果表明:由于参数激励作用使得系统响应具有多频特点,这些频谱成分与系统固有频率、参数激励频率和外激励频率具有密切联系,而且其在频域分布也呈现出一定的规律.此外,参数振动系统具有多个外激励共振点,除了外激励频率等于系统固有频率将发生共振外,当外激励频率等于系统固有频率和参数激励频率的组合值时,同样将发生外激励共振现象.

Utilizing Sylvester＇s theorem and Fourier series approximations,commonly used in the matrix decomposition,the spectral components for both the free and forced responses of linear parametrically excited system are obtained theoretically,and the effects of parametric stability and damping on the spectral amplitudes are discussed in detail.Consequently,the outer excitation resonant condition for parametric system is found. It is concluded from the theoretical results as follows：parametric excitation leads to multi-frequency response; these spectra are closely related to the natural frequency,parametric frequency and the outer excitation frequency （only for the forced response） of the system;the distribution for these spectra in frequency domain follow certain laws;there are multi-resonances caused by outer excitation in parametric vibration system.