利用互相关函数进行环境激励下的模态分析

MODAL PARAMETERS EXTRACTION WITH CROSS CORRELATION FUNCTION UNDER AMBIENT EXCITATION

对互相关函数理论的进一步发展作了详细推导 ,探索出一条将互相关函数理论同多种经典模态分析方法相结合进行环境激励下模态分析的方法。以一悬臂梁为试验模型 ,在白噪声激励下将互相关函数代替脉冲响应函数用于多参考点复指数法和特征实现算法进行模态识别 ,并同功率谱峰值法结果进行了对比。研究表明 。

In most of real operational conditions only response data are measurable while the actual excitations are unknown, so modal parameter must be extracted only from responses. A theory of cross correlation functions is developed in this paper that the cross correlation functions can be expressed as summations of decaying sinusoids as the impulse response functions under white noise excitation. Each decaying sinusoid has a damped natural frequency and a damping ratio that is identical to that of a corresponding structural mode. So cross correlation functions can be applied to some classical modal analysis method instead of the impulse response functions under ambient excitation. The Complex Exponential Method and Eigensystem Realization Algorithm with cross correlation functions are applied to a cantilever beam. The modal properties of the beam from both of these methods are compared with those from peak picking of power spectral density under white noise excitation. The results show that the proposed method in this paper is feasible exactly. The modal analysis method with cross correlation functions opens up a new path of modal analysis under unknown excitation.