工程振动测试技术中实验模态分析方法的改进

Study on Experimental Modal Analysis Method in Engineering Vibration Testing Technology

实验模态分析是工程振动测试技术的基本任务之一。现有的工程振动测试技术教材通常采用频响函数的幅频曲线或者功率谱曲线,通过寻找局部峰值来实现模态参数的识别。该方法原理简单,计算方便,但是通常只能识别前几阶模态参数,而且由于受到分辨率的影响,会带来一定的识别误差。通过将现在广泛应用于环境激励下的随机子空间法加以改进,应用于一般激励下的模态参数识别;构建Hankel矩阵和Toeplitz矩阵,进行奇异值分解,并重构更稳定的结构状态矩阵,形成稳态图来识别结构的模态参数;以一个七层框架结构的数值模拟和一个实验室测试的简支钢梁为例演示了该方法。相比于传统实验模态参数识别方法,改进的方法能识别更高阶的模态参数,而且具有更高的精度,适合编程计算,可作为实验模态分析方法教学的有益补充。

Experimental modal analysis is one of the basic tasks of engineering vibration testing technology.The amplitude frequency of frequency response function or the power spectrum curve combined with the peak picking method are used for obtaining the experimental modal parameters in the existing textbooks of experimental modal analysis.The method has simple principles and can be computed conveniently.However,normally only the first several modal parameters can be identified with some identification errors due to resolving power.At present the stochastic subspace identification method(SSI)is used widely in the ambient vibration.In this paper,it is expanded to the vibrations excited by general excitations such as the impulsive excitation or the harmonic excitation.The modal parameters are identified by constructing the Hankel matrix and Toeplitz matrix,applying the singular value decomposition,reconstructing the structural state matrix and finally forming the stabilization diagram.The proposed method is applied to a seven-floor frame structure and the laboratory test simply supported steel beam and the identification procedure is demonstrated.Compared to the traditional experimental modal parameter identification methods,the proposed method can identify more modes of modal parameters with a higher accuracy,and it is suited for programming calculation.The method can be an important supplementary in teaching the experimental modal analysis.