平稳高斯激励下线性结构随机振动分析的辅助简谐激励广义法

相比于时域法,频域法是更为高效、易行的随机振动分析方法,但对于平稳激励下的随机振动分析,现有频域方法常需振型截断或功率谱矩阵分解,将会影响计算精度和效率.为此,本文在频域法的框架下,针对平稳高斯激励下线性结构的随机振动分析提出了一种精确且高效的辅助简谐激励广义法.首先,引入广义脉冲响应函数和广义频响函数的概念,推导了与...

AUXILIARY HARMONIC EXCITATION GENERALIZED METHOD FOR RANDOM VIBRATION ANALYSIS OF LINEAR STRUCTURES UNDER STATIONARY GAUSSIAN EXCITATION

Compared with the time-domain method, the frequency-domain method is a more efficient and easy-toimplement method for random vibration analysis. However, the existing frequency-domain methods often involve truncation for degree of mode or decomposition of the power spectrum in multi-correlation conditions, which may have impact on the computational accuracy and efficiency of the methods. To this end, an accurate and efficient auxiliary harmonic excitation generalized method is proposed for the analysis of random vibration of linear structures under stationary Gaussian excitation in the framework of the frequency domain method. First, the concepts of generalized impulse response function and generalized frequency response function are introduced, and a generalized analysis method, which is equivalent to the complete quadratic combination method of response power spectrum calculation, is derived. Secondly, replacing the product of generalized frequency response function by the product of response of auxiliary harmonic excitation, a more easily implemented auxiliary harmonic excitation generalized method is further proposed based on generalized analysis method. Third, according to the different calculation methods of response for structure under the auxiliary harmonic excitation, two generalized methods of auxiliary harmonic excitation generalized method with different applicability are proposed, namely, the auxiliary harmonic excitation generalized method based on the mode superposition and the auxiliary harmonic excitation generalized method based on the time analysis. Meanwhile,the computational performance of the above two methods and their comparative analysis with the existing methods are introduced. Finally, the computational accuracy and efficiency of the proposed method are verified by two examples. The results of the examples show that the auxiliary harmonic excitation generalized method has significant advantages of the calculation efficiency over the complete quadratic combination method and the pseudo-excitation method with the same calculation accuracy.