随机振动问题的广义坐标合成法

工程中的随机振动分析多采用完全二次型组合法(CQC)及其改进算法,如虚拟激励法(PEM)和谐波激励法(HEM)。广义坐标合成法(GCS)提出了一种计算随机响应的新思路,其基本原理是将物理空间的计算转移到自由度较小的振型空间进行,从而缩减了计算量和计算规模。对于较大规模结构体系的随机振动问题,GCS方法计算响应协方差矩阵的计算量只相当于PEM的2r/sT,其中s、r和T分别为激励功率谱矩阵的秩、振型总数和离散频率点数。此外,对于给定激励时程的问题,由于GCS方法直接求解广义坐标运动方程,因而可以方便得出响应时程。通过对几种方法的详细对比,说明对于大多数只需要求解响应方差的随机振动问题,GCS是最优的计算方法。PEM只有在s

The generalized coordinates synthesis method for the random vibration analysis

The complete quadratic combination (CQC) method as well as its improved forms,such as the pseudo-excitation method (PEM) and the harmonic excitation method (HEM),is the most common approach to solving the random vibration problem in the engineering application.The generalized coordinates synthesis (GCS) method provides a new approach to accomplishing the random vibration analysis.It conducts the calculation in the modal space firstly and then derives the results to the physical space.Due to the less independent dimensions in the modal space,the calculation amount to obtain the response covariance matrices is significantly reduced.The ratio of the computational efforts between the GCS method and the PEM is only 2r/sT,where s,r and T represent,respectively,the rank of the excitation power spectral density (PSD) matrix,the number of the modes and the total number of the discrete frequency points.Besides,for the random vibration described by the excitation time history the GCS method directly solves the dynamic equations of the generalized coordinates so that the response time history can be calculated handily by the mode superposition.The comprehensive comparison of the different methods shows that the GCS method is the best method for most of the random vibration problems.The PEM will be more efficient only if the response PSD matrices are required and s<r.The HEM is in fact equivalent to the PEM with s=1.