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| The generalized coordinates synthesis method for the random vibration analysis |
| Received:September 11, 2010 Revised:October 24, 2011 |
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| DOI：10.7511/jslx20122004 |
| KeyWord:random vibration complete quadratic combination (CQC) method generalized coordinates synthesis (GCS) method pseudo-excitation method (PEM) harmonic-excitation method (HEM) |
| Author | Institution |
| 陈凯 |
中国建筑科学研究院, 北京 |
| 钱基宏 |
中国建筑科学研究院, 北京 |
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| Abstract: |
| 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. |
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