我所2016年发表论文欣赏-第二十期

地球所研究生会 · 公众号 · · 2017-05-22 15:44

正文

题目

Complex complete quadratic combination method for damped system with repeated eigenvalues

作者

Yu Ruifang , Zhou Xiyuan and Abduwaris Abduwahit

发表刊物

《EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION 》

摘要

A new response-spectrum mode superposition method, entirely in real value form, is developed to analyze the maximum structural response under earthquake ground motion for generally damped linear systems with repeated eigenvalues and defective eigenvectors. This algorithm has clear physical concepts and is similar to the complex complete quadratic
combination (CCQC) method previously established. Since it can consider the effect of repeated eigenvalues, it is called the CCQC-R method, in which the correlation coeffi cients of high-order modal responses are enclosed in addition to the correlation coeffi cients in the normal CCQC method. As a result, the formulas for calculating the correlation coeffi cients of high-order modal responses are deduced in this study, including displacement, velocity and velocity-displacement correlation coeffi cients. Furthermore, the relationship between high-order displacement and velocity covariance is derived to make the CCQC-R algorithm only relevant to the high-order displacement response spectrum. Finally, a practical step-by-step integration procedure for calculating high-order displacement response spectrum is obtained by changing the earthquake ground motion input, which is evaluated by comparing it to the theory solution under the sine-wave input. The method derived here is suitable for generally linear systems with classical or non-classical damping.