Complex complete quadratic combination method for

Authors: Ruifang Yu Xiyuan Zhou Abduwahit Abduwaris

Publish Date: 2016/09/08

Volume: 15, Issue: 3, Pages: 537-550

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Abstract

A new responsespectrum 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 CCQCR method in which the correlation coefficients of highorder modal responses are enclosed in addition to the correlation coefficients in the normal CCQC method As a result the formulas for calculating the correlation coefficients of highorder modal responses are deduced in this study including displacement velocity and velocitydisplacement correlation coefficients Furthermore the relationship between highorder displacement and velocity covariance is derived to make the CCQCR algorithm only relevant to the highorder displacement response spectrum Finally a practical stepbystep integration procedure for calculating highorder displacement response spectrum is obtained by changing the earthquake ground motion input which is evaluated by comparing it to the theory solution under the sinewave input The method derived here is suitable for generally linear systems with classical or nonclassical damping

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