Simplifications of CQC method and CCQC method
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Yu Ruifang (ÓáÈð·¼) and Zhou Xiyuan (ÖÜÎýÔª)
Beijing Laboratory of Earthquake Engineering and Structural Retrofit,
Beijing University of Technology, Beijing 100022, China
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Abstract: The response-spectrum mode
superposition method is widely used for seismic response analyses of linear
systems. In using this method, the complete quadratic combination (CQC) is
adopted for classically damped linear systems and the complex complete quadratic
combination (CCQC) formula is adopted for non-classically damped linear systems.
However, in both cases, the calculation of seismic response analyses is very
time consuming. In this paper, the variation of the modal correlation
coefficients of displacement, velocity and displacement-velocity with frequency
and damping ratios of two modes of interest are studied, Moreover, the
calculation errors generated by using CQC and
square-root-of-the-sum-of-the-squares (SRSS) methods (or CCQC and CSRSS methods)
for different damping combinations are compared. In these analyses, some
boundary lines for classically and non-classically damped systems are plotted to
distinguish the allowed minimum frequency ratio at given geometric mean of the
damping ratios of both modes if their relativity is neglected. Furthermore, the
simplified method, which is a special mode quadratic combination method
considering only relativity of adjacent modes in CQC method and named simplified
CQC or partial quadratic combination (PQC) method for classically damped linear
system, is proposed to improve computational efficiency, and the criterion for
determination of how many correlated modes should be adopted is proposed.
Similarly, the simplified CCQC or complex partial quadratic combination (CPQC)
method for the non-classically damped linear system and the corresponding
criterion are also deduced. Finally, a numerical example is given to illustrate
the applicability, computational accuracy and efficiency of the PQC and CPQC
methods.
Keywords: mode superposition; non-classical
damping; complex complete quadratic combination; partial quadratic combination
(PQC)
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