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Simplifications of CQC method and CCQC method

Earthquake Engineering and Engineering Vibration 2007年第1期6卷 65-76页

作者：俞瑞芳周锡元 Beijing Laboratory of Earthquake Engineering and Structural Retrofit Beijing University of Technology

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-thesquares （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.

关键词： mode superposition non-classical damping complex complete quadratic combination partial quadraticcombination (PQC)

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Approximate analytical solutions and experimental analysis for transient response of constrained damping cantilever beam

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Applied Mathematics and Mechanics(English Edition) 2010年第11期31卷 1359-1370页

作者：胡明勇王安稳章向明 College of Science Naval University of Engineering

Vibration mode of the constrained damping cantilever is built up according to the mode superposition of the elastic cantilever beam. The control equation of the constrained damping cantilever beam is then derived using Lagrange＇s equation. Dynamic response of the constrained damping cantilever beam is obtained according to the principle of virtual work, when the concentrated force is suddenly unloaded. Frequencies and transient response of a series of constrained damping cantilever beams are calculated and tested. Influence of parameters of the damping layer on the response time is analyzed. Analyitcal and experimental approaches are used for verification. The results show that the method is reliable.

关键词： constrained damping cantilever beam transient response Lagrange's equation mode superposition

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PRECISELY COMPENSATED EFFICIENT COMPONENT mode SYNTHESIS METHOD

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Chinese Journal of Mechanical Engineering 2004年第1期17卷 142-144页

作者： ZhuYutian IchiroHagiwara CollegeofMechanicalandAutomobileEngineenng HefeiUniversityofTechnologyHefei230009China DepartmentofMechanicalEngineeringandScience TokyoInstituteofTechnologyTokyo152-8552Japan

Based on the improved mode superposition method proposed by Z. D. Ma and ***, a precisely compensated efficient mode synthesis method is developed. The calculationprocedure is discussed in detail and the truncation error is also analyzed. By comparison, it isshown that this method has a higher accuracy and a less calculation time than the general used ones.

关键词： Component mode synthesis Truncation error mode superposition

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