Generating the simulation transfer function (TF) is indispensable to modal analysis, such as examining modal parameters identification algorithm, and assessing modal analysis software. Comparing 3 feasible algorithms ...Generating the simulation transfer function (TF) is indispensable to modal analysis, such as examining modal parameters identification algorithm, and assessing modal analysis software. Comparing 3 feasible algorithms to simulate TF shows that,one of them is preperable,which is expressing the TF as the function of the complex modal parameters(CMPs),because the deliberate behaviors of CMPs can be implemented easily,such as,dense modals,large damping,and complex modal shape,etc.Nonetheless,even this preferable algorithms is elected,the complex modal shapes cannot be specified arbitrarily,because the number of CMPs far more exceeds that in physical coordinate.So for physical realizable system,there are redundant constraints in CMPs.By analyzing the eigenvalue problem of a complex modal system,and the inversion equations from CMPs to physical parameters,the explicit redundancy constraints were presented.For the special cases,such as the real modal,the damping free modal,and non-complete identification,the specific forms of the redundancy constraints were discussed,along with the number of independent parameters.It is worthy of noting that,redundancy constraints are automatically satisfied for the real modal case.Their equivalent forms on the transfer matrix and a column of transfer matrix were also provided. These results are applicable to generate TF, to implement identification by optimization and appreciate the identification results, to evaluate residual modal, and to verify the complementary of identified modal orders.展开更多
A technique to extract real modes from the identified complex modes is presented in this paper, which enables the normalized real mode shapes, modal masses, and full or reduced mass and stiffness matrices to be obtain...A technique to extract real modes from the identified complex modes is presented in this paper, which enables the normalized real mode shapes, modal masses, and full or reduced mass and stiffness matrices to be obtained. The theoretical derivation of the method is provided in detail. An 11-DOF vibration system is used to validate the algorithm, and to analyze the effects of the number of modes utilized and measurement DOFs on the extraction results. Finally, the method is used to extract real modes from both experimental modal analysis and operational modal analysis.展开更多
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 ...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 coefficients of high-order 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 high-order modal responses are deduced in this study, including displacement, velocity and velocity-displacement correlation coefficients. 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.展开更多
文摘Generating the simulation transfer function (TF) is indispensable to modal analysis, such as examining modal parameters identification algorithm, and assessing modal analysis software. Comparing 3 feasible algorithms to simulate TF shows that,one of them is preperable,which is expressing the TF as the function of the complex modal parameters(CMPs),because the deliberate behaviors of CMPs can be implemented easily,such as,dense modals,large damping,and complex modal shape,etc.Nonetheless,even this preferable algorithms is elected,the complex modal shapes cannot be specified arbitrarily,because the number of CMPs far more exceeds that in physical coordinate.So for physical realizable system,there are redundant constraints in CMPs.By analyzing the eigenvalue problem of a complex modal system,and the inversion equations from CMPs to physical parameters,the explicit redundancy constraints were presented.For the special cases,such as the real modal,the damping free modal,and non-complete identification,the specific forms of the redundancy constraints were discussed,along with the number of independent parameters.It is worthy of noting that,redundancy constraints are automatically satisfied for the real modal case.Their equivalent forms on the transfer matrix and a column of transfer matrix were also provided. These results are applicable to generate TF, to implement identification by optimization and appreciate the identification results, to evaluate residual modal, and to verify the complementary of identified modal orders.
文摘A technique to extract real modes from the identified complex modes is presented in this paper, which enables the normalized real mode shapes, modal masses, and full or reduced mass and stiffness matrices to be obtained. The theoretical derivation of the method is provided in detail. An 11-DOF vibration system is used to validate the algorithm, and to analyze the effects of the number of modes utilized and measurement DOFs on the extraction results. Finally, the method is used to extract real modes from both experimental modal analysis and operational modal analysis.
基金Natural Science Foundation of China under Grant Nos.51478440 and 51108429National Key Technology R&D Program under Grant No.2012BAK15B01
文摘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 coefficients of high-order 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 high-order modal responses are deduced in this study, including displacement, velocity and velocity-displacement correlation coefficients. 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.
