A universal matrix perturbation technique for complex modes is presented. This technique is applicable to all the three cases of complex eigenvalues: distinct, repeated and closely spaced eigenvalues. The lower order ...A universal matrix perturbation technique for complex modes is presented. This technique is applicable to all the three cases of complex eigenvalues: distinct, repeated and closely spaced eigenvalues. The lower order perturbation formulas are obtained hy performing two complex eigensubspace condensations, and the higher order perturbation formulas are derived hy a successive approximation process. Three illustrative examples are given to verify the proposed method and satisfactory results are observed.展开更多
A new matrix perturbation analysis method is presented for efficient approximate solution of the complex modal quadratic generalized eigenvalue problem of viscously damped linear vibration systems. First, the damping ...A new matrix perturbation analysis method is presented for efficient approximate solution of the complex modal quadratic generalized eigenvalue problem of viscously damped linear vibration systems. First, the damping matrix is decomposed into the sum of a proportional-and a nonproportional-damping parts, and the solutions of the real modal eigenproblem with the proportional dampings are determined, which are a set of initial approximate solutions of the complex modal eigenproblem. Second, by taking the nonproportional-damping part as a small modification to the proportional one and using the matrix perturbation analysis method, a set of approximate solutions of the complex modal eigenvalue problem can be obtained analytically. The result is quite simple. The new method is applicable to the systems with viscous dampings-which do not deviate far away from the proportional-damping case. It is particularly important that the solution technique be also effective to the systems with heavy, but not over, dampings. The solution formulas of complex modal eigenvlaues and eigenvectors are derived up to second-order perturbation terms. The effectiveness of the perturbation algorithm is illustrated by an exemplar numerical problem with heavy dampings. In addition, the practicability of approximately estimating the complex modal eigenvalues, under the proportional-damping hypothesis, of damped vibration systems is discussed by several numerical examples.展开更多
In the study of finite element model updating or damage detection,most papers are devoted to undamped systems.Thus,their objective has been exclusively restricted to the correction of the mass and stiffness matrices.I...In the study of finite element model updating or damage detection,most papers are devoted to undamped systems.Thus,their objective has been exclusively restricted to the correction of the mass and stiffness matrices.In contrast,this paper performs the model updating and damage detection for damped structures.A theoretical contribution of this paper is to extend the cross-model cross-mode(CMCM) method to simultaneously update the mass,damping and stiffness matrices of a finite element model when only few spatially incomplete,complex-valued modes are available.Numerical studies are conducted for a 30-DOF(degree-of-freedom) cantilever beam with multiple damaged elements,as the measured modes are synthesized from finite element models.The numerical results reveal that applying the CMCM method,together with an iterative Guyan reduction scheme,can yield good damage detection in general.When the measured modes utilized in the CMCM method are corrupted with irregular errors,assessing damage at the location that possesses larger modal strain energy is less sensitive to the corrupted modes.展开更多
An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the rea...An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the real model superposition approximation method to the seismic response calculation of industrial buildings.The analysis using lumped mass-and-shear spring models indicates that for the equipment-to-structure frequency ratiosγf>1.1 orγf<0.9,the non-classical damping effect is limited,and the real mode superposition approximation method provides accurate estimates.For 0.9<γf<1.1,the system may have a pair of closely spaced frequency modes,and the non-zero off-diagonal damping terms have a non-negligible effect on the damping ratios and mode shape vectors of these modes.For 0.9<γf<1.1 and the equipment-to-structure mass ratiosγm<0.07,the real mode superposition approximation method results in large errors,while the approximation method can provide an accurate estimation for 0.9<γf<1.1 andγm>0.07.Furthermore,extensive parametric analyses are conducted,where both steel structures and reinforced concrete structures with equipment with various damping ratios are considered.Finally,the finite element analysis of a five-story industrial building is adopted to validate the proposed range of applicability.展开更多
文摘A universal matrix perturbation technique for complex modes is presented. This technique is applicable to all the three cases of complex eigenvalues: distinct, repeated and closely spaced eigenvalues. The lower order perturbation formulas are obtained hy performing two complex eigensubspace condensations, and the higher order perturbation formulas are derived hy a successive approximation process. Three illustrative examples are given to verify the proposed method and satisfactory results are observed.
文摘A new matrix perturbation analysis method is presented for efficient approximate solution of the complex modal quadratic generalized eigenvalue problem of viscously damped linear vibration systems. First, the damping matrix is decomposed into the sum of a proportional-and a nonproportional-damping parts, and the solutions of the real modal eigenproblem with the proportional dampings are determined, which are a set of initial approximate solutions of the complex modal eigenproblem. Second, by taking the nonproportional-damping part as a small modification to the proportional one and using the matrix perturbation analysis method, a set of approximate solutions of the complex modal eigenvalue problem can be obtained analytically. The result is quite simple. The new method is applicable to the systems with viscous dampings-which do not deviate far away from the proportional-damping case. It is particularly important that the solution technique be also effective to the systems with heavy, but not over, dampings. The solution formulas of complex modal eigenvlaues and eigenvectors are derived up to second-order perturbation terms. The effectiveness of the perturbation algorithm is illustrated by an exemplar numerical problem with heavy dampings. In addition, the practicability of approximately estimating the complex modal eigenvalues, under the proportional-damping hypothesis, of damped vibration systems is discussed by several numerical examples.
基金the National High-Tech Research and Development Program of China("863")(Grant No.2006AA09Z331)the China National Science Fund for Distinguished Young Scholars(Grant No.50325927)the National Natural Science Foundation of China(Grant No.50739004)
文摘In the study of finite element model updating or damage detection,most papers are devoted to undamped systems.Thus,their objective has been exclusively restricted to the correction of the mass and stiffness matrices.In contrast,this paper performs the model updating and damage detection for damped structures.A theoretical contribution of this paper is to extend the cross-model cross-mode(CMCM) method to simultaneously update the mass,damping and stiffness matrices of a finite element model when only few spatially incomplete,complex-valued modes are available.Numerical studies are conducted for a 30-DOF(degree-of-freedom) cantilever beam with multiple damaged elements,as the measured modes are synthesized from finite element models.The numerical results reveal that applying the CMCM method,together with an iterative Guyan reduction scheme,can yield good damage detection in general.When the measured modes utilized in the CMCM method are corrupted with irregular errors,assessing damage at the location that possesses larger modal strain energy is less sensitive to the corrupted modes.
基金Fund of China National Industrial Building Diagnosis and Reconstruction Engineering Technology Research Center under Grant No.YZA2017Ky03the Beijing Natural Science Foundation under Grant No.JQ18029the National Natural Science Foundation of China under Grant No.52078277。
文摘An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the real model superposition approximation method to the seismic response calculation of industrial buildings.The analysis using lumped mass-and-shear spring models indicates that for the equipment-to-structure frequency ratiosγf>1.1 orγf<0.9,the non-classical damping effect is limited,and the real mode superposition approximation method provides accurate estimates.For 0.9<γf<1.1,the system may have a pair of closely spaced frequency modes,and the non-zero off-diagonal damping terms have a non-negligible effect on the damping ratios and mode shape vectors of these modes.For 0.9<γf<1.1 and the equipment-to-structure mass ratiosγm<0.07,the real mode superposition approximation method results in large errors,while the approximation method can provide an accurate estimation for 0.9<γf<1.1 andγm>0.07.Furthermore,extensive parametric analyses are conducted,where both steel structures and reinforced concrete structures with equipment with various damping ratios are considered.Finally,the finite element analysis of a five-story industrial building is adopted to validate the proposed range of applicability.
