CQC and SRSS methods for non‐classically damped structures

Sinha, Ravi; Igusa, Takeru

doi:10.1002/eqe.4290240410

Cited by 65 publications

(40 citation statements)

References 7 publications

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“…This implies that the coupling between the modal equations due to non-proportional nature of the damping matrix is ignored. Also note that this procedure is not new, as it has been proposed earlier [12][13][14] and has been adopted in the FEMA documents [15; 16]. However, its applicability to asymmetric-plan systems with supplemental damping is explicitly explored for the ÿrst time in this study.…”

Section: Simplified Modal Analysis Of Non-proportional Systemsmentioning

confidence: 94%

“…Although several di erent approaches have been proposed for this purpose, e.g. Reference [11], the most common approach is to simply neglect the o -diagonal elements in the transformed damping matrix [12][13][14]. The modal damping ratios computed from the diagonal terms of the transformed damping matrix are then used in the modal equations that are uncoupled by mode shapes of the undamped system.…”

Section: Introductionmentioning

confidence: 99%

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Simplified analysis of asymmetric structures with supplemental damping

Goel

2001

Earthq Engng Struct Dyn

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SUMMARYThis study investigated the e ects of neglecting o -diagonal terms of the transformed damping matrix on the seismic response of non-proportionally damped asymmetric-plan systems with the speciÿc aim of identifying the range of system parameters for which this simpliÿcation can be used without introducing signiÿcant errors in the response. For this purpose, a procedure is presented in which modal damping ratios computed by neglecting o -diagonal terms of the transformed damping matrix are used in the traditional modal analysis. The e ects of the simpliÿcation are evaluated ÿrst by comparing the aforementioned modal damping ratios with the apparent damping ratios obtained from the complex-valued eigenanalysis. The variation of a parameter that was deÿned by Warburton and Soni as an indicator of the errors introduced by the simpliÿcation is examined next. Finally, edge deformations obtained from the simpliÿed procedure are compared with those obtained from the direct integration of the equations of motion. It is found that the simpliÿed procedure may be used without introducing signiÿcant errors in response for most practical values of the system parameters. Furthermore, estimates of the edge deformations, in general, tend to be on the conservative side.

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Section: Simplified Modal Analysis Of Non-proportional Systemsmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Simplified analysis of asymmetric structures with supplemental damping

Goel

2001

Earthq Engng Struct Dyn

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“…In this way, equation (38) gives (42) gives the modal covariances, without any approximation, exactly as equation (15).…”

Section: Evaluation Of the Covariancesmentioning

confidence: 96%

Cross-correlation coefficients and modal combination rules for non-classically damped systems

Falsone

Muscolino

1999

Earthquake Engng. Struct. Dyn.

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SUMMARYIn stochastic analysis the knowledge of cross-correlation coe$cients is required in order to combine the response of the modal Single-Degree-Of-Freedom (SDOF) oscillators for obtaining the nodal response. Moreover these coe$cients play a fundamental role in the seismic analysis of structures when the response spectrum method is used. In fact they are used in some modal combination rules in order to obtain the maximum response quantities starting from the modal maxima. Herein a method for the evaluation of the cross-correlation coe$cients for non-classically damped systems is presented. It is de"ned in the time domain instead of the frequency domain as usually encountered in the literature. Although non-classically damped structures possess complex eigenproperties, the great advantage in using this approach lies in the fact that the evaluation of these coe$cients does not require complex quantities. Moreover a further particularization of the presented method allows a simple application of the spectrum analysis requiring only one response spectrum for an assigned damping ratio.

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“…Moreover, supplemental dampers should be added in the orthogonal (x) direction to increase the e ectiveness of supplemental damping in reducing structural response (see Figure 15 in Reference [1]). Finally, relative damper sizesc 1 =c y and c 2 =c y , where c y = c 1 +c 2 -can be determined from the e sd value selected to enhance the e ectiveness of supplemental damping in reducing response: c 1 =c y = 0:5 − e sd and c 2 =c y = 0:5 + e sd (3) How then to select the e sd and values? Suppose that earthquake-induced torsion or plan rotation u Âo of an asymmetric one-storey structure cannot exceed some allowable limit, i.e.…”

Section: Design Of Non-linear Supplemental Damping Systemmentioning

confidence: 99%

Asymmetric one‐storey elastic systems with non‐linear viscous and viscoelastic dampers: Simplified analysis and supplemental damping system design

Lin

Chopra

2003

Earthq Engng Struct Dyn

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SUMMARYInvestigated is the accuracy in estimating the response of asymmetric one-storey systems with nonlinear viscoelastic (VE) dampers by analysing the corresponding linear viscous system wherein all non-linear VE dampers are replaced by their energy-equivalent linear viscous dampers. The response of the corresponding linear viscous system is determined by response history analysis (RHA) and by response spectrum analysis (RSA) extended for non-classically damped systems. The exible and sti edge deformations and plan rotation of the corresponding linear viscous system determined by the extended RSA procedure is shown to be su ciently accurate for design applications with errors generally between 10 and 20%. Although similar accuracy is also shown for the 'pseudo-velocity' of non-linear VE dampers, the peak force of the non-linear VE damper cannot be estimated directly from the peak damper force of the corresponding linear viscous system. A simple correction for damper force is proposed and shown to be accurate (with errors not exceeding 15%). For practical applications, an iterative linear analysis procedure is developed for determining the amplitude-and frequency-dependent supplemental damping properties of the corresponding linear viscous system and for estimating the response of asymmetric one-storey systems with non-linear VE dampers from the earthquake design (or response) spectrum. Finally, a procedure is developed for designing non-linear supplemental damping systems that satisfy given design criteria for a given design spectrum.

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CQC and SRSS methods for non‐classically damped structures

Cited by 65 publications

References 7 publications

Simplified analysis of asymmetric structures with supplemental damping

Simplified analysis of asymmetric structures with supplemental damping

Cross-correlation coefficients and modal combination rules for non-classically damped systems

Asymmetric one‐storey elastic systems with non‐linear viscous and viscoelastic dampers: Simplified analysis and supplemental damping system design

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