Suboptimal Rayleigh damping coefficients in seismic analysis of viscously-damped structures

2014 ◽  
Vol 13 (4) ◽  
pp. 653-670 ◽  
Author(s):  
Danguang Pan ◽  
Genda Chen ◽  
Zuocai Wang
Keyword(s):  
Seismic Analysis ◽  
Damping Coefficients ◽  
Rayleigh Damping

A constrained optimal Rayleigh damping coefficients for structures with closely spaced natural frequencies in seismic analysis

2016 ◽  
Vol 20 (1) ◽  
pp. 81-95 ◽  
Author(s):  
DG Pan ◽  
GD Chen ◽  
LL Gao
Keyword(s):  
Seismic Analysis ◽  
Lattice Structure ◽  
Damping Ratio ◽  
Optimization Method ◽  
Accurate Analysis ◽  
Damping Coefficients ◽  
Rayleigh Damping ◽  
Optimal Load ◽  
Parametric Studies ◽  
Response Spectral Analysis

A constrained optimization method is proposed to determine Rayleigh damping coefficients for the accurate analysis of complex structures. To this end, an objective function was defined to be a complete quadratic combination of the modal errors of a peak base reaction evaluated by response spectral analysis. An optimization constraint was enforced to make the damping ratio of a prominent contribution mode exact. Parametric studies were conducted to investigate the effects of the constraint, the cross term of modes, and weighting factors on the optimization objective. A two-story building and a real-world lattice structure were analyzed under six earthquake ground motions to understand the characteristics and demonstrate the accuracy and effectiveness of the proposed optimization method. Unlike the conventional Rayleigh damping, the optimization method provided an optimal load-dependent reference frequencies that account for varying frequency characteristics of earthquakes around the prominent contribution mode.

scholarly journals Computation of Rayleigh Damping Coefficients for the Seismic Analysis of a Hydro-Powerhouse

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Zhiqiang Song ◽  
Chenhui Su
Keyword(s):  
Seismic Response ◽  
Seismic Analysis ◽  
Damping Ratio ◽  
Least Square Method ◽  
Least Square ◽  
Dynamic Responses ◽  
Damping Coefficients ◽  
Rayleigh Damping ◽  
Damping Matrix ◽  
Fundamental Frequencies

The mass and stiffness of the upper and lower structures of a powerhouse are different. As such, the first two vibration modes mostly indicate the dynamic characteristics of the upper structure, and the precise seismic response of a powerhouse is difficult to obtain on the basis of Rayleigh damping coefficients acquired using the fundamental frequencies of this structure. The damping ratio of each mode is relatively accurate when the least square method is used, but the accuracy of the damping ratios that contribute substantially to seismic responses is hardly ensured. The error of dynamic responses may even be amplified. In this study, modes that greatly influence these responses are found on the basis of mode participation mass, and Rayleigh damping coefficients are obtained. Seismic response distortion attributed to large differences in Rayleigh damping coefficients because of improper modal selection is avoided by using the proposed method, which is also simpler and more accurate than the least square method. Numerical experiments show that the damping matrix determined by using the Rayleigh damping coefficients identified by our method is closer to the actual value and the seismic response of the powerhouse is more reasonable than that revealed through the least square method.

scholarly journals Approach for Selection of Rayleigh Damping Parameters Used for Time History Analysis

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
R. E. Spears ◽  
S. R. Jensen
Keyword(s):  
Seismic Analysis ◽  
Time History ◽  
System Response ◽  
Piping System ◽  
Nuclear Facilities ◽  
Rayleigh Damping ◽  
Modal Damping ◽  
American Society ◽  
Selection Of ◽  
Civil Engineers

Nonlinearities, whether geometric or material, need to be addressed in seismic analysis. One good analysis method that can address these nonlinearities is direct time integration with Rayleigh damping. Modal damping is the damping typically specified in seismic analysis Codes and Standards (ASCE 4-98, 1998, “Seismic Analysis of Safety-Related Nuclear Structures and Commentary,” American Society of Civil Engineers, Reston, Virginia and ASCE/SEI 43-05, 2005, “Seismic Design Criteria for Structures, Systems, and Components in Nuclear Facilities,” American Society of Civil Engineers, Reston, Virginia.). Modal damping is constant for all frequencies where Rayleigh damping varies with frequency. An approach is proposed here for selection of Rayleigh damping coefficients to be used in seismic analyses that is consistent with given modal damping. The approach uses the difference between the modal damping response and the Rayleigh damping response along with effective mass properties of the model being evaluated to match overall system response levels. This paper provides a simple example problem to demonstrate the approach. It also provides results for a finite element model representing an existing piping system. Displacement, acceleration, and stress results are compared from model runs using modal damping and model runs using Rayleigh damping with coefficients selected using the proposed method.

scholarly journals A constrained optimization solution for Caughey damping coefficients in seismic analysis

2017 ◽  
Vol 34 (3) ◽  
pp. 682-708
Author(s):  
Danguang Pan ◽  
Chenfeng Li
Keyword(s):  
Seismic Analysis ◽  
Response Spectrum ◽  
Programming Approach ◽  
Content Type ◽  
Practical Applications ◽  
Damping Coefficients ◽  
Modal Damping ◽  
Orthogonality Conditions ◽  
Optimal Damping ◽  
Damping Model

Purpose Extended from the classic Rayleigh damping model in structural dynamics, the Caughey damping model allows the damping ratios to be specified in multiple modes while satisfying the orthogonality conditions. Despite these desirable properties, Caughey damping suffers from a few major drawbacks: depending on the frequency distribution of the significant modes, it can be difficult to choose the reference frequencies that ensure reasonable values for all damping ratios corresponding to the significant modes; it cannot ensure all damping ratios are positive. This paper aims to present a constrained quadratic programming approach to address these issues. Design/methodology/approach The new method minimizes the error of the structural displacement peak based on the response spectrum theory, while all modal damping ratios are constrained to be greater than zero. Findings Several comprehensive examples are presented to demonstrate the accuracy and effectiveness of the proposed method, and comparisons with existing approaches are provided whenever possible. Originality/value The proposed method is highly efficient and allows the damping ratios to be conveniently specified for all significant modes, producing optimal damping coefficients in practical applications.

scholarly journals Computation of Rayleigh damping coefficient of a rectangular submerged floating tunnel (SFT)

2020 ◽  
Vol 2 (5) ◽  
Author(s):  
Md. Hafizur Rahman ◽  
Chhavi Gupta
Keyword(s):  
Dynamic Analysis ◽  
Modal Analysis ◽  
Fundamental Frequency ◽  
Significant Role ◽  
Analytical Study ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Damping Coefficients ◽  
Rayleigh Damping ◽  
Submerged Floating Tunnel

Abstract The dynamic behaviors of the submerged floating tunnel, a buoyant structure of high slenderness, are a matter of concern since it is surrounded by the huge hazardous effects called hydrodynamic, seismic and functional action. Modal analysis and Rayleigh damping coefficients play a significant role in dynamic analysis, but it is not sufficiently simple to predict the reasonable damping coefficients named α and β. The present paper outlines the modal analysis and the calculation of Rayleigh damping coefficients that provide the natural frequencies, mode shapes, mode’s motion as well as coefficients α and β. To compute the Rayleigh damping coefficients, 2–10% damping to the critical damping has been assumed for this analytical study. For the analysis, an FEA-based software ANSYS is utilized successfully. It has been seen that the fundamental frequency and Rayleigh damping coefficients (α = 0.946 and β = 0.00022) of the SFT are reasonably high and it is under noticeable damping.

scholarly journals Approach for Selection of Rayleigh Damping Parameters Used for Time History Analysis

2009 ◽  
Author(s):  
R. E. Spears ◽  
S. R. Jensen
Keyword(s):  
Seismic Analysis ◽  
Time Integration ◽  
Time History ◽  
Element Model ◽  
System Response ◽  
Piping System ◽  
Rayleigh Damping ◽  
Modal Damping ◽  
The Difference ◽  
Selection Of

Nonlinearities, whether geometric or material, need to be addressed in seismic analysis. One good analysis method that can address these nonlinearities is direct time integration with Rayleigh damping. Modal damping is the damping typically specified in seismic analysis Codes and Standards [1, 2]. Modal damping is constant for all frequencies where Rayleigh damping varies with frequency. An approach is proposed here for selection of Rayleigh damping coefficients to be used in seismic analyses that are consistent with given Modal damping. The approach uses the difference between the modal damping response and the Rayleigh damping response along with effective mass properties of the model being evaluated to match overall system response levels. This paper provides a simple example problem to demonstrate the approach. It also provides results for a finite element model representing an existing piping system. Displacement, acceleration, and stress results are compared from model runs using modal damping and model runs using Rayleigh damping with coefficients selected using the proposed method.

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