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Seismic Engineering

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

[+] Author and Article Information
R. E. Spears

Senior Research Engineer
Idaho National Laboratory,
P.O. Box 1625,
Idaho Falls, ID 83415-3720
e-mail: Robert.Spears@inl.gov

S. R. Jensen

Senior Analysis Integrator
Idaho National Laboratory,
P.O. Box 1625,
Idaho Falls, ID 83415-3650
e-mail: Stuart.Jensen@inl.gov

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the Journal of Pressure Vessel Technology. Manuscript received September 1, 2009; final manuscript received April 25, 2012; published online October 18, 2012. Assoc. Editor: Tomoyo Taniguchi.

The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this work, or allow others to do so, for United States government purposes.

J. Pressure Vessel Technol 134(6), 061801 (Oct 18, 2012) (7 pages) doi:10.1115/1.4006855 History: Received September 01, 2009; Revised April 25, 2012

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.

Copyright © 2012 by ASME
Topics: Damping
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References

ASCE 4-98, 1998, “Seismic Analysis of Safety-Related Nuclear Structures and Commentary,” American Society of Civil Engineers, Reston, Virginia.
ASCE/SEI 43-05, 2005, “Seismic Design Criteria for Structures, Systems, and Components in Nuclear Facilities,” American Society of Civil Engineers, Reston, Virginia.
Parametric Technology Corporation, 2007, mathcad14.0, 2007.
2007 American Society of Mechanic Engineers (ASME) Boiler & Pressure Vessel Code BPVC,” Section III, Division 1 — Subsection NB, “Class 1 Components,” ASME International, New York, NY.
ABAQUS Inc., 2007, abaqus Standard, Version6.7-5.

Figures

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Fig. 1

Example shear frame

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Fig. 2

Example earthquake ground motion

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Fig. 3

Example cumulative effective mass ratio

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Fig. 10

Test model cumulative effective mass ratio

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Fig. 11

Sixteen scaled response difference curves

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Fig. 12

Sixteen damping versus frequency curves

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Fig. 13

Sixteen pairs of test model response spectra

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Fig. 9

Test finite element model

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Fig. 19

Extreme modal stress comparison

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Fig. 8

Modal and Rayleigh damped response spectra

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Fig. 7

Scaled response difference

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Fig. 6

Second iteration damping versus frequency

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Fig. 5

Scaled response difference

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Fig. 4

First iteration damping versus frequency

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Fig. 14

Rayleigh and modal displacement comparison

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Fig. 15

Rayleigh and modal acceleration comparison

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Fig. 16

Rayleigh and modal stress comparison

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Fig. 17

Extreme modal displacement comparison

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Fig. 18

Extreme modal acceleration comparison

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