Consideration of uncertainties in seismic analysis of non-classically damped coupled systems
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Date
2009-04-22
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Abstract
The objective of this study is to investigate the effect of uncertainties in modal properties of
uncoupled primary and secondary systems in the seismic analysis of non-classically damped
Multi Degree of Freedom (MDOF) primary – MDOF secondary coupled systems by response
spectrum method.
The design response of the secondary system is evaluated by conducting multiple
analyses of coupled system with randomly sampled sets of uncoupled natural frequencies of
primary and secondary systems. Generating the random samples of frequencies require
knowledge of their probability density functions. When the individual probability density
functions overlap, generating sample sets by assuming the frequencies to be independent
random variables can lead to incorrect sets of frequencies in the sense that the frequencies do
not remain as ordered pairs or ordered sets. The frequencies of any uncoupled primary or
secondary system should all be in an ascending order. This necessitates the need for
considering correlations between such closely spaced frequencies. However, determination
of correlations between the natural frequencies of a structure is either not possible or
impractical. So, any sampling scheme should consider the constraint that any randomly
sampled set of uncoupled frequencies be an ordered set. Moreover, rejecting the incorrect
samples result in individual density functions that are significantly different from the
distributions initially assumed for sampling of each natural frequency. A formulation for a
joint probability density function for the frequencies is developed using fundamental probability approaches. Sampling the frequencies by using the joint density function ensures
that each sampled set remains ordered while maintaining the individual density functions.
Development of formulation for the joint density function of frequencies enabled the
application of the Square-root-of-mean-of-squares (SRMS) method proposed by Gupta and
Choi (2005) to MDOF primary – MDOF secondary systems. Two types of MDOF primary –
MDOF secondary system configurations considered in this validation and verification study
are (i) singly-connected secondary systems and (ii) multiply-connected secondary systems.
Various degrees of tuning between primary and secondary systems were considered. The
modified SRMS method is validated for both types of configurations.
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Keywords
uncertainties in modal properties, structural dynamics, coupled systems, probability density function of natural frequenci, building piping systems
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Degree
MS
Discipline
Civil Engineering