Consideration of uncertainties in seismic analysis of non-classically damped coupled systems

Tadinada, Sashi Kanth; Gupta, Abhinav

doi:10.1016/j.nucengdes.2011.02.011

Cited by 3 publications

(2 citation statements)

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“…Moreover, knowledge of correlations does not ensure that the randomly sampled sets of natural frequencies will remain as ordered sets. Tadinada shows that explicit consideration of correlation coefficients between the natural frequencies may not ensure correct sampling unless the frequencies are perfectly correlated. The frequencies of a structure are perfectly correlated if and only if the uncertainty in the structure is dominated by a single parameter, which is not usually the case.…”

Section: Motivationmentioning

confidence: 99%

“…The evaluation of the joint density function would be simplified if the joint density function is assumed to be centrally symmetric. In the case of two modes with closely‐spaced frequencies, the assumption of central symmetry appears reasonable because the frequencies tend to be strongly and positively correlated . The assumption, however, would not hold when the two frequencies are negatively correlated.…”

Section: Formulation For Joint Probability Density Functionmentioning

confidence: 99%

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Sampling of closely‐spaced ordered set of uniformly distributed random variables

Tadinada

Gupta

2011

Numerical Meth Engineering

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SUMMARYWhen the individual PDFs of closely-spaced random variables such as natural frequencies of a structure overlap, generation of 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 sets. Rejection of such disordered sample sets results in individual density functions that are significantly different from the distributions initially assumed for sampling each random variable. One way to overcome this constraint in the simulation of an ordered set of random variables is to consider them in an implicit manner using a joint PDF. In this paper, we present a formulation for a joint density function that is developed using fundamental probability approaches. The formulation ensures that the sampled random variables always remain as ordered sets and maintain the individual density functions for each variable. Application of the proposed formulation is illustrated for cases with not just two closely-spaced variables but also for a case with multiple closely-spaced variables such that the PDFs of more than two random variables overlap with each other. An expression is presented to determine the exact number of terms needed in the formulation. However, it is also illustrated that only two terms are sufficient in most applications even when the exact number of terms needed is very high.

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Section: Motivationmentioning

confidence: 99%

Section: Formulation For Joint Probability Density Functionmentioning

confidence: 99%