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

uncertainties in modal properties;structural dynamics;coupled systems;probability density function of natural frequenci;building piping systems

Tadinada, Sashi Kanth ; Dr. Vernon C. Matzen, Committee Co-Chair,Dr. James M. Nau, Committee Member,Dr. Abhinav Gupta, Committee Chair,Tadinada, Sashi Kanth ; Dr. Vernon C. Matzen ; Committee Co-Chair ; Dr. James M. Nau ; Committee Member ; Dr. Abhinav Gupta ; Committee Chair

University:North Carolina State University

关键词: uncertainties in modal properties;    structural dynamics;    coupled systems;    probability density function of natural frequenci;    building piping systems;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/2134/etd.pdf?sequence=1&isAllowed=y

美国|英语

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【 摘 要 】

The objective of this study is to investigate the effect of uncertainties in modal properties ofuncoupled primary and secondary systems in the seismic analysis of non-classically dampedMulti Degree of Freedom (MDOF) primary – MDOF secondary coupled systems by responsespectrum method.The design response of the secondary system is evaluated by conducting multipleanalyses of coupled system with randomly sampled sets of uncoupled natural frequencies ofprimary and secondary systems. Generating the random samples of frequencies requireknowledge of their probability density functions. When the individual probability densityfunctions overlap, generating sample sets by assuming the frequencies to be independentrandom variables can lead to incorrect sets of frequencies in the sense that the frequencies donot remain as ordered pairs or ordered sets. The frequencies of any uncoupled primary orsecondary system should all be in an ascending order. This necessitates the need forconsidering correlations between such closely spaced frequencies. However, determinationof correlations between the natural frequencies of a structure is either not possible orimpractical. So, any sampling scheme should consider the constraint that any randomlysampled set of uncoupled frequencies be an ordered set. Moreover, rejecting the incorrectsamples result in individual density functions that are significantly different from thedistributions initially assumed for sampling of each natural frequency. A formulation for ajoint probability density function for the frequencies is developed using fundamental probability approaches. Sampling the frequencies by using the joint density function ensuresthat each sampled set remains ordered while maintaining the individual density functions.Development of formulation for the joint density function of frequencies enabled theapplication of the Square-root-of-mean-of-squares (SRMS) method proposed by Gupta andChoi (2005) to MDOF primary – MDOF secondary systems. Two types of MDOF primary –MDOF secondary system configurations considered in this validation and verification studyare (i) singly-connected secondary systems and (ii) multiply-connected secondary systems.Various degrees of tuning between primary and secondary systems were considered. Themodified SRMS method is validated for both types of configurations.