The Earthquake Engineering Online Archive

Dynamic analysis of multiply tuned and arbitrarily supported secondary systems

Igusa, Takeru; Der Kiureghian, Armen

UCB/EERC-83/07, Earthquake Engineering Research Center, University of California, Berkeley, 1983-07, 227 pages (530/I38/1983)

This study was designed to include all of the important and complicated dynamic characteristics in a dynamic analysis of linear, multidegree-of-freedom (MDOF) secondary subsystems with multiple support points attached to linear MDOF primary subsystems. These characteristics are interaction between the two subsystems; cross-correlations between motions of the support points and modal responses for stochastic input; resonance or tuning phenomena observed when a set of frequencies of one system is tuned with one or more frequencies of the other system; and non-classical damping effects observed when the damping ratios of the two subsystems are different. The basic approach of the analysis is to consider the combined primary and secondary subsystems as a single dynamic assemblage. Such an approach implicitly includes the effects of interaction, multiple support motions, resonance, and non-classical damping, but was avoided in the past due to the size and complexity of the resulting eigenvalue problem and the fact that such systems are nonclassically damped. The main results of the analysis are applied to several representative example systems and compared with results obtained from numerical analysis.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-83-07.pdf (12 MB)