Seismic response spectra of a combined system by Green's functions

F. M. Lavelle, L. A. Bergman, P. D. Spanos

Research output: Contribution to journalArticlepeer-review


A parametric study of the response of a class of linear secondary systems to earthquake excitations is made. The combined dynamical system studied consists of a single-degree-of-freedom oscillator attached to a continuous cantilever beam. The generalized differential equation governing free vibration is solved exactly for the modes of the combined system. Floor response spectra for records from the 1985 Mexico City and the 1940 El Centro earthquakes are presented in several formats. The floor response spectrum concept is an extension of the widely used ground response spectrum and may provide useful insight into the behavior of linear secondary systems. The effects of each of the system parameters are examined. It is shown that the frequency characteristics of the excitation modify the relative importance of the system parameters. The study also demonstrates the effectiveness and limitations of the cascade approximation which is often applied as an approximate solution to the problem.

Original languageEnglish (US)
Pages (from-to)93-100
Number of pages8
JournalSoil Dynamics and Earthquake Engineering
Issue number2
StatePublished - Feb 1991
Externally publishedYes


  • Green's function
  • cascade
  • combined systems
  • floor response spectrum
  • interaction
  • modal analysis
  • non-proportional damping
  • secondary systems

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Geotechnical Engineering and Engineering Geology
  • Soil Science


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