The Earthquake Engineering Online Archive

On response of structures to stationary excitation

Der Kiureghian, Armen

UCB/EERC-79/32, Earthquake Engineering Research Center, University of California, Berkeley, 1979-12, 42 pages (555.2/D43/1979)

Stationary responses of single- and multidegree-of-freedom structures subjected to stationary input excitations are studied. By means of a modal superposition procedure, closed-form solutions are derived for the first three spectral moments of response to white noise and filtered white noise inputs. These solutions account for the correlation between modal responses of multidegree structures; thus, they are applicable to structures with closely spaced modes. Special attention is given to excitations which are typical of earthquake ground motions. Various quantities of response can be obtained in terms of the three spectral moments. These include the mean squares of the response and its time derivative and, in the special case of Gaussian response, the mean zero-crossing rate and the mean, variance, and distribution of the peak response over a specified duration. In this regard, improved, semi-empirical relations for the mean and variance of the peak of a stationary Gaussian process are developed. Results from the study demonstrate the range of applicability of the white noise model as an approximation for wide-band inputs.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-79-32.pdf (1 MB)