Structural Response to Stationary Excitation

Stationary responses of single-and multi-degree-of-freedom structures subjected to stationary input excitations are studied. Using a modal superposition prodedure, closed-form solutions for the first three spectral moments of response to white-noise and filtered white-noise inputs are derived. These solutions are in terms of cross-modal contributions and explicitly account for the correlation between modal responses of multi-degree structures; thus, they are applicable to structures with closely spaced frequencies. Speical attention is given a excitations which are typical of earthquake ground motions. Various quantities of response can be obtained in terms of the three spectral moments. These include mean zero-crossing rate and mean, variance, and distribution of 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 study demonstrate range of applicability of white-noise model as an approximation for wide-band inputs.