Structural Response to Stationary Excitation

TLDR

The study examines stationary responses of single‑ and multi‑degree‑of‑freedom structures to stationary excitations, deriving cross‑modal solutions applicable to closely spaced frequencies and emphasizing earthquake‑like inputs. Closed‑form modal‑superposition expressions for the first three spectral moments of white‑noise and filtered‑white‑noise responses are derived, enabling calculation of mean, variance, zero‑crossing rate, and peak‑response statistics, and yielding improved semi‑empirical peak‑moment relations. The results show that the white‑noise model approximates wide‑band inputs over a broad range of applicability.

Abstract

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.