Time-Dependent Spectral Content of System Response

Random vibration analysis provides a meaningful way to assess the ability of a structure to withstand seismic and wind forces. In the former case the nonstationarity of the mean square value and relative frequency content is important. The concept of a time-dependent frequency domain description of a random process is applied to a linear one degree-of-freedom system suddenly exposed to a zero-mean steady wide-band random excitation. The evolving bandwidth of the oscillator response can be measured by a shape function in terms of the first few spectral moments of the response time-dependent spectral density function. The shape depends on the oscillator damping and the number of cycles of response. The result can be used to estimate the equivalent viscous damping from recorded structural response to earthquake or wind excitation. Record length and oscillator period and damping affect the reliability of the damping estimate.