Nonstationary Response Analysis of Long Span Bridges under Spatially Varying Differential Support Motions Using Continuous Wavelet Transform

Abstract

An input-output relation for the nonstationary response of long-span bridges subjected to random differential support motions is proposed in the present study. The proposed methodology is more general than the existing ones, in the sense that it can evaluate nonstationarity in both the intensity and frequency content of the response statistics for spatially correlated multipoint random excitations. Furthermore, because the input-output relation is established through the transfer functions of dynamic systems, the proposed wavelet-based methodology can easily be used to predict the stochastic response of any structural systems in conjunction with available finite-element software. The input-output formulation is also not restricted to a particular wavelet basis function, since it has been derived by following a general wavelet-based description of input nonstationary processes. The bridge has been modeled as a simply supported beam with multispans in a finite-element framework to obtain the dynamic properties. With a modified form of the Littlewood-Paley (real part of harmonic) wavelet basis function, the support motion has been modeled as a summation of independent random processes in different nonoverlapping frequency bands. At each frequency band, the random process is expressed as a product of a stationary orthogonal process and a deterministic envelope function that depends on the scale. An exponential coherence function is used to model the spatial variation of the ground motion. The response statistics are obtained by using a random vibration formulation in the wavelet domain. The results demonstrate the effects of frequency nonstationarity on the response of a multispan bridge with closely spaced modes and excitation of higher modes locally in time.