The long-span bridge response to nonstationary multiple seismic random excitations is investigated using the PEM (pseudo excitation method). This method transforms the nonstationary random response analysis into ordinary direct dynamic analysis, and therefore, the analysis can be solved conveniently using the Newmark, Wilson-9 schemes or the precise integration method. Numerical results of the seismic response for an actual long-span bridge using the proposed PEM are given and compared with the results based on the conventional stationary analysis. From the numerical comparisons, it was found that both the seismic spatial effect and the nonstationary effect are quite important, and that both stationary and nonstationary seismic analysis should pay special attention to the wave passage effect.
The seismic analysis of long-span bridges subjected to multiple ground excitations is an important problem. The conventional response spectrum method neglects the spatial effects of ground motion,and therefore may result in questionable conclusions.The random vibration approach has been regarded as more reliable.Unfortunately,so far, computational difficulties have not yet been satisfactorily resolved.In this paper,an accurate and efficient random vibration approach—pseudo excitation method (PEM),by which the above difficulties are overcome,is presented.It has been successfully used in the three dimensional seismic analysis of a number of long-span bridges with thousands of degrees of freedom and dozens of supports.The numerical results of a typical bridge show that the seismic spatial effects~ particularly the wave passage effect,are sometimes quite important in evaluating the safety of long-span bridges.
Propagation of stationary random waves in viscoelastic stratified transverse isotropic materials is investigated. The solid was considered multi-layered and located above the bedrock, which was assumed to be much stiffer than the soil, and the power spectrum density of the stationary random excitation was given at the bedrock. The governing differential equations are derived in frequency and wave-number domains and only a set of ordinary differential equations ( ODEs) must be solved. The precise integration algorithm of two-point boundary value problem was applied to solve the ODEs. Thereafter, the recently developed pseudo-excitation method for structural random vibration is extended to the solution of the stratified solid responses.
