The sequence Fourier transform method for the analysis of a periodic viaduct subjected to non-uniform seismic waves

Abstract

This study is concerned with the analysis of the dynamic response of an infinite periodic viaduct to non-uniform seismic waves. The periodic viaduct is assumed to be composed of an infinite number of spans, and each span is supposed to consist of a pier, two longitudinal beams (left and right beams) and three linking springs. The sequence Fourier transform method is used to decompose a non-uniform seismic wave into a set of spatially harmonic waves. By using the periodic condition of the viaduct and the transfer matrix method, the wavenumber domain response of the viaduct to each component of the non-uniform seismic wave is obtained. The space-domain response of the periodic viaduct is retrieved by applying the inverse sequence Fourier transform to the wavenumber domain solutions. Numerical results for energy bands of the periodic viaduct and those for the dynamic responses of the periodic viaduct to spatially harmonic waves as well as to non-uniform seismic waves are presented. It is found that there exist three kinds of characteristic waves for both the in-plane and out-of-plane wave vibrations of the periodic viaduct. Also, proposed numerical results show that when the periodic viaduct is subjected to traveling waves, serious resonance may occur. Resonance may occur at the bounding frequencies of the passbands for the characteristic waves. Also, due to the coincidence effect between traveling seismic waves and the characteristic waves, resonance may occur at frequencies in the passbands of the characteristic waves.