Dynamic response of a periodic viaduct to a moving point loading

Abstract

In this study, dynamic response of a periodic viaduct to a moving loading is investigated. Based on the impulse response function of the viaduct, the time domain response of the periodic viaduct to a moving loading is represented by a Duhamel integral. Applying the Fourier transform to the time domain response, the frequency domain response of the viaduct is obtained. By means of the Floquet transform method, the frequency domain response of the viaduct is reduced to an integral of the frequency–wavenumber domain response function over the representative span of the viaduct. The frequency–wavenumber domain response function is then derived via the transfer matrix method. Applying the inverse Fourier transform to the frequency domain response, the time domain response of the viaduct is retrieved. Based on the proposed model, numerical results about the dynamic responses of the viaduct to the moving loading with different velocities in the frequency and time domains are presented. It is found that the resonance peak of the response of the viaduct most likely occurs in the passbands of the viaduct. When the velocity of the loading is small, the time domain response of the viaduct is almost symmetrical with respect to the arrival time of the loading. However, with increasing velocity, the response of the viaduct becomes asymmetrical with respect to the arrival time. When the velocity of the loading is large enough, the shock wave-like vibration occurs in the periodic viaduct. The mechanism responsible for the shock wave-like vibration in the periodic viaduct is proposed based on the energy bands of the periodic viaduct.