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Abstract In this study, the dynamic response of a periodic viaduct to a moving mass is investigated. In view of the periodicity of the viaduct, the mass-viaduct interaction force is expanded into a Fourier series first, each term of which represents one component of the interaction force. By using the Fourier transform method and finite element method (FEM), the frequency domain response of the periodic viaduct to each interaction force component is obtained. The time domain response of the periodic viaduct to the force component can be recovered by applying the inverse Fourier transform to the corresponding frequency domain response. With the mass-viaduct coupling condition and the time domain response of the viaduct to the force component, the Fourier coefficients of the mass-viaduct interaction force are obtained. Superposing the responses of the periodic viaduct due to all the interaction force components yields the response of the periodic viaduct to the moving mass. Numerical results show that the force-weight ratio increases with increasing mass and speed of the mass, suggesting that the inertial effect of the moving mass should be taken into account for the large mass with high speeds. Also, it is found that for the case of the large moving mass with high speeds, the mass-viaduct interaction force may become negative, indicating that the mass has a tendency to separate from the viaduct in this case. Highlights • A model is developed for the dynamic response of a periodic viaduct to a moving mass. • The convergence of the proposed model is confirmed by numerical simulations and some numerical results are presented. • The occurrence of the negative mass-viaduct interaction force is found by numerical simulations. [ABSTRACT FROM AUTHOR]

The dynamic response of an infinitely long circular tunnel embedded in the saturated soil to a series of equidistant moving loads (SEML) is investigated in this study. The saturated soil surrounding the tunnel is described by Biot's theory. Two scalar potentials and one vector potential are introduced to represent the displacement of the solid skeleton and the pore pressure. Based on Biot's theory, the Helmholtz equations for the potentials are derived using the Fourier transform method. Performing the Fourier transform with respect to the longitudinal coordinate on the Helmholtz equations gives the frequency-wavenumber domain general solutions for the potentials. With the general solutions and the boundary conditions along the tunnel surface, the solution for the circular tunnel subjected to a single moving load (SML) is obtained. Superposition of the solutions for SMLs gives the representation for the response of the tunnel to a SEML, with which the resonance and cancelation conditions for the SEML are derived. Numerical simulations suggest that for the circular infinite tunnel there is a critical velocity. When the load moves with the critical velocity, the frequency domain response of the tunnel exhibits some dominant peak. Further, for a SEML moving with the critical velocity, the resonance and cancelation phenomena in the time domain may occur when the aforementioned resonance and cancelation conditions are fulfilled. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic response of a periodic pile-supported viaduct to a moving loading when considering the pile-soil-structure interaction is investigated. By using the Duhamel integral, the Fourier and Floquet transform methods, the frequency domain response of the viaduct to the moving loading is represented by an integral of the frequency-wavenumber domain response function over the representative span of the viaduct. The time domain response of the viaduct can be retrieved by the inversion of the Fourier transform. By means of the wavenumber domain boundary element method model for the periodic pile row supporting the viaduct, the compliances of the pile row are obtained. Employing the compliances of the pile row and coupling the superstructure of the viaduct with the pile row, the frequency-wavenumber domain response function of the viaduct is determined. With the proposed model, the dynamic responses of the pile-supported viaduct to the moving loading in both the frequency and time domains are presented. It is found that resonance peaks of the frequency domain response of the viaduct are more likely to occur in the passbands of the viaduct, and the number of the resonance peaks decreases with increasing velocity. When the velocity of the loading is small, the time domain response of the viaduct is almost symmetrical about the loading. However, as the velocity increases, the response of the viaduct becomes asymmetric. Further, when the velocity of the loading is large enough, shockwave-like vibration occurs in the periodic viaduct. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: In this study, a new model is developed for the aseismic design of a periodic viaduct when the pile–soil–structure interaction is considered. To account for the influence of the pile–soil–structure interaction, a wavenumber domain boundary element method (WDBEM) model for the periodic pile row supporting the viaduct is developed using the sequence Fourier transform as well as the boundary element method for the elastic medium. By using the WDBEM model for the pile row, the transfer matrices for the beams and piers, the joint conditions at the beam–beam–pier (BBP) junction as well as the periodicity condition for the viaduct, the wavenumber domain response of the periodic viaduct to spatially harmonic waves is determined. Based on the wavenumber domain response of the viaduct, the space-domain response of the viaduct to an arbitrary seismic wave can be obtained by invoking the inverse sequence Fourier transform method. Numerical results show that when the periodic viaduct is exposed to the spatially harmonic wave, resonances may occur at the bounding frequencies of the passbands of the characteristic waves of the viaduct. Also, it is found that the coincidence between the traveling seismic wave and characteristic waves of the viaduct will generate additional resonant frequencies located in passbands of the characteristic waves. [Copyright &y& Elsevier]

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. [ABSTRACT FROM AUTHOR]

The dynamic response of a single pile embedded in a layered poroelastic half-space to an axial harmonic load is investigated in this study. Based on Biot’s theory, the frequency domain fundamental solution for a vertical circular patch load applied in a layered poroelastic half-space is derived via the transmission and reflection matrices method. Utilizing Muki and Sternberg’s method, the second kind of Fredholm integral equations describing the dynamic interaction between the layered half-space and the pile subjected to a harmonic axial load is constructed. The proposed model is validated by comparing a special case of our model with an existing result. Based on numerical results of this paper, it is concluded that the presence of a stiffer or a softer middle layer in the layered half-space will affect the impedance of the pile considerably and the inhomogeneity of the half-space will enhance the pore pressure significantly. [ABSTRACT FROM AUTHOR]

Abstract: The isolation of the vibration due to moving loads using pile rows embedded in a poroelastic half-space is investigated in this study. Based on Biot''s theory and integral transform method, the free field solution for a moving load applied on the surface of a poroelastic half-space and the fundamental solution for a harmonic circular patch load applied in the poroelastic half-space are derived first. Using Muki and Sternberg''s method and the fundamental solution for the circular patch load as well as the obtained free field solution for the moving load, the second kind of Fredholm integral equations in the frequency domain describing the dynamic interaction between pile rows and the poroelastic half-space is developed. Numerical solution of the frequency domain integral equations and numerical inversion of the Fourier transform yield the time domain response of the pile–soil system. Comparison of our results with some known results shows that our results are in a good agreement with existing ones. Numerical results of this study show that velocity of moving loads has an important impact on the vibration isolation effect of pile rows. The same pile row has a better vibration isolation effect for the lower speed moving loads than for the higher speed ones. Also, the optimal length of piles for higher speed moving loads is shorter than that for lower speed moving loads. Moreover, stiff pile rows tend to produce a better vibration isolation effect than flexible pile rows do. [Copyright &y& Elsevier]

Abstract: The transmission and reflection matrices (TRM) method for a layered poroelastic half space subjected to moving loads is developed in this study. Applying the triple Fourier transformation, the general solutions for the displacements, the stresses and the pore pressure are derived from the governing equations of Biot’s theory. Utilizing the continuity conditions between each layer and the boundary conditions at the half space surface, the transformed domain solutions for the displacements, the pore pressures and the stresses are established by the transmission and reflection matrices (TRM) method. Numerical results in the time–space domain are obtained by performing the inverse Fourier transform with respect to frequency and the horizontal wavenumbers. Moreover, some numerical examples and corresponding analysis are presented in the paper. Numerical results show that the occurrence of a softer middle layer in the layered half space will enhance the vertical displacement and the pore pressure of the layered half space. Besides, the presence of a softer middle layer tends to make the response of the layered half space exhibit more oscillatory nature. [Copyright &y& Elsevier]

Dynamic response of an infinite beam resting on a layered poroelastic half-space subjected to moving loads is investigated in this study. The equivalent stiffness of the layered poroelastic half-space is obtained via the transmission and reflection matrices (TRM) method in the frequency wavenumber domain. Based on the obtained equivalent stiffness, the frequency wavenumber domain solution of the beam–half-space system is obtained by the compatibility condition between the beam and the half-space. The time domain solution for the beam and the layered half-space is obtained by means of the inverse Fourier transform method. Also, the influences of the load speed and material parameters of the poroelastic half-space on the responses of the beam as well as the layered half-space are investigated. In order to demonstrate the proposed method, some time–space domain examples and corresponding analysis are presented in the paper. [Copyright &y& Elsevier]

Abstract: In this paper, an analytical solution for the dynamic response of a half-space porous medium subjected to a moving point load is derived. In the model, the displacements of the solid skeleton and the pore pressure are expressed in terms of two scalar potentials and one vectorial potential. Based on Biot’s theory, the frequency domain Holmholtz equations for the potentials are derived through the Fourier transformation with respect to time. The general solutions for the potentials are derived through the Fourier transformation with respect to the horizontal coordinates. Numerical results suggest that moving loads have very complicated effects on the dynamic response of the porous medium. Generally speaking, a moving load with a high speed will generate a larger response in the porous medium than a static or a lower speed load. [Copyright &y& Elsevier]