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In this paper, the resonance and cancellation phenomena occurring in a periodic structure-- a pile-supported periodic viaduct subjected to multiple equidistant moving loadings (MEML) are investigated. For this purpose, the representation for the dynamic response of the periodic viaduct to a single moving loading (SML) is introduced first. In order to take account of the pile-soil-structure interaction when evaluating the response of the periodic viaduct to a SML, a wavenumber domain boundary element method (WDBEM) model for the pile-row-soil system is employed to determine the compliances of the piles. By superposing the responses of the viaduct to all SMLs constituting the MEML, the representation for the dynamic response of the periodic viaduct to the MEML is obtained. With the representation for the MEML response of the viaduct, the resonance and cancellation conditions for the viaduct are derived. For the high speed MEML, when the time interval between two neighboring moving loadings is equal to the integer or half-integer multiples of the period of one of the dominant resonance peaks of the corresponding SML response of the viaduct, resonance or cancellation occurs. The predicted resonance and cancellation phenomena are confirmed by the numerical results presented in this paper. [ABSTRACT FROM AUTHOR]

In this study, the wave localization in a disordered periodic bridge (DPB) with the pile-soil-water-structure (PSWS) coupling is investigated For simplicity, each span of the bridge is assumed to be composed of a pile foundation, a pier, two composite beams and three linking springs. To determine the compliances of the pile foundations, the pile-soil-water (PSW) interaction is simulated by the boundary element method (BEM). In terms of the compliances of the piles and the transfer matrices of the piers and beams, the transfer matrices of the spans of the periodic bridge are derived, by which the wave transfer matrices of the spans are obtained. Using Wolf's algorithm and the wave transfer matrices obtained, the localization factor characterizing the wave localization in the DPB is determined. With the proposed model, the effect of the beam-length disorder on wave localization is examined. Moreover, based on the wave transfer matrix method, the wave mode of a DPB segment and the wave conversion and power flow in the DPB segment are investigated. Numerical results show that due to the energy transmission from the superstructure of the bridge to the half-space soil via the pile foundations, the power flow associated with a complexband wave along the open DPB is usually nonzero and the power flow of a pseudo passband wave along the spans of the open DPB is no longer a constant. [ABSTRACT FROM AUTHOR]

In this study, a numerical model is developed for the analysis of the free vibration of an open-type periodic structure, namely, a periodic viaduct supported by pile foundations. The viaduct is supposed to be composed of infinite spans, with each span consisting of a pile foundation, a pier, two longitudinal beams (left and right beams), and three linking springs. The boundary-element method (BEM) is used to solve the pile-soil interaction problem first. Based on the developed BEM model for the pile-soil system, the compliances of the pile foundation are obtained. By using the compliances of the pile foundation, the joint conditions at the beam-beam-pier (BBP) junction and the transfer matrix method, the eigenvalue equation for the periodic viaduct is established. Numerical results for the energy bands of the viaduct show that there are three kinds of characteristic waves propagating in the periodic viaduct. The first and second kinds of waves are highly decaying. The third characteristic wave can propagate in pseudopassbands with a small attenuation. Also, it is found that, unlike a closed periodic structure, because of the energy transmission from the viaduct to the half-space soil, all energy bands for the open viaduct considered in this study are complex bands with nonzero imaginary wave numbers. [ABSTRACT FROM AUTHOR]

Abstract: In this study, a numerical model is developed to investigate the dynamic response of a defected periodic bridge (DPB) when considering pile–soil–water–structure (PSWS) interaction. In order to determine the dynamic response of the DPB, the DPB is decomposed into three parts – left and right semi-infinite periodic bridges and the defected span. To account for the coupling between the superstructure of the bridge and the pile foundations, a coupled boundary element method (BEM) model is used to model the pile–soil–water (PSW) interaction. By using the PSW BEM model, the transfer matrices for the pier and beam, the joint condition at the beam–beam–pier (BBP) junction, the response of the DPB to the characteristic wave is obtained. To investigate the relation between the response of the DPB and the defect state of the corresponding super-cell, the super-cell method is developed for the DPB. Numerical results for the energy bands of the super-cell show that the defected span of the DPB may give rise to additional passband frequencies, namely, the defect state frequencies. Moreover, when the DPB is subjected to a characteristic wave with frequency equal to the defect state frequency, resonance may occur and the response of the DPB corresponding to the resonance is localized around the defected span. [Copyright &y& Elsevier]

In this study, a new kind of pile structure, namely linked periodic pile rows, is proposed for the vibration isolation facility. The proposed linked periodic pile rows consist of pile rows with pile tops rigidly linked by beams. To investigate the vibration isolation effect of linked pile rows, a numerical model is developed for the simulation of the dynamic response of linked pile rows. To address the pile-soil interaction problem, based on the sequence Fourier transform method, a wavenumber domain boundary element method is developed for the pile-soil system. The beams linking the pile tops are dealt with by the bar and beam vibrational theories. By using the coupling conditions between the pile tops and linking beams as well as the periodicity condition for the beam-pile-soil system, the complementary equations for the system are established. With the proposed model, the vibration isolation effects of the linked pile rows are investigated and compared with those of free pile rows. The comparison indicates that linked pile rows usually yield a better isolation vibration effect than free pile rows. Hence, linked pile rows are a more effective wave barrier for vibration isolation than free pile rows. [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]

Abstract: A coupled model is developed to investigate the dynamic interaction between an offshore pile, a porous seabed and seawater when subjected to the pseudo-Stoneley wave along the seabed and the seawater interface. The pile and the seabed are treated as the porous medium governed by Biot''s theory, while the seawater is considered as an acoustic medium and is described by the conventional Helmholtz equation. The free field solution of the incident pseudo-Stoneley wave is obtained using Biot''s theory and the potential method. Based on the boundary element method (BEM) for the porous medium and the acoustic medium, three BEM formulations are constructed for the pile, the seabed and the seawater, respectively, which are combined together using the continuity conditions between the pile, the seabed and the seawater to formulate the coupled model for the system. As shown in numerical examples, when the system is subjected to the pseudo-Stoneley wave, the maximum pore pressure of the seabed usually occurs at the region near the interfaces between the seabed and the seawater. [Copyright &y& Elsevier]

Abstract: The 3-D boundary integral equation is derived in terms of the reciprocal work theorem and used along with the 2.5-D Green’s function developed in Part I [Lu, J.F., Jeng, D.S., Williams, S., submitted for publication. A 2.5-D dynamic model for a saturated porous medium: Part I. Green’s function. Int. J. Solids Struct.] to develop the 2.5-D boundary integral equation for a saturated porous medium. The 2.5-D boundary integral equations for the wave scattering problem and the moving load problem are established. The Cauchy type singularity of the 2.5-D boundary integral equation is eliminated through introduction of an auxiliary problem and the treatment of the weakly singular kernel is also addressed. Discretisation of the 2.5-D boundary integral equation is achieved using boundary iso-parametric elements. The discrete wavenumber domain solution is obtained via the 2.5-D boundary element method, and the space domain solution is recovered using the inverse Fourier transform. To validate the new methodology, numerical results of this paper are compared with those obtained using an analytical approach; also, some numerical results and corresponding analysis are presented. [Copyright &y& Elsevier]

Lu, J.-F. and Jeng, D.-S., 2007. A coupled model for an offshore pile, seabed and seawater interaction. Journal of Coastal Research, SI 50 (Proceedings of the 9th International Coastal Symposium), 389 – 393. Gold Coast, Australia, ISSN 0749.0208 A coupled model is developed to investigate the dynamic interaction between an offshore pile, poroelastic seabed and sea water. The pile and the seabed are treated as saturated porous media described by Biot's dynamic theory. The sea water is regarded as an acoustic medium which is characterised by the Helmholtz equation. Three boundary element formulations are constructed for the pile, the seabed and the sea water, respectively. The three boundary element method formulations and the continuity conditions (stress and displacement) between the pile, the seabed and the sea water are used to formulate the coupled model for the system. Airy linear wave theory is used to evaluate the external force applied on the pile and the seabed due to the incident and the scattered water waves. The dynamic response of the system is calculated by the coupled boundary element method formulation. A numerical example is used to demonstrate the capacity of the coupled model. [ABSTRACT FROM AUTHOR]