Vibration Isolation Using Pile Rows in a Layered Poroelastic Half-Space Against the Vibration Due to Harmonic Loads

2010 ◽  
Author(s):  
Jian-Fei Lu ◽  
Bin Xu ◽  
Jian-Hua Wang
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Vibration Isolation ◽  
Dynamic Interaction ◽  
Isolation Effect ◽  
Fredholm Integral Equations ◽  
Vertical Load ◽  
Large Length ◽  
Patch Load ◽  
Transmission And Reflection

The isolation of the vibration due to a harmonic vertical load using pile rows embedded in a layered poroelastic half-space 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 (TRM) method. Utilizing Muki and Sternberg’s method, the second kind of Fredholm integral equations describing the dynamic interaction between the pile rows and the layered poroelastic half-space subjected to a harmonic vertical load is constructed. The isolation effect of piles rows for the vibration due to the harmonic vertical load is investigated via numerical solution of the integral equations. Numerical results of this study show that a stiffer upper layer overlying a softer bottom half-space will worsen the vibration isolation effect of pile rows and vice versa. Also, pile rows with large length are preferable for a better vibration isolation effect.

scholarly journals A Semi-Analytical Model for the Simulation of the Isolation of the Vibration Due to a Harmonic Load Using Pile Rows Embedded in a Saturated Half-Space

2010 ◽  
Vol 4 (1) ◽  
pp. 38-56 ◽  
Author(s):  
Bin Xu ◽  
Jian-Fei Lu ◽  
Jian-Hua Wang
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Analytical Model ◽  
Vibration Isolation ◽  
Fredholm Integral Equations ◽  
Harmonic Load ◽  
Dynamical Interaction ◽  
Vibration Effect ◽  
Patch Load ◽  
Isolation Vibration

The isolation of the vibration due to a harmonic vertical load using pile rows embedded in a saturated poroelastic half-space is investigated in this study. Using the fundamental solution for a circular patch load and Muki’s method, the second kind of Fredholm integral equations describing the dynamical interaction between the pile rows and the saturated poroelastic half-space are obtained. Numerical solution of the integral equations yields the dynamic response of the pile-half-space system. The vibration isolation effect of the pile rows is investigated via the proposed semi-analytical model. Numerical results indicate that stiffer piles have better isolation vibration effect than flexible piles. Moreover, the pile length and the spacing between neighboring piles in one pile row have significant influence on the isolation vibration effect of pile rows, while the influence of the spacing between neighboring pile rows is relatively smaller.

The Influnce of Velocity for a Moving Load on the Vibration Isolation Using Pile Group

2012 ◽  
Vol 204-208 ◽  
pp. 210-214
Author(s):  
Man Qing Xu ◽  
Bin Xu
Keyword(s):  
Integral Equation ◽  
Fundamental Solution ◽  
Frequency Domain ◽  
Half Space ◽  
Vibration Isolation ◽  
Moving Load ◽  
Free Field ◽  
Isolation Effect ◽  
Moving Loads ◽  
Patch Load

Based on Biot’s theory and integral transform method, the velocity of moving loads impact on the vibration isolation effect of pile rows embedded in a poroelastic half space is investigated in this study. 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’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 equation 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 equation and numerical inversion of the Fourier transform yield the time domain response of the pile-soil system. Numerical results of this study show that the same pile rows can achieve a better vibration isolation effect for the lower load speed than for the higher speed. Also, the optimal length of piles for higher speed moving loads is shorter than that for lower speed moving loads.

The Vibration of Pile Groups Embedded in a Layered Poroelastic Half Space Subjected to Harmonic Axial Loads by Using Integral Equations Method

2012 ◽  
Vol 204-208 ◽  
pp. 1170-1173
Author(s):  
Chun Bo Cheng ◽  
Man Qing Xu ◽  
Bin Xu
Keyword(s):  
Dynamic Response ◽  
Layer Thickness ◽  
Integral Equations ◽  
Half Space ◽  
Pile Group ◽  
Dynamic Interaction ◽  
Fredholm Integral Equations ◽  
Pile Groups ◽  
Axial Loads ◽  
Layered Half Space

The dynamic response of a pile group embedded in a layered poroelastic half space subjected to axial harmonic loads is investigated in this study. Based on Biot's theory and utilizing Muki's method, the second kind of Fredholm integral equations describing the dynamic interaction between the layered half space and the pile group is constructed. Numerical results show that in a two-layered half space, for the closely populated pile group with a rigid cap, the upper softer layer thickness has considerably different influence on the center pile and the corner piles, while for sparsely populated pile group, it has almost the same influence on all the piles.

On the Torsion of Elastic Half Spaces With Embedded Penny-Shaped Flaws

1972 ◽  
Vol 39 (3) ◽  
pp. 786-790 ◽  
Author(s):  
R. D. Low
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Rigid Inclusion ◽  
Elastic Half Space ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Graphical Displays ◽  
Penny Shaped Crack ◽  
Shaped Crack

The investigation is concerned with some of the effects of embedded flaws in an elastic half space subjected to torsional deformations. Specifically two types of flaws are considered: (a) a penny-shaped rigid inclusion, and (b) a penny-shaped crack. In each case the problem is reduced to a system of Fredholm integral equations. Graphical displays of the numerical results are included.

Elastic Layer Pressed Against a Half Space

1974 ◽  
Vol 41 (3) ◽  
pp. 703-707 ◽  
Author(s):  
K. C. Tsai ◽  
J. Dundurs ◽  
L. M. Keer
Keyword(s):  
Eigenvalue Problem ◽  
Integral Equations ◽  
Half Space ◽  
Elastic Layer ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Auxiliary Functions ◽  
Receding Contact ◽  
Two Bodies

The paper considers the elastic layer which is pressed against a half space by loads that are not necessarily symmetric about the center of the loaded region. It is shown that the receding contact between the two bodies can be treated by means of superposition, leading to two homogeneous Fredholm integral equations for auxiliary functions that are directly related to the contact tractions. The determination of the extent of contact and the shift between the load and contact intervals can be viewed as an eigenvalue problem of the homogeneous integral equations. Specific numerical results are given for two types of triangular loads, and a comparison is made with certain symmetric loads.

scholarly journals Dynamic Behavior of an Embedded Foundation under Horizontal Vibration in a Poroelastic Half-Space

2019 ◽  
Vol 9 (4) ◽  
pp. 740 ◽  
Author(s):  
Yang Chen ◽  
Wen Zhao ◽  
Pengjiao Jia ◽  
Jianyong Han ◽  
Yongping Guan
Keyword(s):  
Integral Equations ◽  
Half Space ◽  
Mixed Boundary ◽  
Fredholm Integral Equations ◽  
Wave Forces ◽  
Dual Integral Equations ◽  
Horizontal Vibration ◽  
Embedded Foundation ◽  
Embedded Foundations ◽  
Caisson Foundations

More and more huge embedded foundations are used in large-span bridges, such as caisson foundations and anchorage open caisson foundations. Most of the embedded foundations are undergoing horizontal vibration forces, that is, wind and wave forces or other types of dynamic forces. The embedded foundations are regarded as rigid due to its high stiffness and small deformation during the forcing process. The performance of a rigid, massive, cylindrical foundation embedded in a poroelastic half-space is investigated by an analytical method developed in this paper. The mixed boundary problem is solved by reducing the dual integral equations to a pair of Fredholm integral equations of the second kind. The numerical results are compared with existing solutions in order to assess the accuracy of the presented method. To further demonstrate the applicability of this method, parametric studies are performed to evaluate the dynamic response of the embedded foundation under horizontal vibration. The horizontal dynamic impedance and response factor of the embedded foundation are examined based on different embedment ratio, foundation mass ratio, relative stiffness, and poroelastic material properties versus nondimensional frequency. The results of this study can be adapted to investigate the horizontal vibration responses of a foundation embedded in poroelastic half-space.

Dynamic Responses of Pile Groups Embedded in a Layered Poroelastic Half-Space to Harmonic Axial Loads

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Bin Xu ◽  
Jian-Fei Lu ◽  
Jian-Hua Wang
Keyword(s):  
Half Space ◽  
Middle Layer ◽  
Pile Group ◽  
Dynamic Responses ◽  
Fredholm Integral Equations ◽  
Pile Groups ◽  
Axial Loads ◽  
Reflection Matrix ◽  
Patch Load ◽  
Layered Half Space

The dynamic responses of a pile group embedded in a layered poroelastic half-space subjected to axial harmonic loads is investigated in this study. Based on Biot’s theory, the frequency domain fundamental solution for a vertical circular patch load applied in the layered poroelastic half-space is derived via the transmission and reflection matrix (TRM) method. Utilizing Muki’s method, the second kind of Fredholm integral equations describing the dynamic interaction between the layered half-space and the pile group is constructed. The proposed methodology was validated by comparing the results of this paper with a known result. Numerical results show that in a two-layered half-space, for the closely populated pile group with a rigid cap, the upper softer layer thickness has different influences on the central pile and the corner piles, while for the sparse pile group, it has almost the same influence on all the piles. For a three-layer half-space, the presence of a stiffer middle layer in the layered half-space will enhance the impedance of the pile group significantly, while a softer middle layer will reduce the impedance of the pile group.

Steady Motion of a Rigid Strip Bonded to an Elastic Half Space

1971 ◽  
Vol 38 (2) ◽  
pp. 328-334 ◽  
Author(s):  
M. A. Oien
Keyword(s):  
Approximate Solution ◽  
Galerkin Method ◽  
Integral Equations ◽  
Half Space ◽  
Steady Motion ◽  
Elastic Half Space ◽  
Fredholm Integral Equations ◽  
Harmonic Waves ◽  
Forced Motion ◽  
Inertia Properties

The diffraction of harmonic waves by a movable rigid strip bonded to the surface of an elastic half space is divided into two more fundamental problems, the diffraction of waves by a fixed strip and the forced motion of an inertialess strip. These problems are formulated in terms of a pair of coupled Fredholm integral equations of the first kind. An approximate solution for the resultant loads acting on the strip is obtained using the Bubnov-Galerkin method. These loads provide a simple means of studying the excited motion of a movable strip having a variety of inertia properties.

Axisymmetric stress-transfers from an embedded elastic cylindrical shell to a half-space

1993 ◽  
Vol 441 (1912) ◽  
pp. 237-259 ◽  
Keyword(s):  
Cylindrical Shell ◽  
Integral Equations ◽  
Half Space ◽  
Contact Stress ◽  
Mathematical Formulation ◽  
Numerical Procedure ◽  
Fredholm Integral Equations ◽  
Elastic Cylindrical Shell ◽  
Stress Distributions ◽  
Axisymmetric Stress

Within the framework of three-dimensional classical elastostatics and thin shell theories, a rigorous mathematical formulation is presented for the torsionless axisymmetric stress-transfer problem of a cylindrical shell of finite length embedded in a semi-infinite solid. By virtue of a set of ring-load Green’s functions for the shell and a group of fundamental solutions for the half-space, the mechanical interaction problem is shown to be reducible to a pair of Fredholm integral equations. Through the analysis of an auxiliary set of Cauchy integral equations, the singularities of the resultant contact stress distributions are rendered explicit, the results of which are incorporated in a numerical procedure. Typical solutions for the axial and radial load-transfers, contact stress distributions, as well as other related responses are included as illustrations. In addition to furnishing results of direct relevance to a number of engineering applications, the present treatment is apt to be useful as a basis of assessment for various approximate methods for this class of contact problems.

scholarly journals Numerical Analysis of Vibration Isolation Using Pile Rows against the Vibration due to Moving Loads in a Viscoelastic Medium

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Bin Xu ◽  
Man-Qing Xu
Keyword(s):  
Numerical Analysis ◽  
Numerical Method ◽  
Half Space ◽  
Viscoelastic Medium ◽  
Vibration Isolation ◽  
Moving Load ◽  
Vertical Vibration ◽  
Isolation Effect ◽  
Moving Loads ◽  
Cole Model

A numerical method for evaluating the vertical vibration isolation effect of pile rows embedded in a viscoelastic half space subjected to a moving load is developed in this paper on the basis of the Cole-Cole model and Muki’s method. Based on the proposed method, the influence of various parameters on the vibration isolation effect of pile rows embedded in the viscoelastic half space is investigated numerically.

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