Vertical vibration of a rigid strip footing on viscoelastic half‐space

Zheng, Changjie; Luan, Lubao; Kouretzis, George; Ding, Xuanming

doi:10.1002/nag.3108

Cited by 10 publications

(4 citation statements)

References 12 publications

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“…Of course, ignoring hysteretic damping results in significantly underestimating the amplitude of ground waves generated from footing vibrations. Another finding worth emphasizing on is that the pattern of the steady‐state horizontal soil displacements is considerably different in the case of horizontal footing vibrations, compared to the case where the footing is subjected to vertical loads (Zheng et al 21 …”

Section: Discussionmentioning

confidence: 99%

“…If we perform the operation

\partial (1) / \partial z + \partial (2) / \partial x

on Equations (1) and (2), we also obtain the following expression for e :

false(λ^{*} + 2 false) false(1 + 2 β normali false) \nabla^{2} e = - a_{0}^{2} e .

As mentioned in the introduction, we will use the Fourier transform to convert the governing equations into a set of Jacobi orthogonal polynomials, as in Zheng et al 21 . It is reminded that the Fourier integral transform of a function

f (x, z)

with regard to x and its inverse transform are expressed as:

\tilde{f} false(ζ, z false) = \int_{- \infty}^{\infty} f (x, z) e^{normali ζ x} d x,

f false(x, z false) = \frac{1}{2 π} \int_{- \infty}^{\infty} \overset{f}{true} (ζ, z) e^{- normali ζ x} d ζ,

where ζ is the Fourier transform parameter.…”

Section: Formulation and Solution Of The Governing Equationsmentioning

confidence: 99%

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Horizontal vibration of a rigid strip footing on viscoelastic half‐space

Zheng

Cai

Luan

et al. 2020

Num Anal Meth Geomechanics

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This paper presented an analytical method for determining the response of a rigid strip foundation resting on the surface of a viscoelastic half‐space to horizontal dynamic loads, and the associated transient soil displacements resulting from the vibration of the footing. This mixed boundary value problem was solved by means of Jacobi orthogonal polynomials, a more efficient method compared to transforming the dual integral equations resulting from the boundary conditions to Fredholm integral equations. Displacements and stresses of the soil‐footing system were accordingly obtained by applying the inverse Fourier transform. Finally, we used the proposed solution to investigate the effects of material damping and Poisson's ratio of soil on the dynamic response of the strip footing, and the resulting soil displacements.

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Section: Discussionmentioning

confidence: 99%

“…If we perform the operation

\partial (1) / \partial z + \partial (2) / \partial x

on Equations (1) and (2), we also obtain the following expression for e :

false(λ^{*} + 2 false) false(1 + 2 β normali false) \nabla^{2} e = - a_{0}^{2} e .

f (x, z)

with regard to x and its inverse transform are expressed as:

\tilde{f} false(ζ, z false) = \int_{- \infty}^{\infty} f (x, z) e^{normali ζ x} d x,

f false(x, z false) = \frac{1}{2 π} \int_{- \infty}^{\infty} \overset{f}{true} (ζ, z) e^{- normali ζ x} d ζ,

where ζ is the Fourier transform parameter.…”

Section: Formulation and Solution Of The Governing Equationsmentioning

confidence: 99%

Horizontal vibration of a rigid strip footing on viscoelastic half‐space

Zheng

Cai

Luan

et al. 2020

Num Anal Meth Geomechanics

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the context of applied mathematics and engineering mechanics, the foregoing category on this complicated topic is mainly relevant to the study of load‐displacement transfer relationship, failure modes and stress concentration effect associated with natural soil 8–10 . For instance, the soil response to various loading forms has been systematically studied by some investigators, where the displacements, strains and stresses expressions have been presented by use of elasticity theory and Green's functions 11–12 . On the other hand, the force acting the surface of elastic soil should be recognized as time‐dependent rather than static, such as moving traffic, earthquake and machine vibration, etc 13–15 .…”

Section: Introductionmentioning

confidence: 99%

“…[8][9][10] For instance, the soil response to various loading forms has been systematically studied by some investigators, where the displacements, strains and stresses expressions have been presented by use of elasticity theory and Green's functions. [11][12] On the other hand, the force acting the surface of elastic soil should be recognized as time-dependent rather than static, such as moving traffic, earthquake and machine vibration, etc. [13][14][15] Similar assumptions have been also considered when investigating the corresponding soil-structure interaction problems for steady-state case, and this kind is a classical example for understanding the dynamic behavior of foundations.…”

Section: Introductionmentioning

confidence: 99%

Frequency‐dependent response of a rigid disk on a transversely isotropic soil layer subjected to horizontal motion

Yang

2023

Earthq Engng Struct Dyn

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The transverse isotropy of soil induced by geological processes over a long period has attracted considerable attention, which can lead to significant differences in the origination, propagation and attenuation of the stand waves compared with purely isotropic soil. Considering that the circular geometry is most common in many engineering, an analytical investigation of the dynamic behavior of a rigid disk resting on the transversely isotropic soil layer overlying the rigid bedrock under forced horizontal displacements is presented in this paper. Firstly, the governing equations of soil motion are established based on the elasticity theory of cylindrical coordinate system. Secondly, a set of partial differential equations for this class of problems are decoupled to ordinary differential forms by virtue of complete potential functions, Fourier expansion method and Hankel transform technique. Furthermore, the displacements, strains and stresses formulation in term of the spatial domain under general boundary conditions are obtained with success. For validation, dynamic boundary value problems in the finite‐layered soil containing transversely isotropic materials are degenerated to the isotropic solution corresponding to elastic half‐space. After that, various examples are also included to investigate the influence of the elastic modulus ratio, shear modulus ratio and thickness of soil layer on the dynamic response of the system. The numerical results suggest that the soil anisotropy and soil layer thickness have a non‐neglectful effect on the horizontal dynamic vibration of the rigid disk.

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Dynamic contact problem for a viscoelastic orthotropic coated isotropic half plane

Çömez

2022

Acta Mech

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Vertical vibration of a rigid strip footing on viscoelastic half‐space

Cited by 10 publications

References 12 publications

Horizontal vibration of a rigid strip footing on viscoelastic half‐space

Horizontal vibration of a rigid strip footing on viscoelastic half‐space

Frequency‐dependent response of a rigid disk on a transversely isotropic soil layer subjected to horizontal motion

Dynamic contact problem for a viscoelastic orthotropic coated isotropic half plane

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