scholarly journals Exact Solution for the Torsional Vibration of an Elastic Pile in a Radially Inhomogeneous Saturated Soil

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Xibin Li ◽  
Zhiqing Zhang ◽  
Jianchao Sheng
Keyword(s):  
Exact Solution ◽  
Torsional Vibration ◽  
Saturated Soil ◽  
Exponential Form ◽  
Soil System ◽  
Time Harmonic ◽  
Radial Inhomogeneity ◽  
Inner Region ◽  
Radially Inhomogeneous ◽  
Mathematical Derivation

An exact solution is proposed to study the time-harmonic torsional vibration of an elastic pile embedded in a radially inhomogeneous saturated soil. The radially inhomogeneous saturated soil is composed of inner disturbed and outer semi-infinite undisturbed concentric annular regions, with the shear modulus of the inner region changing in an exponential form along the radial direction. The governing equation of each region of the saturated soil is solved through rigorous mathematical derivation and the soil torsional impedance is derived with an exact and explicit expression. Making use of the boundary and continuity conditions of the pile-soil system, the torsional complex stiffness at the pile top is obtained in an exact closed form in the frequency domain. Selected numerical results are presented to investigate the influence of the radial inhomogeneity of the surrounding soil on the vibration characteristics of the pile-soil system.

Torsional Vibration of a Pile Embedded in Saturated Soil Considering Pile Construction Effect

2014 ◽  
Vol 904 ◽  
pp. 377-382
Author(s):  
Zhi Qing Zhang ◽  
Rui Fu Qin
Keyword(s):  
Governing Equation ◽  
Torsional Vibration ◽  
Soil Layer ◽  
Complex Impedance ◽  
Saturated Soil ◽  
Shear Rigidity ◽  
Disturbed Zone ◽  
Radial Inhomogeneity ◽  
Radially Inhomogeneous ◽  
Surrounding Soil

The torsional vibration of an elastic supporting pile embedded in a radially inhomogeneous saturated soil due to construction disturbance is investigated. At first, the composite soil layer is divided into outer semi-infinite undisturbed and inner annular disturbed zones, and the inner disturbed zone is subdivided into N thin concentric annular sub-layers. Then, the complex impedance at the top end of the pile is derived by substituting the available analytical expression for the shear rigidity of the composite soil layer into the governing equation of the pile. Finally, selected numerical results are obtained to analyze the influence of the radial inhomogeneity of the surrounding soil on the torsional vibration characteristics of the pile.

scholarly journals Time-Harmonic Response of an Elastic Pile in a Radially Inhomogeneous Poroelastic Medium

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Xibin Li ◽  
Wenhui Xu ◽  
Zhiqing Zhang
Keyword(s):  
Twist Angle ◽  
Engineering Practice ◽  
Zone Model ◽  
Poroelastic Medium ◽  
Soil System ◽  
Harmonic Response ◽  
Disturbed Soil ◽  
Time Harmonic ◽  
Radially Inhomogeneous ◽  
Surrounding Soil

The time-harmonic response of an elastic pile embedded in a radially inhomogeneous poroelastic medium and subjected to a torsional loading is studied in the present article. In engineering practice, the surrounding soil may be weakened due to the disturbance effect caused by pile driving. To simulate the weakened surrounding soil, a boundary zone model with the complex shear modulus of the inner disturbed soil changing in a parabolic form along the radial direction is proposed. In view of the axis-symmetric deformation of the surrounding soil under torsional load, the equation of motion of the saturated soil is solved in the cylindrical coordinate system. The vibration displacement and shear stress solutions for the inner disturbed soil are gained by expanding the displacement as a power series, and those for the outer undisturbed soil are obtained by solving the partial differential equation. By virtue of continuity conditions at the interface between inner and outer soil regions, the torsional impedance of the radially inhomogeneous soil is solved. Then, via the boundary and continuity conditions of the pile-soil system, the twist angle and torque of the pile are obtained in the frequency domain. Finally, selected numerical results are conducted to investigate the influence of the material damping, softening degree, and softening range of the inner soil on the distribution of the twist angle and torque of the pile along the depth direction.

Dynamic Torsional Response of a Pile Partially Embedded in Saturated Soil

2014 ◽  
Vol 509 ◽  
pp. 27-33
Author(s):  
Rui Fu Qin ◽  
Zhi Qing Zhang ◽  
Rong Fa Chen
Keyword(s):  
Inverse Fourier Transform ◽  
Vertical Direction ◽  
Sine Wave ◽  
Saturated Soil ◽  
Soil System ◽  
Impedance Function ◽  
Torsional Response ◽  
Time Harmonic ◽  
Velocity Response ◽  
The Time Domain

The dynamic response of an elastic supporting pile partially embedded in a saturated soil and subjected to a time-harmonic torsional loading is investigated. At first, the pile is divided into two parts along the vertical direction, pile part above the soil and pile part embedded in the soil. Then, based on boundary and continuity conditions of the pile-soil system, the torsional impedance at the top end of the pile part embedded in the soil is obtained. By utilizing the transfer technique of impedance function, the admittance function of the pile top is defined in the frequency domain. By virtue of inverse Fourier transform and convolution theorem, a semi-analytical solution for the velocity response of a pile subjected to a semi-sine wave exciting torque is obtained in the time domain. Finally, selected numerical results are obtained to analyze the influence of main parameters on the torsional vibration characteristics of the pile.

On wave transmission in saturated soil system separated by a nonlinear isolated layer

2021 ◽  
Vol 136 ◽  
pp. 104211
Author(s):  
Song Xu ◽  
L.H. Tong ◽  
Changjie Xu ◽  
Haibin Ding
Keyword(s):  
Wave Transmission ◽  
Saturated Soil ◽  
Soil System

scholarly journals Cosmological constant in chameleon Brans–Dicke theory

2019 ◽  
Vol 28 (01) ◽  
pp. 1950022 ◽  
Author(s):  
Yousef Bisabr
Keyword(s):  
Exact Solution ◽  
Scalar Field ◽  
Cosmological Constant ◽  
Exact Solutions ◽  
Effective Mass ◽  
Potential Function ◽  
Power Law ◽  
Exponential Form ◽  
First Case ◽  
Different Types

We consider a generalized Brans–Dicke model in which the scalar field has a self-interacting potential function. The scalar field is also allowed to couple nonminimally with the matter part. We assume that it has a chameleon behavior in the sense that it acquires a density-dependent effective mass. We consider two different types of matter systems which couple with the chameleon, dust and vacuum. In the first case, we find a set of exact solutions when the potential has an exponential form. In the second case, we find a power-law exact solution for the scale factor. In this case, we will show that the vacuum density decays during expansion due to coupling with the chameleon.

scholarly journals Exact Solution for Viscoelastic Flow in Pipe and Experimental Validation

Polymers ◽  
2022 ◽  
Vol 14 (2) ◽  
pp. 334
Author(s):  
Ekaterina Vachagina ◽  
Nikolay Dushin ◽  
Elvira Kutuzova ◽  
Aidar Kadyirov
Keyword(s):  
Experimental Data ◽  
Exact Solution ◽  
Analytical Methods ◽  
Experimental Validation ◽  
Parametric Method ◽  
Fluid Flows ◽  
Parametric Representation ◽  
Viscoelastic Flow ◽  
Exponential Form ◽  
Image Velocimetry

The development of analytical methods for viscoelastic fluid flows is challenging. Currently, this problem has been solved for particular cases of multimode differential rheological equations of media state (Giesekus, the exponential form of Phan-Tien-Tanner, eXtended Pom-Pom). We propose a parametric method that yields solutions without additional assumptions. The method is based on the parametric representation of the unknown velocity functions and the stress tensor components as a function of coordinate. Experimental flow visualization based on the SIV (smoke image velocimetry) method was carried out to confirm the obtained results. Compared to the Giesekus model, the experimental data are best predicted by the eXtended Pom-Pom model.

scholarly journals Elastodynamics of radially inhomogeneous spherically anisotropic elastic materials in the Stroh formalism

2011 ◽  
Vol 468 (2138) ◽  
pp. 467-484 ◽  
Author(s):  
A. N. Norris ◽  
A. L. Shuvalov
Keyword(s):  
Displacement Field ◽  
Separation Of Variables ◽  
Transverse Isotropy ◽  
Stroh Formalism ◽  
Elastic Materials ◽  
Spherical Coordinate ◽  
Vector Spherical Harmonics ◽  
Time Harmonic ◽  
Anisotropic Elastic ◽  
Radially Inhomogeneous

A method for solving elastodynamic problems in radially inhomogeneous elastic materials with spherical anisotropy is presented, i.e. materials having c ijkl = c ijkl ( r ) in a spherical coordinate system { r , θ , ϕ }. The time-harmonic displacement field u ( r , θ , ϕ ) is expanded in a separation of variables form with dependence on θ , ϕ described by vector spherical harmonics with r -dependent amplitudes. It is proved that such separation of variables solution is generally possible only if the spherical anisotropy is restricted to transverse isotropy (TI) with the principal axis in the radial direction, in which case the amplitudes are determined by a first-order ordinary differential system. Restricted forms of the displacement field, such as u ( r , θ ), admit this type of separation of variables solution for certain lower material symmetries. These results extend the Stroh formalism of elastodynamics in rectangular and cylindrical systems to spherical coordinates.

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