scholarly journals New Analytical Solutions for Longitudinal Vibration of a Floating Pile in Layered Soils with Radial Heterogeneity

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1294 ◽  
Author(s):  
Zhimeng Liang ◽  
Chunyi Cui ◽  
Kun Meng ◽  
Yu Xin ◽  
Huafu Pei ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Analytical Solutions ◽  
Longitudinal Vibration ◽  
Three Dimensional ◽  
Complex Impedance ◽  
Vibration Characteristics ◽  
Layered Soils ◽  
Transform Method ◽  
Floating Pile ◽  
The Time Domain

Based on the theory of wave propagation in three-dimensional (3D) continuum, a new analytical approach for the longitudinal vibration characteristics of a floating pile in layered soils with radial heterogeneity is developed by employing a viscous-type damping model. Firstly, an analytical solution for the longitudinal complex impedance at the pile head is deduced by employing the Laplace transform and complex stiffness technique with the compatibility conditions of the pile and radially inhomogeneous surrounding soil. Secondly, a semi-analytical solution in the time domain is further acquired by using the inverse Fourier transform method. Furthermore, the corresponding analytical solutions are validated through contrasts with previous solutions. Finally, parametric analyses are underway to investigate the effect of radial heterogeneity of surrounding soils on longitudinal vibration characteristics of floating piles. It is indicated that the proposed approach and corresponding solutions can provide a more wide-ranging application than the simple harmonic vibration for longitudinal vibration analysis of a floating pile in soils.

Analytical solution for longitudinal vibration of a floating pile in saturated porous media based on a fictitious saturated soil pile model

2021 ◽  
Vol 131 ◽  
pp. 103942
Author(s):  
Chunyi Cui ◽  
Kun Meng ◽  
Chengshun Xu ◽  
Zhimeng Liang ◽  
Haijiang Li ◽  
...  
Keyword(s):  
Porous Media ◽  
Analytical Solution ◽  
Longitudinal Vibration ◽  
Saturated Soil ◽  
Saturated Porous Media ◽  
Floating Pile ◽  
Pile Model

Study on Longitudinal Vibration of Pile in the Viscous Damping Layered Soils

2010 ◽  
Vol 168-170 ◽  
pp. 2450-2457
Author(s):  
Yin Hui Wang ◽  
Kui Hua Wang ◽  
Zhi Xiang Zha ◽  
Ren Bo Que
Keyword(s):  
Analytical Solution ◽  
Frequency Domain ◽  
Time Domain ◽  
Longitudinal Vibration ◽  
Exciting Force ◽  
Viscous Damping ◽  
Layered Soils ◽  
Pile Head ◽  
Wave Effect ◽  
Velocity Response

Taking axisymmetric wave effect of soil into account, longitudinal vibration of pile in viscous damping layered soils undergoing arbitrary load is theoretically investigated. An analytical solution for admittance at the level of the pile head in frequency domain is yielded. So is a semi-analytical solution for velocity response in time-domain subjected to a semi-sine exciting force. Based on the solutions proposed herein, the effects of variety of soil modulus on admittance curves and reflection wave curves are emphatically discussed. The conclusions can provide theoretical guidance for non-destruction test of piles.

scholarly journals 2D Plane Strain Consolidation Process of Unsaturated Soil with Vertical Impeded Drainage Boundaries

Processes ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 5 ◽  
Author(s):  
Minghua Huang ◽  
Dun Li
Keyword(s):  
Analytical Solution ◽  
Laplace Transform ◽  
Plane Strain ◽  
Unsaturated Soil ◽  
Analytical Solutions ◽  
Soil Layer ◽  
Permeability Ratio ◽  
Consolidation Process ◽  
The Time Domain ◽  
Excess Pore Pressures

The consolidation process of soil stratum is a common issue in geotechnical engineering. In this paper, the two-dimensional (2D) plane strain consolidation process of unsaturated soil was studied by incorporating vertical impeded drainage boundaries. The eigenfunction expansion and Laplace transform techniques were adopted to transform the partial differential equations for both the air and water phases into two ordinary equations, which can be easily solved. Then, the semi-analytical solutions for the excess pore-pressures and the soil layer settlement were derived in the Laplace domain. The final results in the time domain could be computed by performing the numerical inversion of Laplace transform. Furthermore, two comparisons were presented to verify the accuracy of the proposed semi-analytical solutions. It was found that the semi-analytical solution agreed well with the finite difference solution and the previous analytical solution from the literature. Finally, the 2D plane strain consolidation process of unsaturated soil under different drainage efficiencies of the vertical boundaries was illustrated, and the influences of the air-water permeability ratio, the anisotropic permeability ratio and the spacing-depth ratio were investigated.

Formulation of a three dimensional analytical solution to evaluate stresses in backfilled vertical narrow openings

2005 ◽  
Vol 42 (6) ◽  
pp. 1705-1717 ◽  
Author(s):  
Li Li ◽  
Michel Aubertin ◽  
Tikou Belem
Keyword(s):  
Numerical Modeling ◽  
Analytical Solution ◽  
Analytical Solutions ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Earth Pressure ◽  
The State ◽  
Experimental Results ◽  
State Of Stress ◽  
Earth Pressures

The mechanical response of backfill in narrow openings is significantly influenced by its interaction with the surrounding walls. Previous work conducted on backfilled trenches and mining stopes indicates that the theory of arching can be used to estimate earth pressures in narrow, vertical backfilled openings. In this paper, a 3D analytical solution is proposed to evaluate the state of stress along the boundaries of the openings. The proposed solution, based on a generalized version of the Marston approach, is compared with numerical modeling and laboratory experimental results taken from the literature. A discussion follows on some particular features and limitations of the analytical solutions.Key words: backfill, earth pressure, 3D openings, analytical solutions, trenches, mining stopes.

Some Applications of CDL-BIEM

1994 ◽  
Author(s):  
Nhan Phan-Thien ◽  
Sangtae Kim
Keyword(s):  
Analytical Solution ◽  
Numerical Method ◽  
Analytical Solutions ◽  
Spherical Inclusion ◽  
Three Dimensional ◽  
Simple Problem ◽  
Benchmark Problem ◽  
Bounding Surface ◽  
Rigid Displacement ◽  
Particulate Solids

This chapter presents some selected three-dimensional applications of the CDL-BIEM in elasticity and Stokes flows, especially to particulate solids for which the method is devised. It is paramount that any numerical method should be validated against known analytical solutions. The method will therefore be benchmarked against known simple solutions of the type reported in chapters 2 and 5. Some selected nontrivial examples, where no analytical solutions are available, will also be presented. The translating sphere is a simple problem with known analytical solution and smooth bounding surface; it is a popular benchmark problem for boundary element codes. Here a rigid spherical inclusion of radius a, centered at x = 0, is displaced by either (1) a constant vector U or (2) acted on by a force F, and we seek the force in the case of problem (1), or the rigid displacement in problem (2).

scholarly journals An Analytical Solution for Longitudinal Impedance of a Large-Diameter Floating Pile in Soil with Radial Heterogeneity and Viscous-Type Damping

2020 ◽  
Vol 10 (14) ◽  
pp. 4906 ◽  
Author(s):  
Kun Meng ◽  
Chunyi Cui ◽  
Zhimeng Liang ◽  
Haijiang Li ◽  
Huafu Pei
Keyword(s):  
Analytical Solution ◽  
Analytical Model ◽  
Longitudinal Vibration ◽  
Large Diameter ◽  
Pile Shaft ◽  
Vibration Problem ◽  
Floating Pile ◽  
Longitudinal Impedance ◽  
Present Solution ◽  
Surrounding Soil

An analytical model is presented for solving the longitudinal complex impedance of a large-diameter floating pile in viscoelastic surrounding soil with radial heterogeneity and viscous-type damping, taking the effect of three-dimensional wave propagation of soil and lateral inertia of the pile shaft into account. The corresponding analytical solution for longitudinal impedance is also derived and validated via comparisons with existing solutions. The influences of the pile length, Poisson’s ratio of the pile shaft and the viscous damping coefficient, as well as the degree and radius of disturbed surrounding soil, on the longitudinal impedance of the pile shaft are examined by performing parametric analyses. It is demonstrated that the proposed analytical model and solution are suitable for the longitudinal vibration problem of a large-diameter pile and radially inhomogeneous surrounding soil, especially when the pile slenderness is low. In addition, the present solution can be easily degenerated to describe the longitudinal vibration problem relating to a large-diameter floating pile in radially homogenous soil or a pile with fixed-end supports.

scholarly journals TLM Z-transform method modelling of Lossy Grin MTM with different refractive index profiles

2012 ◽  
Vol 25 (2) ◽  
pp. 103-112
Author(s):  
Nebojsa Doncov ◽  
Tatjana Asenov ◽  
Zoran Stankovic ◽  
John Paul ◽  
Bratislav Milovanovic
Keyword(s):  
Refractive Index ◽  
3D Model ◽  
Three Dimensional ◽  
Refractive Index Profile ◽  
Index Profile ◽  
Transmission Line Matrix ◽  
Hyperbolic Tangent ◽  
Transform Method ◽  
Left Handed ◽  
The Time Domain

In this paper, a numerical three-dimensional (3D) model of electromagnetic lefthanded metamaterials (LH MTM) is applied for the modelling of composite right-left handed (RH/LH) structures with a graded refractive index profile commonly named GRIN MTM. The core of this model is Transmission Line Matrix (TLM) Z-transform method that incorporates the Drude function to account for dispersive LH MTM properties in the time-domain. Lossy GRIN slabs with abrupt, hyperbolic tangent, cosine, and linear refractive index profiles have been considered. The accuracy, efficiency and stability of the proposed approach are verified using analytical solution.

scholarly journals A New Approximate Analytical Solutions for Two- and Three-Dimensional Unsteady Viscous Incompressible Flows by Using the Kinetically Reduced Local Navier-Stokes Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-19
Author(s):  
Abdul-Sattar J. Al-Saif ◽  
Assma J. Harfash
Keyword(s):  
Analytical Solutions ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Transform Method ◽  
Navier Stokes Equations ◽  
Good Convergence ◽  
Flow Problems ◽  
Approximate Analytical Solutions

In this work, the kinetically reduced local Navier-Stokes equations are applied to the simulation of two- and three-dimensional unsteady viscous incompressible flow problems. The reduced differential transform method is used to find the new approximate analytical solutions of these flow problems. The new technique has been tested by using four selected multidimensional unsteady flow problems: two- and three-dimensional Taylor decaying vortices flow, Kovasznay flow, and three-dimensional Beltrami flow. The convergence analysis was discussed for this approach. The numerical results obtained by this approach are compared with other results that are available in previous works. Our results show that this method is efficient to provide new approximate analytic solutions. Moreover, we found that it has highly precise solutions with good convergence, less time consuming, being easily implemented for high Reynolds numbers, and low Mach numbers.

Researching on the Theory of Horizontal Vibration of the Pile in the Radial Inhomogeneous Viscoelastic Saturated Soil

2014 ◽  
Vol 1065-1069 ◽  
pp. 180-189
Author(s):  
Shu Zhen Feng ◽  
Jin Shan Wang ◽  
Hai Cui
Keyword(s):  
Analytical Solution ◽  
Complex Impedance ◽  
Vibration Characteristics ◽  
Saturated Soil ◽  
Horizontal Vibration ◽  
Reasonable Number ◽  
Radial Inhomogeneity

Consideration of radial inhomogeneity of soil, an analytical solution to horizontal vibration of pile in radial inhomogeneous soil is deduced, and the parameters influencing the horizontal vibration characteristics of the pile in radial inhomogeneous soil is analyzed carefully. The number of the radial layers of the inner soil, the thickness of the inner soil, the weakened degree and the ratio of length and radius can obviously affect complex impedance of the top of the pile. Before analyzing horizontal vibration of pile, choice a reasonable number of the radial layers of the inner soil and proper thickness of the inner soil, which is crucial. The more is the weakened degree of the inner soil, the stronger the fluctuations of horizontal vibration of pile are. The ratio of length and radius can influent horizontal vibration of pile within a certain range.

Predicting spatial activity patterns in a neural map from a probabilistic atlas of 3-D reconstructed neurons

1995 ◽  
Vol 53 ◽  
pp. 812-813
Author(s):  
G. Jacobs ◽  
F. Theunissen
Keyword(s):  
Activity Patterns ◽  
Three Dimensional ◽  
Sensory System ◽  
Neural System ◽  
Probabilistic Atlas ◽  
Uniform Sample ◽  
Dimensional Reconstruction ◽  
The Time Domain ◽  
And Function ◽  
Visualization Techniques

In order to understand how the algorithms underlying neural computation are implemented within any neural system, it is necessary to understand details of the anatomy, physiology and global organization of the neurons from which the system is constructed. Information is represented in neural systems by patterns of activity that vary in both their spatial extent and in the time domain. One of the great challenges to microscopists is to devise methods for imaging these patterns of activity and to correlate them with the underlying neuroanatomy and physiology. We have addressed this problem by using a combination of three dimensional reconstruction techniques, quantitative analysis and computer visualization techniques to build a probabilistic atlas of a neural map in an insect sensory system. The principal goal of this study was to derive a quantitative representation of the map, based on a uniform sample of afferents that was of sufficient size to allow statistically meaningful analyses of the relationships between structure and function.

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