• Interaction and multiscale mechanics
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• v.6 no.1
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• pp.31-50
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• 2013

A five parameter viscoelastic model is developed to study harmonic waves propagating in the non-homogeneous viscoelastic filaments of varying density. The constitutive relation for five parameter model is first developed and then it is applied for harmonic waves in the specimen. In this study, it is assumed that density, rigidity and viscosity of the specimen i.e., rod are space dependent. The specimen is non-homogeneous, initially unstressed and at rest. The method of non-linear partial differential equation has been used for finding the dispersion equation of harmonic waves in the rods. A simple method is presented for reflections at the free end of the finite non-homogeneous viscoelastic rods. The harmonic wave propagation in viscoelastic rod is also presented numerically with MATLAB.

• Interaction and multiscale mechanics
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• v.6 no.1
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• pp.1-14
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• 2013

The aim of this paper is to study the propagation of torsional surface waves in non-homogeneous isotropic layer of finite thickness placed over a homogeneous viscoelastic half-space, when both density and rigidity of the non-homogeneous medium are assumed to vary exponentially with depth. The frequency equations are obtained by using simple method of separation of variables. Further, it is seen that when viscoelastic parameter and non-homogeneity parameter is neglected, the dispersion equation gives the dispersion equations of Love waves in homogeneous, elastic and isotropic layer placed over homogeneous viscoelastic medium. The problem has been solved numerically and the effects of various inhomogeneities of the medium on torsional waves have been illustrated graphically.

• Journal of the Korean Geotechnical Society
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• v.15 no.6
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• pp.29-44
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• 1999

This paper shows the results of model tests on the lateral behavior of single rigid pile, which was constructed by driving, in homogeneous and non-homogeneous (two layered) NakDong River sands. The purpose of the present paper is to investigate the effect of ratio of lower layer thickness to embedded pile length, relative density of sand and pile construction conditions (Driven & Embedded piles) on the characteristics of lateral behavior of single pile. These effects can be quantified only by the results of model tests. As a model result, the lateral behavior depends upon the pile construction condition in loose-density soil more than in high-density soil. If the pile construction depends upon driving construction, the decrease of deflection remarkably increases for both loose homogeneous sand and non-homogeneous soil$(E_{h1}/E_{h2}/=0.18)$ with high thickness of upper layer but the decrease of maximum bending moment shows the opposite result to the decrease of deflection. And, with respect to deflection, it was found that the deflection ratio $(y_{Driven}y_{Embedded})$ of embedded to driven piles has the ranges of 0.65 - 0.88 $(D_r=90%)$0.38 - 0.65 $(D_r=61.8%)$ for each relative density of homogeneous soil and the range of 0.6 - 0.88 for non-homogeneous soil. Also, in this study, the experimental equation for the effects of drop height (DH) and H/L on the ratios of $y_D/y_E\; and MBM_D/MBM_ E$ is suggested from model tests.

• Geomechanics and Engineering
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• v.7 no.1
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• pp.1-36
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• 2014

The effect of various parameters on the propagation of surface waves in electro-magneto thermoelastic orthotropic granular non-homogeneous medium subjected to gravity and initial compression has been studied. All material coefficients are obeyed the same exponent-law dependence on the depth of the granular elastic half space. Some special cases investigated by earlier researchers have also been deduced. Dispersion curves are computed numerically and presented graphically.

• Geomechanics and Engineering
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• v.15 no.5
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• pp.1071-1080
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• 2018

The study of behavior and values of deformations in the geological medium makes the scientific basis of the methodology of synthesis of true values of parameters of its physico-mechanical and density properties taking into account the influence of geodynamic impacts. The segments of continuous variation of homogeneous elastic uniform deformations are determined under overall compression of the medium. The limits of these segments are defined according to the criteria of instability (on geometric form changes and on "internal" instability). Analytical formulae are obtained to calculate current and limiting (critical) values of deformations within the framework of various variants of small and large initial deformations of the non-classically linearized approach of non-linear elastodynamics. The distribution of deformation becomes non-uniform in the medium while the limiting values of deformations are achieved. The proposed analytical formulae are applicable only within homogeneous distribution of deformations. Numerical experiments are carried out for various elastic potentials. It is found that various forms of instability can precede phase transitions and destruction. The influence of these deformation phenomena should be removed while the physico-mechanical and density parameters of the deformed media are determined. In particular, it is necessary to use the formulae proposed in this paper for this purpose.

• Steel and Composite Structures
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• v.35 no.3
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• pp.449-462
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• 2020

This work aims to study effects of the crack and the surface energy on the free longitudinal vibration of axially functionally graded nanorods. The surface energy parameters considered are the surface stress, the surface density, and the surface Lamé constants. The cracked nanorod is modelled by dividing it into two parts connected by a linear spring in which its stiffness is related to the crack severity. The surface and bulk material properties are considered to vary in the length direction according to the power law distribution. Hamilton's principle is implemented to derive the governing equation of motion and boundary conditions. Considering the surface stress causes that the derived governing equation of motion becomes non-homogeneous while this was not the case in works that only the surface density and the surface Lamé constants were considered. To extract the frequencies of nanorod, firstly the non-homogeneous governing equation is converted to a homogeneous one using an appropriate change of variable, and then for clamped-clamped and clamped-free boundary conditions the governing equation is solved using the harmonic differential quadrature method. Since the present work considers effects of all the surface energy parameters, it can be claimed that this is a comprehensive work in this regard.

• Proceedings of the Korean Geotechical Society Conference
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• 1999.10a
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• pp.3-44
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• 1999

This paper discusses the lateral behavior of single and group piles in homogeneous and non-homogeneous(two layered) soil. In the single pile, the model tests were conducted to investigate the effects on ratio of lower layer height to embedded pile length, ratio of soil modules of upper layer to lower layer, boundary rendition of pile head and tip, embedded pile length, pile construction condition, ground condition with saturate and moisture state in Nak-Dong river sand. Also, in the group pile, the model tests were to investigate the effects on spacing-to-diameter ratio of pile, pile array, ratio of pile spacing, boundary condition of pile head and tip, eccentric load and ground condition. The maximum bending moment and deflection induced in active piles were found to be highly dependent on the relative density, pile construction condition, boundary condition of pile head and tip. Based on the results obtained, it was found that the decrease of lateral bearing capacity in saturated sand was in the range of 31% - 53% as compared with the case of dry sand. Also, in the group pile, a spacing-to-diameter of 6.0 seems to be large enough to eliminate the group effect for the case of relative density of 61.8%, and 32.8%, and then each pile in such a case behaves essentially the same as a single pile. In this study, the program is developed by using the modified Chang method which used p - y method and the exact solution of governing equation of pile and it can be used to calculate the deflection, bending moment and soil reaction with FDM in non-homogeneous soil. In comparing the modified Chang method with field test results, the predict results shows better agreement with measured results in field tests.

• Interaction and multiscale mechanics
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• v.6 no.3
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• pp.287-300
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• 2013

In this paper, the effect of impulsive line on the propagation of shear waves in non-homogeneous elastic layer is investigated. The rigidity and density in the intermediate layer is assumed to vary quadratic as functions of depth. The dispersion equation is obtained by using the Fourier transform and Green's function technique. The study ends with the mathematical calculations for transmitted wave in the layer. These equations are in complete agreement with the classical results when the non-homogeneity parameters are neglected. Various curves are plotted to show the effects of non-homogeneities on shear waves in the intermediate layer.

• Structural Engineering and Mechanics
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• v.61 no.2
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• pp.295-316
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• 2017

Element based differential quadrature method (EDQM) has been applied to analyze static, stability and free vibration of non-homogeneous orthotropic rectangular plates of variable or stepped thickness. The Young's modulus and the density are assumed to vary in exponential form in X-direction whereas the thickness is assumed to vary linear, parabolic or exponential variation in one or two directions. In-plane loading is assumed to vary linearly. Various combinations of clamped, simply supported and free edge conditions (regular and irregular boundary) have been considered. Continuous plates could also be handled with ease. In this paper, formulation for equilibrium, buckling and free vibration problems is discussed and several numerical examples are solved using EDQM and compared with the published results.

• Geotechnical Engineering
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• v.13 no.5
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• pp.59-74
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• 1997

This paper shows the results of a series of model bests on the behavior of single steel pipe pile which is subjected to lateral load in Nak-dong river sand. The purpose of the present paper is to estimate the effect of Non -homogeneous soil, constraint condition of pile head, lateral load velocity, relative density of soil, embedded pile length, and flexural stiffness of pile on the behavior of single pile which is embedded in Nak-dong river strand. These effects can be quantined only by the results of model tests. The nonlinear responses of lateral loadieflection relationships are fitted to 2nd polynomial equations by model tests results. Also, the lateral load of a deflection, yield and ultimate lateral load max. bending moment, and yield bending moment can be expressed as exponential function in terms of relative density and deflection ratio. By comparing Brom's results with model results on the lateral ultimate load, it is found that short and long pile show the contrary results with each other. The contrary results are due to the smaller assumed soil reaction than the soil reaction of the Nakiong river sand at deep point. By comparing lateral behavior on the homogeneous soil with non-homogeneous soil, it is shown that lateral loadieflection relationship is very dependent on the upper relative density. This phenomenon is shown remarkably as the difference between upper and lower relative density increases.