• Interaction and multiscale mechanics
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• 제6권1호
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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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• 제6권1호
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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.

• 한국지반공학회논문집
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• 제15권6호
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• pp.29-44
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• 1999

본 논문은 균질 및 비균질의 사질토 지반에서 항타 시공된 단일 강성말뚝의 수평거동에 대한 모형실험 결과들을 고찰하였다. 본 연구의 목적은 말뚝의 수평거동 특성에 대한 말뚝 시공상태 (Driven & Embedded), 말뚝 근입길이에 대한 하부지반의 두께비 (H/L),그리고 지반의 상대밀도의 영향에 관하여 실험적인 연구를 수행하고 이러한 영향들을 정량화 할 수 있는 실험결과를 얻었다. 모형 실험 결과들에 의하면, 수평거동은 느슨한 균질지반에서 시공방법에 상당히 의존하는 것으로 나타났다. 말뚝시공시 항타방법에 의존할 경우 균질지반에서는 느슨한 지반일수록 그리고 비균질 지반 $(E_{h1}/E_{h2}/=0.18)$에서는 상부층 두께가 클수록 수평변위 감소에 상당한 효과를 얻을 수 있으나, 최대 휨모멘트 감소는 수평변위 감소와 정반대의 결과를 나타냈다. 수평변위 측면에서, 매입말뚝에 대한 항타말뚝의 변위비 $(y_{Driven}y_{Embedded})$는 균질지반의 각 상대 밀도에 대하여 0.65-0.88 $(D_r=90%)$와 0.38-0.65 (D$_{r}$=61.8%)의 범위로 그리고 비균질지반에서 0.6-0.88 의 범위로 나타났다. 또한, 본 연구에서는 $y_D/y_E \;와\; NBM_D/MBM_E$에 대한 항타고와 H/L의 영향들을 모형실험 결과들로부터 실험식으로 제안하였다.

• Geomechanics and Engineering
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• 제7권1호
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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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• 제15권5호
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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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• 제35권3호
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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.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 1999년도 가을 학술발표회 논문집
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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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• 제6권3호
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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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• 제61권2호
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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.

• 한국지반공학회지:지반
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• 제13권5호
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• pp.59-74
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• 1997

본 논문은 낙동강 유역의 사질토 지반에서 수평하중을 받는 강관 말둑의 수평거동을 모형실첨을 통해 관찰하였다. 븐 연구의 목적은 말뚝의 수평거동(하중-변위 잔계,지반내 말뚝의 모멘트 분포, 최대 모멘트-변위 관계 등)에 대한 말뚝의 강성, 말뚝의 근입길이, 지반의 상대밀도, 하중 재하속도, 말뚝두부의 구속조건, 그리고 지반내의 비균질토의 영향에 관하여 실험적인 연구를 수행하고 이러한 영향들을 정량화 할 수 있는 결과들을 얻고자 한다. 비선형적인 하중-변위 관계는 모형실험의 결과들로부터 2차 곡선방정식으로 회귀분석하여 구하였으며, 임의 수평 변위에 대한 수평하중, 항복하중, 극한하중 그리고 최대 휭모멘트와 항복쉽모멘트는 상대밀도를 포함하는 지수함수식의 형태로 회귀분석하여 구하였다. 수평 극한하중에 관한 Brom's의 이론 결과와 실험결과 비교에서, 짧은 말뚝과 긴 말뚝의 결과가 서로 반대로 나타난 것은 가정한 지반반력이 깊은 지점에서 낙동강 사질토의 지반반력보다 작아서 나타나는 것으로 판단된다. 균질충과 비균질토 지반의 수평거동 비교에서, 하부지반의 상 대밀도보다 상부지반의 상대 밀도가 하중-변위관계에 더 큰 영향을 끼치고 있으며, 하부와 상부 지반의 상대밀도 차가 클수록 그런현상은 뚜렷하게 나타났다.