• Coupled systems mechanics
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• 제13권1호
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• pp.43-60
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• 2024

This work presents an analytical approach to investigate wave propagation in bi-directional functionally graded cantilever porous beam. The formulations are based on Touratier's higher-order shear deformation beam theory. The physical properties of the porous functionally graded material beam are graded through the width and thickness using a power law distribution. Two porosities models approximating the even and uneven porosity distributions are considered. The governing equations of the wave propagation in the porous functionally graded beam are derived by employing the Hamilton's principle. Closed-form solutions for various parameters and porosity types are obtained, and the numerical results are compared with those available in the literature.The numerical results show the power law index, number of wave, geometrical parameters and porosity distribution models affect the dynamic of the FG beam significantly.

• Structural Engineering and Mechanics
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• 제75권2호
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• pp.193-209
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• 2020

This paper presents a new hyperbolic shear deformation plate theory including the stretching effect for free vibration of the simply supported functionally graded plates in thermal environments. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. This theory has only five unknowns, which is even less than the other shear and normal deformation theories. The present one has a new displacement field which introduces undetermined integral variables. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume power laws of the constituents. The equation of motion of the vibrated plate obtained via the classical Hamilton's principle and solved using Navier's steps. The accuracy of the proposed solution is checked by comparing the present results with those available in existing literature. The effects of the temperature field, volume fraction index of functionally graded material, side-to-thickness ratio on free vibration responses of the functionally graded plates are investigated. It can be concluded that the present theory is not only accurate but also simple in predicting the natural frequencies of functionally graded plates with stretching effect in thermal environments.

• Korean Journal of Acupuncture
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• 제27권2호
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• pp.107-120
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• 2010

Objectives : The aim of this study is to measure pulse waveforms by applying 5-level graded pressure, and selecting optimum pulse waveforms. Also to proposing the possibility of using AW(Area of the 1/3 upper height of h1) rate in respect to AT(Total Area) for risk assessment of hypertension or arteriosclerosis is another aim of the study. Methods : Pulse waveforms of normotensive were measured by 5-level graded pressure. The pulse waveforms well reflecting properties of blood vessel(having the largest h1) were selected for optimum pulse waveforms. Various parameters(h-parameter, t-parameter, and others) of optimum pulse waveforms were analyzed. AIx(Augmentation index) was calculated by height-parameters to assess arterial stiffness. The area rate of the 1/3 upper height for h1 in respect to total area was analyzed according to aging. Results : According to aging 1. in height-parameter, h2 and h3 were increased but h5 was decreased. 2. In time-parameter, t2, t3, and t5 were getting short. 3. Area of systolic period was increased, and that of diastolic period decreased. 4. AIx rose by aging. 5. AW was significantly increased despite no changes in AT. Conclusions : By analyzing optimum pulse waveforms of 5-level graded pressure method, we could complement weakness of single graded pressure method. Also, possibility of applying the AW rate to risk assessment of hypertension or arteriosclerosis was confirmed in normotensive population which might not be assessed by AIx.

• Steel and Composite Structures
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• 제52권3호
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• pp.273-291
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• 2024

This paper presents a three-dimensional displacement-based formulation to investigate the free vibration of functionally graded nanoplates resting on a Winkler-Pasternak foundation based on the nonlocal elasticity theory. The material properties of the FG nanoplate are considered to vary continuously through the thickness of the nanoplate according to the power-law distribution model. A general three-dimensional displacement field is considered for the plate, which takes into account the out-of-plane strains of the plate as well as the in-plane strains. Unlike the shear deformation theories, in the present formulation, no predetermined form for the distribution of displacements and transverse strains is considered. The equations of motion for functionally graded nanoplate are derived based on Hamilton's principle. The solution is obtained for simply-supported nanoplate, and the predicted results for natural frequencies are compared with the predictions of shear deformation theories which are available in the literature. The predictions of the present theory are discussed in detail to investigate the effects of power-law index, length-to-thickness ratio, mode numbers and the elastic foundation on the dynamic behavior of the functionally graded nanoplate. The present study presents a three-dimensional solution that is able to determine more accurate results in predicting of the natural frequencies of flexural and thickness modes of nanoplates. The effects of parameters that play a key role in the analysis and mechanical design of functionally graded nanoplates are investigated.

• 대한전기학회논문지
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• 제45권1호
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• pp.146-158
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• 1996

The WKB method has been widely used in evaluating of the propagation characteristics of planar waveguides with graded-index profiles. This method, however, yields large errors when a turning point is near or at the discontinuity in the presence of the index discontinuity or index slope discontinuity. Especially, in the case of a truncated-index profile, this phenomenon appears more clearly in the low-order modes and near the cutoff regions. The MWKB method is introduced to reduce these inherent errors of the conventional WKB method. The MWKB method is based on both the linearization of the index profile from an index discontinuity and the introduction of a virtual turning point. It is noticed that the b-v curves obtained by the MWKB method agree well with those of the finite-difference method, and that the phase shift at a turning point depends on both the index profile and its propagation constant. (author). refs., figs.

• 한국방재학회 논문집
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• 제7권5호
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• pp.61-71
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• 2007

Navier 해 및 유한요소 해를 두께 방향으로 재료의 성질이 변하는 점진기능재료 판 및 쉘의 해석을 위해 제시하였다. 판과 쉘의 두께를 따라 완만하게 변하는 등방성 구조물의 두께방향에 따른 역학적 특성을 고려하기 위하여 S 형상 함수를 적용한 점진기능재료를 고려하였다. 비선형 9 절점 요소기저 Lagrangian 쉘 요소의 정식화를 기하학적 비선형 해석을 위해 제시하였다. 자연 좌표계에 의한 변형률이 본 연구의 쉘요소에 사용된다. 1차 전단변형이론에 의한 수치 해석 예제로 상면과 하면의 탄성 계수의 변화, 하중조건, 형상 비 그리고 폭-두께 비에 따른 역학적 거동을 연구하였다. 또한 거듭제곱 매개 변수의 변화에 따른 점진기능재료 구조물의 결과들을 조사하였다.

• Advances in nano research
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• 제12권5호
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• pp.467-482
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• 2022

In the current work, static and free torsional vibration of functionally graded (FG) nanorods are investigated using Fourier sine series. The boundary conditions are described by the two elastic torsional springs at the ends. The distribution of functionally graded material is considered using a power-law rule. The systems of equations of the mechanical response of nanorods subjected to deformable boundary conditions are achieved by using the modified couple stress theory (MCST) and taking the effects of torsional springs into account. The idea of the study is to construct an eigen value problem involving the torsional spring parameters with small scale parameter and functionally graded index. This article investigates the size dependent free torsional vibration based on the MCST of functionally graded nano/micro rods with deformable boundary conditions using a Fourier sine series solution for the first time. The eigen value problem is constructed using the Stokes' transform to deformable boundary conditions and also the convergence and accuracy of the present methodology are discussed in various numerical examples. The small size coefficient influence on the free torsional vibration characteristics is studied from the point of different parameters for both deformable and rigid boundary conditions. It shows that the torsional vibrational response of functionally graded nanorods are effected by geometry, small size effects, boundary conditions and material composition. Furthermore, for all deformable boundary conditions in the event of nano-sized FG nanorods, the incrementing of the small size parameters leads to increas the torsional frequencies.

• 대한토목학회논문집
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• 제35권6호
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• pp.1367-1375
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• 2015

제강슬래그 골재를 사용한 박층 아스팔트 포장공법을 위해 10 mm 밀입도 아스팔트 혼합물의 골재 입도기준을 제시하고자 하였다. 기존 WC-1, WC-3과 같은 밀입도 아스팔트 혼합물의 골재 입도기준은 퓰러모델에 의해 제시되었으나 10 mm 밀입도 아스팔트의 경우 최대밀도선과 유사한 입도를 얻게 되어 부드러운 혼합물이 되는 경향을 나타내었다. 국외 입도기준을 참고하여 골재 맞물림과 최소 골재간극률을 확보하기 유리한 입도를 제시하였다. 제시된 입도의 검증을 위해 골재 입도특성지표인 입도비(GR)와 골재다짐밀도(CAD)를 사용하여 혼합물 물성과의 상관관계를 분석하였다. 골재 입도 및 다양한 특성을 반영할 수 있는 CAD 지표의 $R^2$가 0.86~0.99로 매우 높게 나타났다. CAD 지표를 이용하여 다양한 골재 입도를 검토한 결과 제시 입도기준이 마샬안정도와 VMA 등 배합설계 인자에 보다 안정적인 것으로 나타났다. 또한 균열저항성 향상을 위해 0.3 mm 이하 골재의 통과중량백분율을 10% 이상으로 제한함으로서 터프니스가 약 15% 향상되어 효과적임을 확인 할 수 있었다.

• 대한전자공학회논문지SD
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• 제37권2호
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• pp.28-37
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• 2000

수정된 Airy 함수들과 WKB 시도해를 조합하여 언덕형 굴절율 분포를 가지는 광섬유에 대한 매우 정확한 고유방정식을 수학적으로 유도하였다. 적절한 경계조건을 적용하여 일반적인 WKB 방법이 가지는 고유한 오차 문제를 개선하도록 위상 천이 보정항 δ를 이끌어냈다. 모의 전산을 통하여, 유도된 고유방정식의 결과가 유한차분법에 의한 결과와 잘 일치함을 보였다.

• Smart Structures and Systems
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• 제8권5호
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• pp.433-447
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• 2011

The present paper addresses the nonlinear response of a FG square plate with two smart layers as a sensor and actuator under pressure. Geometric nonlinearity was considered in the strain-displacement relation based on the Von-Karman assumption. All the mechanical and electrical properties except Poisson's ratio can vary continuously along the thickness of the plate based on a power function. Electric potential was assumed as a quadratic function along the thickness direction and trigonometric function along the planar coordinate. By evaluating the mechanical and electrical energy, the total energy equation can be minimized with respect to amplitude of displacements and electrical potential. The effect of non homogenous index was investigated on the responses of the system. Obtained results indicate that with increasing the non homogenous index, the displacements and electric potential tend to an asymptotic value. Displacements and electric potential can be presented in terms of planar coordinate system. A linear analysis was employed and then the achieved results are compared with those results that are obtained using the nonlinear analysis. The effect of the geometric nonlinearity is investigated by using the comparison between the linear and nonlinear results. Displacement-load and potential-load curves verified the necessity of a nonlinear analysis rather than a linear analysis. Improvement of the previous results (by the linear analysis) through employing a nonlinear analysis can be presented as novelty of this study.