• Structural Engineering and Mechanics
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• 제23권1호
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• pp.97-113
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• 2006

A simply supported hybrid plate consisting of top and bottom functionally graded elastic layers and an intermediate actuating or sensing homogeneous piezoelectric layer is investigated by an elasticity (piezoelasticity) method, which is based on state space formulations. The general spring layer model is adopted to consider the effect of bonding adhesives between the piezoelectric layer and the two functionally graded ones. The two functionally graded layers are inhomogeneous along the thickness direction, which are approached by laminate models. The effect of interlaminar bonding imperfections on the static bending and free vibration of the smart plate is discussed in the numerical examples.

• 한국전기전자재료학회논문지
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• 제24권10호
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• pp.784-789
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• 2011

A linear spring model, where the interactions among atoms are assumed to be isotropic and elastic, is employed for the study of non-polar optical phonon scattering in the valence band of alloy semiconductors. The force equations of n atoms are used in the spring model for the consideration of the random distribution of constituent atoms in an alloy semiconductor. When the number of atoms in a unit cell is assumed to be two based on the experimental result, the optical deformation potent is valid for compound semiconductors as well as alloy semiconductors.

• 한국도로학회논문집
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• 제10권3호
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• pp.209-220
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• 2008

본 논문은 지반위에 놓인 콘크리트 슬래브가 환경하중에 의해 컬링 할 때의 거동을 해석할 경우에 하부층의 모델링 방법에 따른 해석 결과의 차이를 분석한 내용을 기술하였다. 지반위에 놓인 슬래브 시스템을 전체 3차원 모델, 3차원 슬래브와 하부층을 스프링으로 구성한 모델, 그리고 2차윈 슬래브와 하부층을 스프링으로 구성한 모델 등으로 개발하여 해석을 수행하였다. 먼저 하부층이 단일 층으로 구성되어 있을 경우에 하부층 모델링 방법에 따른 컬링 거동의 차이를 분석하였다. 그리고 하부층이 서로 다른 재료와 두께로 구성되어 있는 복층일 경우에 하부층 모델링에 따른 컬링 거동의 특성을 비교 분석하였다. 연구결과 하부층을 무인장 스프링으로 모델링 하면 하부층이 단층일 경우에는 일반적으로는 상당히 정확한 해석결과를 얻을 수 있으나, 하부층이 복층일 경우에는 상위하부층의 탄성계수가 클 때, 하위하부층의 탄성계수가 작을 때, 그리고 상위하부층과 하위하부층의 두께가 두꺼울 때는 컬링 시에 슬래브의 수직변위 차이를 과대평가하게 되며 최대응력은 과소평가하게 된다.

• Smart Structures and Systems
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• 제21권3호
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• pp.349-358
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• 2018

This paper investigates the free vibration analysis of double-beam system coupled by a two-degree-of-freedom mass-spring system. In order to generalize the model, the main beams are assumed to be elastically restrained against translation and rotation at one end and free at the other. Furthermore, the mass-spring system is elastically connected to the beams at adjustable positions by means of four translational and rotational springs. The governing differential equations of the beams and the mass-spring system are derived and analytically solved by using the Fourier transform method. Moreover, as a second way, a finite element solution is derived. The frequency parameters and mode shapes of some diverse cases are obtained using both methods. Comparison of obtained results by two methods shows the accuracy of both solutions. The influence of system parameters on the free vibration response of the studied mechanical system is examined.

• Structural Engineering and Mechanics
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• 제59권6호
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• pp.1139-1153
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• 2016

Elastic constraints are usually simplified as "spring forces" exerted on beam ends without considering the "spring deformation". The partial differential equation governing the free vibrations of a cantilever Bernoulli-Euler beam considering the deformation of elastic constraints is firstly established, and is nondimensionalized to obtain two dimensionless factors, $k_v$ and $k_r$, describing the effects of elastically vertical and rotational end constraints, respectively. Then the frequency equation for the above Bernoulli-Euler beam model is derived using the method of separation of variables. A numerical analysis method is proposed to solve the transcendental frequency equation for the continuous change of the frequency with $k_v$ and $k_r$. Then the mode shape functions are given. Finally, effects of $k_v$ and $k_r$ on free vibration characteristics of the beam with different slenderness ratios are calculated and analyzed. The results indicate that the effects of $k_v$ are larger on higher-order free vibration characteristics than on lower-order ones, and the impact strength decreases with slenderness ratio. Under a relatively larger slenderness ratio, the effects of $k_v$ can be neglected for the fundamental frequency characteristics, while cannot for higher-order ones. However, the effects of $k_r$ are large on both higher- and lower-order free vibration characteristics, and cannot be neglected no matter the slenderness ratio is large or small.

• Interaction and multiscale mechanics
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• 제3권1호
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• pp.95-110
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• 2010

In recent years, study of the static response of pavements to moving vehicle and aircraft loads has received significant attention because of its relevance to the design of pavements and airport runways. The static response of beams resting on an elastic foundation and subjected to moving loads was studied by several researchers in the past. However, most of these studies were limited to steady-state analytical solutions for infinitely long beams resting on Winkler-type elastic foundations. Although the modelling of subgrade as a continuum is more accurate, such an approach can hardly be incorporated in analysis due to its complexity. In contrast, the two-parameter foundation model provides a better way for simulating the underlying soil medium and is conceptually more appealing than the one-parameter (Winkler) foundation model. The finite element method is one of the most suitable mathematical tools for analysing rigid pavements under moving loads. This paper presents an improved solution algorithm based on the finite element method for the static analysis of rigid pavements under moving vehicular or aircraft loads. The concrete pavement is discretized by finite and infinite beam elements, with the latter for modelling the infinity boundary conditions. The underlying soil medium is modelled by the Pasternak model allowing the shear interaction to exist between the spring elements. This can be accomplished by connecting the spring elements to a layer of incompressible vertical elements that can deform in transverse shear only. The deformations and forces maintaining equilibrium in the shear layer are considered by assuming the shear layer to be isotropic. A parametric study is conducted to investigate the effect of the position of moving loads on the response of pavement.

• 비파괴검사학회지
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• 제31권2호
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• pp.174-180
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• 2011

본 연구에서는 초음파원자현미경을 이용하여 비파괴적인 표면탄성이미지 분석과 나노표면에서의 기계적 물성 평가를 연구하였다. 이를 위해 접촉역학 특성에 따른 캔틸레버의 공진주파수 변화를 이론적으로 해석하고 실험적으로 측정하였다. 스프링-질량 모델과 Herzian 이론을 이용하여 계산한 이론적인 접촉공천주파수는 초음파원자현미경 캔틸레버의 실험적인 접촉 공진주파수의 변화와 매우 유사하였다. 결과적으로, 초음파원자현미경의 표면 높이 이미지와 진폭이미지를 성공적으로 얻을 수 있었고 진폭신호를 통하여 시료표면에서의 탄성특성을 정성적으로 평가하였다.

• 대한기계학회논문집
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• 제18권12호
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• pp.3185-3194
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• 1994

In this study, an impact model and impact response analysis method was suggested for the impacts between arbitrary shaped bodies. Unlike the impacts between geometrically simple structures, there is no rules to analyze the impacts between general elastic structures First of all, it has been attempted to explain the impoot between arbitrary elastic structures as the elastic deformation of a virtual contact spring in the vicinity of contact points. The contact stiffness and the exponent are determined from the Hertz's contact theory and F. E. analysis. In order to evaluate the validities and limitations of the proposed methods, an impact tester and the miniature of container, missile and isolators have been provided and tested experimentally. All the experiments were performed with various impact conditions. The results obtained by the proposed methods were directly compared with the measured values in terms of maximum contract force, contact duration, the shape of contact force and the structure responses. The computed contact force and responses, using this proposed methods, were very close to the measured results, unless any plastic deformations were presented.

• Advances in nano research
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• 제6권3호
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• pp.279-298
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• 2018

Present investigation deals with the free vibration characteristics of nanoscale-beams resting on elastic Pasternak's foundation based on nonlocal strain-gradient theory and a higher order hyperbolic beam model which captures shear deformation effect without using any shear correction factor. The nanobeam is lying on two-parameters elastic foundation consist of lower spring layers as well as a shear layer. Nonlocal strain gradient theory takes into account two scale parameters for modeling the small size effects of nanostructures more accurately. Hamilton's principal is utilized to derive the governing equations of embedded strain gradient nanobeam and, after that, analytical solutions are provided for simply supported conditions to solve the governing equations. The obtained results are compared with those predicted by the previous articles available in literature. Finally, the impacts of nonlocal parameter, length scale parameter, slenderness ratio, elastic medium, on vibration frequencies of nanosize beams are all evaluated.

• 한국생산제조학회지
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• 제24권4호
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• pp.421-427
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• 2015

In this paper, a description is given of finite element method (FEM) simulations of the elastic bending modulus of multi-layered graphene sheets that were carried out to investigate the mechanical behavior of graphene sheets with different gap thicknesses through molecular mechanics theory. The interaction forces between layers with various gap thicknesses were considered based on the van der Waals interaction. A finite element (FE) model of a multi-layered rectangular graphene sheet was proposed with beam elements representing bonded interactions and spring elements representing non-bonded interactions between layers and between diagonally adjacent atoms. As a result, the average elastic bending modulus was predicted to be 1.13 TPa in the armchair direction and 1.18 TPa in the zigzag direction. The simulation results from this work are comparable to both experimental tests and numerical studies from the literature.