• Advances in nano research
• /
• 제16권2호
• /
• pp.175-186
• /
• 2024

Dynamical behaviors of one-dimensional (1D) nano-sized structures are of great importance in nanotechnology applications. Therefore, the torsional dynamic response of functionally graded nanorods which could be used to model the nano electromechanical systems or micro electromechanical systems with torsional motion about the center of twist is examined based on the theory of strain gradient nonlocal elasticity in this work. The mathematical background is constructed based on both strain gradient theory and Eringen's nonlocal elasticity theory. The equation of motions and boundary conditions of radially functionally graded nanorods are derived using Hamilton's principle and then transformed into the eigenvalue analysis by using Fourier sine series. A general coefficient matrix is obtained to assemble the Stokes' transformation. The case of a restrained functionally graded nanorod embedded in two elastic springs against torsional rotation is then deeply investigated. The effect of changing the functionally graded index, the stiffness of elastic boundary conditions, the length scale parameter and nonlocal parameter are investigated in detail.

• 한국생물정보학회:학술대회논문집
• /
• 한국생물정보시스템생물학회 2004년도 The 3rd Annual Conference for The Korean Society for Bioinformatics Association of Asian Societies for Bioinformatics 2004 Symposium
• /
• pp.265-271
• /
• 2004

The interaction network of protein -protein plays an important role to understand the various biological functions of cells. Currently, the high -throughput experimental techniques (two -dimensional gel electrophoresis, mass spectroscopy, yeast two -hybrid assay) provide us with the vast amount of data for protein-protein interaction at the proteome scale. In order to recognize the role of each protein in their network, the efficient bioinformatical and computational analysis methods are required. We propose a systematic and mathematical method which can analyze the protein -protein interaction network rigorously and enable us to capture the biological and physical essence of a topological character and stability of protein -protein network, and sensitivity of each protein along the biological pathway of their network. We set up a Laplacian matrix of spectral graph theory based on the protein-protein network of yeast proteome, and perform an eigenvalue analysis and apply a perturbation method on a Laplacian matrix, which result in recognizing the center of protein cluster, the identity of hub proteins around it and their relative sensitivities. Identifying the topology of protein -protein network via a Laplacian matrix, we can recognize the important relation between the biological pathway of yeast proteome and the formalism of master equation. The results of our systematic and mathematical analysis agree well with the experimental findings of yeast proteome. The biological function and meaning of each protein cluster can be explained easily. Our rigorous analysis method is robust for understanding various kinds of networks whether they are biological, social, economical...etc

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 1995년도 가을 학술발표회 논문집
• /
• pp.225-233
• /
• 1995

This paper presents an efficient numerical method for computation of eigenpair derivatives for the real symmetric eigenvalue problem with distinct and multiple eigenvalues. The method has very simple algorithm and gives an exact solution. Furthermore, it saves computer storage and CPU time. The algorithm preserves the symmetry and band of the matrices, allowing efficient computer storage and solution techniques. Thus, the algorithm of the proposed method will be inserted easily in the commercial FEM codes. Results of the proposed method for calculating the eigenpair derivatives are compared with those of Rudisill and Chu's method and Nelson's method which is efficient one in the case of distinct natural frequencies. As an example to demonstrate the efficiency of the proposed method in the case of distinct eigenvalues, a cantilever plate is considered. The design parameter of the cantilever plate is its thickness. For the eigenvalue problem with multiple natural frequencies, the adjacent eigenvectors are used in the algebraic equation as side conditions, they lie adjacent to the m (multiplicity of multiple natural frequency) distinct eigenvalues, which appear when design parameter varies. As an example to demonstrate the efficiency of the proposed method in the case of multiple natural frequencies, a cantilever beam is considered. Results of the proposed method fDr calculating the eigenpair derivatives are compared with those of Bailey's method (an amendation of Ojalvo's work) which finds the exact eigenvector derivatives. The design parameter of the cantilever beam is its height. Data is persented showing the amount of CPU time used to compute the first ten eigenpair derivatives by each method. It is important to note that the numerical stability of the proposed method is proved.

• 대한토목학회논문집
• /
• 제28권4A호
• /
• pp.465-474
• /
• 2008

일반적으로, 보-기둥 부재로 구성된 강뼈대구조물의 설계는 개별부재의 유효좌굴길이를 고려하여 설계기준에서 제시한 안정성 평가식을 적용하고 있다. 그러나 이 방법은 구조물에서 상대적으로 작은 압축력이 적용되는 부재에서는 유효좌굴길이가 커지는 문제가 발생하게 된다. 이러한 문제를 극복하고자 본 연구에서는 대상 구조물의 초기결함(initial imperfection)을 고려한 2차 탄성해석법을 제시한다. 이 방법은 탄성좌굴 고유치해석으로 산정된 좌굴모드 및 좌굴고유치, 개별부재의 축력을 이용하여, 가장 작은 무차원 세장비를 가진 부재를 선정하고, 그 부재에 대하여 기하적, 재료적인 효과가 고려된 설계기준의 기준강도곡선으로부터 좌굴모드에 대한 증폭량을 산정한다. 이렇게 결정된 증폭량을 대상 구조물의 좌굴모드에 증폭시켜 2차 탄성해석을 수행하고, 개별부재의 안정성을 평가한다. 본 방법의 타당성을 확인하기 위하여, 8층 및 4층으로 이루어진 평면 강뼈대구조물에 적용시키고, 설계기준에서 제시하는 안정성 평가법과 비교한다.

• 한국해안해양공학회지
• /
• 제4권2호
• /
• pp.91-107
• /
• 1992

Heaps(1972)가 사용한 천해균질류에 대한 선형 기본방정식을 수심평균류속과 해수면변리를 계산하는 External mode와 수심변이 유속을 계산하는 Internal mode로 분리시킨 다음, Internal mode식에 Galerkin Method를 적용하였다. Internal mode유속을 수평좌표, 시간에 따라 변하는 계수와 대직좌표에 따라 변하는 Basis function들의 곱의 형태로 선형전개하며, 난류확산계수를 포함하는 2차미분항으로부터 해수면에 Homogeneous boundary condition과 해저면에 Sheared boundary condition이 가해지는 Sturm-Liouville system을 구성, Eigenfunctions 해를 구하여 Basis function으로 사용하였다. 모델의 성능을 검토하기 위하여 수립된 모델을 정상균일풍이 가해지는 1차원 수노에 적용하여 Cooper and Pearce(1977)가 제시한 해저면 비활동조건하의 무한 및 유한수노 연직류원분포에 대한 해석각와 비교하였으며, North Sea 규모의 등수심 장방형 Basin(Heaps' Basin)에 적용하여 정상균일풍에 대한 Heaps(1972)의 계산결과와 비교하였다.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2003년도 추계학술대회논문집
• /
• pp.572-578
• /
• 2003

The free vibration of a spinning flexible disk-spindle system supported by hydro dynamic bearings in a HDD is analyzed by FEM. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The flexible supporting structure with a complex shape which includes stator core, housing, base plate, sleeve and thrust pad is modeled by using a 4-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility. The dynamic coefficients of HDB are calculated from the HDB analysis program, which solves the perturbed Raynolds equation using FEM. Introducing the virtual nodes and the rigid link constraints defined in the center of HDB, beam elements of the shaft are connected to the solid elements of the sleeve and thrust pad through the spring and damper element. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigenvalue problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies with the experimental ones. Also the effect of supporting structures to the natural modes of the total HDD system is rigorously analyzed.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2006년도 춘계학술대회논문집
• /
• pp.660-665
• /
• 2006

This paper presents a finite element method to analyze the free and forced vibration of a hard disk drive (HDD) considering the flexibility of a spinning disk-spindle with fluid dynamic bearings (FDBs), an actuator with pivot bearings, an air bearing between head-disk interface and the base with complicated geometry. Finite element equation of each component is consistently derived with the satisfaction of the geometric compatibility of the internal boundary between each component. The spinning disk, hub and FDBs are modeled by annular sector elements, beam elements and stiffness and damping elements, respectively. The actuator am, E-block, suspension and base plate are modeled by tetrahedral elements. The pivot bearing in the actuator and the air bearing between head-disk interfaces are modeled by the stiffness element with five degrees of freedom and the axial stiffness, respectively. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem with the restarted Arnoldi iteration method. Modal and shock testing are performed to show that the proposed method well predicts the vibration characteristics of a HDD.

• 한국전자파학회논문지
• /
• 제21권7호
• /
• pp.805-814
• /
• 2010

기존 Crank-Nicolson FDTD 기법(CN FDTD 기법)의 비등방성 분산 특성을 개선하기 위한 CN ID-FDTD 기법을 제안하였다. 제안한 CN ID-FDTD 기법은 공간 미분 연산을 위해 기존 CN FDTD 기법의 centered 유한 차분식 (Finite Difference equation: FD 연산식)이 아닌 isotropic-dispersion 유한 차분식(ID-FD 연산식)$^{[1],[2]}$을 이용한다. 본 논문에서는 손실 매질에 대한 CN ID-FDTD 기법의 분산 관계식을 유도하였고, 이 분산 관계식을 이용해 ID-FD 연산식에서 분산 오차(dispersion error)를 줄이는 가중치(weighting factor)와 보정값(scaling factor)을 제시하였다. 그리고 해석 결과의 정확성 비교를 통해 CN ID-FDTD 기법에서는 기존 CN FDTD 기법의 단점이었던 비등방성 분산 오차가 확연하게 감소하는 것을 확인하였다.

• Structural Engineering and Mechanics
• /
• 제66권5호
• /
• pp.583-594
• /
• 2018

A theoretical formulation based on the linearized potential theory, the Descartes' rule and the extremum optimization method is presented to calculate the critical distance of lifting points of the fully balanced hoist vertical ship lift, and to study pitching stability of the ship lift. The overturning torque of the ship chamber is proposed based on the Housner theory. A seven-free-degree dynamic model of the ship lift based on the Lagrange equation of the second kind is then established, including the ship chamber, the wire rope, the gravity counterweights and the liquid in the ship chamber. Subsequently, an eigenvalue equation is obtained with the coefficient matrix of the dynamic equations, and a key coefficient is analyzed by innovative use of the minimum optimization method for a stability criterion. Also, an extensive influence of the structural parameters contains the gravity counterweight wire rope stiffness, synchronous shaft stiffness, lifting height and hoists radius on the critical distance of lifting points is numerically analyzed. With the Runge-Kutta method, the four primary dynamical responses of the ship lift are investigated to demonstrate the accuracy/reliability of the result from the theoretical formulation. It is revealed that the critical distance of lifting points decreases with increasing the synchronous shaft stiffness, while increases with rising the other three structural parameters. Moreover, the theoretical formulation is more applicable than the previous criterions to design the layout of the fully balanced hoist vertical ship lift for the ensuring of the stability.

• 복합신소재구조학회 논문집
• /
• 제4권2호
• /
• pp.39-44
• /
• 2013

This study is aimed to examine the influence of the rotational stiffness of U-shaped ribs on the local buckling behaviors of laminated composite plates. Applying the orthotropic plates with eight layers of the layup $[(0^{\circ})4]s$ and $[(0^{\circ}/90^{\circ})2]s$, 3-dimensional finite element models for the U-rib stiffened plates were setup by using ABAQUS and then a series of eigenvalue analyses were conducted. There is a need to develope a simple design equation to establish the rotational stiffness effect, which could be easily quantified by comparing the theoretical critical stress equation for laminated composite plates with elastic restraints based on the Classical laminated plate theory. Through the parametric numerical studies, it is confirmed that there should clearly exist an increasing effect of local plate buckling strength due to the rotational stiffness by closed-section ribs. An applicable coefficient for practical design should be verified and proposed for future study. This study will contribute to the future study for establishing an increasing coefficient for the design strength and optimum design of U-rib stiffened plates.