• Steel and Composite Structures
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• 제26권5호
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• pp.649-662
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• 2018

In this study, based on the three-dimensional theory of elasticity, free vibration characteristics of sandwich sectorial plates with multiwalled carbon nanotube-(MWCNT)-reinforced composite core are considered. Modified Halpin-Tsai equation is used to evaluate the Young's modulus of the MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the MWCNTs wt% range considered. In this paper, free vibration of thick functionally graded sandwich annular sectorial plates with simply supported radial edges and different circular edge conditions including simply supported-clamped, clamped-clamped, and free-clamped is investigated. A semi-analytical approach composed of two-dimensional differential quadrature method and series solution are adopted to solve the equations of motion. The material properties change continuously through the core thickness of the plate, which can vary according to a power-law, exponentially, or any other formulations in this direction. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated sectorial plates.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 춘계학술대회논문집
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• pp.435-440
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• 2002

The free vibration of partially embedded piles is investigated. The pile model is based on the Bernoulli-Euler beam theory and the soil is idealized as a Winkler model for mathematical simplicity. The governing differential equation for the free vibrations of such members is solved numerically The piles with one typical end constraint (clamped/hinged/free) and the other hinged end with rotational spring are applied in numerical examples. The lowest three natural frequencies are calculated over a range of non-dimensional system parameters: the rotational spring parameter, the relative stiffness and the embedded ratio.

• 복합신소재구조학회 논문집
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• 제3권3호
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• pp.22-30
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• 2012

This study deals with an enhanced assumed strain (EAS) three-dimensional element for free vibration analysis of laminated composite and sandwich structures. The three-dimensional finite element (FE) formulation based on the EAS method for composite structures shows excellence from the standpoints of computational efficiency, especially for distorted element shapes. Using the EAS FE formulation developed for this study, the effects of side-to-thickness ratios, aspect ratios and ply orientations on the natural frequency are studied and compared with the available elasticity solutions and other plate theories. The numerical results obtained are in good agreement with those reported by other investigators. The new approach works well for the numerical experiments tested, especially for complex structures such as sandwich plates with laminated composite faces.

• Structural Engineering and Mechanics
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• 제50권6호
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• pp.773-796
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• 2014

This paper deals with free vibration analysis of continuous grading fiber reinforced (CGFR) and bi-directional FG annular sector plates on two-parameter elastic foundations under various boundary conditions, based on the three-dimensional theory of elasticity. The plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. Results indicate that the non-dimensional natural frequency parameter of a functionally graded fiber volume fraction is larger than that of a discrete laminated and close to that of a 2-layer. It results that the CGFR plate attains natural frequency higher than those of traditional discretely laminated composite ones and this can be a benefit when higher stiffness of the plate is the goal and that is due to the reduction in spatial mismatch of material properties. Moreover, it is shown that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional one-dimensional functionally graded material. The multidirectional graded material can likely be designed according to the actual requirement and it is a potential alternative to the unidirectional functionally graded material. The new results can be used as benchmark solutions for future researches.

• 대한조선학회지
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• 제11권2호
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• pp.1-6
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• 1974

The three-dimensional correction factor of the added mass of finite-length elliptic cylinders in vertical vibration in a free surface was calculated. This problem has already been dealt by T. Kumai[5] to contribute to analytical prediction of the three-dimensional correction factor for the added mass in vertical vibration of ships. In Kumai's work, the body boundary condition involved in the appropriate boundary value problem was approximately treated in the course of obtaining the solution. In this work, obtaining the solution derived from mathematically exact treatment of the body boundary condition, the author recalculated the three-dimensional correction factor for length-beam ratio $4{\sim}8$, beam-draught ratio $2.00{\sim}4.50$ and number of nodes from 2 to 7. And the numerical results were compared with both Kumai's results and the author's experimental data for two and three-noded vibrations of the cylinder of beam-draught ratio 2.40 The comparison of the numerical results shows that the author's are always higher than the Kumai's as expected. And the comparison of the numerical results with experimental data shows that the Kumai's numerical results have less deviation in case of two-noded vibration, and that, in case of three-noded vibration, the author's numerical results are in fairly good correspondence.

• The Journal of the Acoustical Society of Korea
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• 제25권2E호
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• pp.85-88
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• 2006

Blade-vortex interaction (BVI) is one of the most important phenomena in rotor flow since it causes undesirable intense vibration and noise. Since three dimensional Euler or Navier-Stokes solutions to BVI require very high computational cost, BVI has been approximated by airfoil-vortex interaction (AVI) in chordwise planes. To describe more realistic situations with AVI, three dimensional vortex informations such as position, core size and strength are embedded artificially to Computational Aeroacoustics (CAA) calculation at each computational time step. To implement this requirement, in this paper, a technique called free vortex embedded method was used. And the solution by this method was compared with the solution by conventional method for interaction between freely convected vortex and airfoil. For the application to three dimensional free vortex embedded CAA, two dimensional free vortex embedded CAA method was validated in advance.

• Advances in nano research
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• 제7권4호
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• pp.277-292
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• 2019

In this present paper, a new two dimensional (2D) and quasi three dimensional (quasi-3D) nonlocal shear deformation theories are formulated for free vibration analysis of size-dependent functionally graded (FG) nanoplates. The developed theories is based on new description of displacement field which includes undetermined integral terms, the issues in using this new proposition are to reduce the number of unknowns and governing equations and exploring the effects of both thickness stretching and size-dependency on free vibration analysis of functionally graded (FG) nanoplates. The nonlocal elasticity theory of Eringen is adopted to study the size effects of FG nanoplates. Governing equations are derived from Hamilton's principle. By using Navier's method, analytical solutions for free vibration analysis are obtained through the results of eigenvalue problem. Several numerical examples are presented and compared with those predicted by other theories, to demonstrate the accuracy and efficiency of developed theories and to investigate the size effects on predicting fundamental frequencies of size-dependent functionally graded (FG) nanoplates.

• 복합신소재구조학회 논문집
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• 제3권1호
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• pp.1-7
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• 2012

본 연구에서는 고체요소를 사용하여 내재된 층간분리의 크기 및 위치 변화에 대한 복합소재 적층구조의 자유진동 특성을 분석한다. 본 연구에서 제시하는 3차원 유한요소 모델은 기존의 접근 방법에 비하여 정확성 뿐만 아니라 전체 진동 모드를 보여준다는 점에서 장점을 갖는다. ABAQUS가 적용된 유한요소 모델은 다양한 내재된 층간분리를 포함하는 적층구조의 자유진동을 분석하기 위하여 사용되었다. 도출된 수치해석 결과는 기존의 연구결과와 비교하여 잘 일치함을 보였다. 특히, 본 연구에서 제시한 결과는 층간분리의 크기, 길이-두께의 비율, 그리고 층간분리의 위치변화에 대하여 국부 진동 모드에 미치는 중요한 영향들에 대하여 초점을 둔다.

• Structural Engineering and Mechanics
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• 제23권2호
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• pp.115-127
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• 2006

The axisymmetric free vibrations of transversely isotropic magnetoelectroelastic laminated circular plates are studied. Based on the three-dimensional governing equations of magnetoelectroelastic medium, the state space equations of laminated circular plates are obtained. By using the finite Hankel transform and rendering the free terms left by the transform in terms of the boundary quantities, the solutions of the state space equations are given for two kinds of boundary conditions. The frequency equations of the free vibration are derived using the propagator matrix method and the boundary conditions at top and bottom surfaces. By virtue of the inverse Hankel transform, the mode shapes are also determined. Since the solutions strictly satisfy the governing equations in the region and the boundary conditions at the edges, they are the three-dimensionally exact. Finally, the natural frequencies of such plates are tabulated and compared with those of the piezoelectric and elastic plates in the numerical example.

• 한국소음진동공학회논문집
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• 제15권4호
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• pp.457-464
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• 2005

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution, Unlike conventional shell theories, which are mathematically two-dimensional (2-D). the present method is based upon the 3-D dynamic equations of elasticity. Displacement components $u_{r},\;u_{z},\;and\;u_{\theta}$ in the radial, axial, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in , and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the conical shells are formulated, the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of theconical shells. Novel numerical results are presented for thick, complete conical shells of revolution based upon the 3-D theory. Comparisons are also made between the frequencies from the present 3-D Ritz method and a 2-D thin shell theory.