• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권1호
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• pp.17-35
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• 2016

In this study, the dynamic behaviour of a rotating Timoshenko beam when under the actions of a variable magnitude load moving at non-uniform speed is carried out. The effect of cross-sectional dimension and damping on the flexural motions of the elastic beam was neglected. The coupled second order partial differential equations incorporating the effects of rotary and gyroscopic moment describing the motions of the beam was scrutinized in order to obtain the expression for the dynamic deflection and rotation of the vibrating system using an elegant technique called Galerkin's Method. Analyses of the solutions obtained were carried out and various results were displayed in plotted curve. It was found that the response amplitude of the simply supported beam increases with an increase in the value of the foundation reaction modulus. Effects of other vital structural parameters were also established.

• Structural Engineering and Mechanics
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• 제74권2호
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• pp.297-311
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• 2020

The main purpose of this study is to analyze the effects of external pressure on the vibration and buckling of functionally graded (FG) spherical panels resting of elastic medium. The material characteristics of the FG sphere continuously vary through the thickness direction based on the power-law rule. In accordance with first-order shear deformation shell theory and by the use of Ritz formulation the governing equations are presented. In this regard, the beam functions are applied in two-dimensions for different sets of boundary supports. The Winkler and Pasternak models of elastic foundations are also taken into account. In order to show the validity and applicability of the presented formulation, various comparison studies are given. Furthermore, a diverse range of numerical results is reported to check the impacts of geometrical and material parameters along with external pressure on the vibration and buckling analysis of FG spherical panels.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 춘계학술대회논문집
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• pp.952-956
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• 2004

The soil-structure interactions are caused by the point sources of explosions, deriving piles, compaction of foundations and excavations those are frequently arose in the construction sites. Thus the analysis of soil-structure interactions is one of the most important subjects in the fields of dynamic analysis and vibration control. From this viewpoint, the aim of this study is to collect the basic data for designing foundation structures throughout understanding the dynamic structural behavior, which is embodied by the dynamic analysis of soil-structure systems. In this study, the dynamic analyses of stiffened thick plates subjected to in-plane stress on elastic foundations are carried out. The foundation is modeled as Pasternak foundation that includes the continuity effect of foundations. Also both the Mindlin plate theory and Timoshenko beam-column theory are used for analyzing the thick plates and beams, respectively.

• 한국전산구조공학회논문집
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• 제18권2호
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• pp.151-158
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• 2005

본 연구에서는 유한요소법을 이용하여 Pasternak 지반 위에 놓인 보강판의 고유치해석을 수행하였다. 보강판 해석은 Mindlin 판 이론과 Timoshenko 보-기둥 이론을 적용하여 해석하였으며, 유한요소법 적용시 판요소는 8절점 Serendipity 요소계를, 보요소는 3절점 유한요소를 적용하였다. 탄성지반은 지반의 연속성을 고려한 Pasternak 지반으로 모형화하였다. 본 연구의 타당성을 검증하기 위하여 이 연구의 결과를 문헌, 실험 및 SAP 2000의 결과와 비교하였다. 이 연구의 결과로 문헌 해가 존재하지 않는 Pasternak 지반 위에 놓인 보강판의 지반 변수의 변화 및 보강재 크기에 따른 고유진동수를 산정하였다.

• Computers and Concrete
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• 제19권3호
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• pp.333-338
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• 2017

In this paper, nonlinear vibration of embedded nanocomposite concrete is investigated based on Timoshenko beam model. The beam is reinforced by with agglomerated silicon dioxide (SiO2) nanoparticles. Mori-Tanaka model is used for considering agglomeration effects and calculating the equivalent characteristics of the structure. The surrounding foundation is simulated with Pasternak medium. Energy method and Hamilton's principal are used for deriving the motion equations. Differential quadrature method (DQM) is applied in order to obtain the frequency of structure. The effects of different parameters such as volume percent of SiO2 nanoparticles, nanoparticles agglomeration, elastic medium, boundary conditions and geometrical parameters of beam are shown on the frequency of system. Numerical results indicate that with increasing the SiO2 nanoparticles, the frequency of structure increases. In addition, considering agglomeration effects leads to decrease in frequency of system.

• Advances in Computational Design
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• 제5권2호
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• pp.177-193
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• 2020

In the present research, dynamic analysis of functionally graded (FG) graphene-reinforced beams under thermal loading has been carried out based on finite element approach. The presented formulation is based on a higher order refined beam element accounting for shear deformations. The graphene-reinforced beam is exposed to transverse periodic mechanical loading. Graphene platelets have three types of dispersion within the structure including uniform-type, linear-type and nonlinear-type. Convergences and validation studies of derived results from finite element approach are also presented. This research shows that the resonance behavior of a nanocomposite beam can be controlled by the GPL content and dispersions. Therefore, it is showed that the dynamical deflections are notably influenced by GPL weight fractions, types of GPL distributions, temperature changes, elastic foundation and harmonic load excitation frequency.

• Structural Monitoring and Maintenance
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• 제6권2호
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• pp.147-159
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• 2019

In present article, a size-dependent refined thick beam element has been established based upon nonlocal elasticity theory. Next, it is used to explore vibration response of porous metal foam nanobeams on elastic medium. The established beam element introduces ten degrees of freedom. Different porosity distributions called uniform, symmetric and asymmetric will be employed. Herein, introduced thick beam element contains shear deformations without using correction factors. Convergence and verification studies of obtained results from finite element method are also provided. The impacts of nonlocality factor, foundation factors, shear deformation, slenderness ratio, porosity kinds and porosity factor on vibration frequencies of metal foam nano-sized beams have been explored.

• Wind and Structures
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• 제14권2호
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• pp.85-112
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• 2011

Wind turbine structures are long slender columns with a rotor and blade assembly placed on the top. These slender structures vibrate due to dynamic environmental forces and its own dynamics. Analysis of the dynamic behavior of wind turbines is fundamental to the stability, performance, operation and safety of these systems. In this paper a simplied approach is outlined for free vibration analysis of these long, slender structures taking the soil-structure interaction into account. The analytical method is based on an Euler-Bernoulli beam-column with elastic end supports. The elastic end-supports are considered to model the flexible nature of the interaction of these systems with soil. A closed-form approximate expression has been derived for the first natural frequency of the system. This new expression is a function of geometric and elastic properties of wind turbine tower and properties of the foundation including soil. The proposed simple expression has been independently validated using an exact numerical method, laboratory based experimental measurement and field measurement of a real wind turbine structure. The results obtained in the paper shows that the proposed expression can be used for a quick assessment of the fundamental frequency of a wind turbine taking the soil-structure interaction into account.

• Structural Engineering and Mechanics
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• 제67권5호
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• pp.517-525
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• 2018

In this study, we investigate the vibration of single-walled carbon nanotubes embedded in a polymeric matrix using nonlocal elasticity theories with account arbitrary boundary conditions effects. A Winkler type elastic foundation is employed to model the interaction of nanobeam and the surrounding elastic medium. Influence of all parameters such as nonlocal small-scale effects, Winkler modulus parameter, vibration mode and aspect ratio of nanobeam on the vibration frequency are analyzed and discussed. The mechanical properties of carbon nanotubes and polymer matrix are treated and an analytical solution is derived using the governing equations of the nonlocal Euler-Bernoulli beam models. Solutions have been compared with those obtained in the literature and The results obtained show that the non-dimensional natural frequency is significantly affected by the small-scale coefficient, the vibrational mode number and the elastic medium.

• 한국소음진동공학회논문집
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• 제11권8호
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• pp.357-363
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• 2001

This paper presents the application of the technique Q( differential transformation to the vibration analysis of beams resting on variable two-parameter elastic foundations. The closed form series solutions for beams are obtained for various boundary conditions. Numerical calculations are carried out and compared with previously published results. The results obtained by the present method agree very well with those reported in the previous works. The present analysis shows the usefulness and validity of differential transformation in solving nonlinear problem of the free vibration.