• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.1073-1077
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• 2001

The objective of this paper is to apply an experimental method based on the principle of reciprocity to measuring the structural intensity. Since only one accelerometer is used in this method it has the advantages of shortening measurement time. reducing accelerometer phase error. overcoming the limitation that the situation should be stationary during the experiment. It has been used to measure the vibration intensity of an infinite beam (beam with damped ends) and a semi-infinite beam (beam with simply supported and damped ends). Results showed that the experiment method based on the principle of reciprocity can be effectively used to measure the structural intensity.

• Advances in nano research
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• 제7권2호
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• pp.99-108
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• 2019

Higher-order theories are very important to investigate the mechanical properties and behaviors of nanoscale structures. In this study, a free vibration behavior of SiNW resting on elastic foundation is investigated via Eringen's nonlocal elasticity theory. Silicon Nanowire (SiNW) is modeled as simply supported both ends and clamped-free Euler-Bernoulli beam. Pasternak two-parameter elastic foundation model is used as foundation. Finite element formulation is obtained nonlocal Euler-Bernoulli beam theory. First, shape function of the Euler-Bernoulli beam is gained and then Galerkin weighted residual method is applied to the governing equations to obtain the stiffness and mass matrices including the foundation parameters and small scale parameter. Frequency values of SiNW is examined according to foundation and small scale parameters and the results are given by tables and graphs. The effects of small scale parameter, boundary conditions, foundation parameters on frequencies are investigated.

• Steel and Composite Structures
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• 제42권5호
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• pp.649-655
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• 2022

In presented paper, moving load problem of simply supported axially functionally graded (AFG) beam is investigated under temperature rising based on the first shear beam theory. The material properties of beam vary along the axial direction. Material properties of the beam are considered as temperature-dependent. The governing equations of problem are derived by using the Lagrange procedure. In the solution of the problem the Ritz method is used and algebraic polynomials are used with the trivial functions for the Ritz method. In the solution of the moving load problem, the Newmark average acceleration method is used in the time history. In the numerical examples, the effects of material graduation, temperature rising and velocity of moving load on the dynamic responses ofAFG beam are presented and discussed.

• Computers and Concrete
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• 제26권3호
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• pp.285-292
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• 2020

In engineering structures, to having the projected structure to serve all the engineering purposes, the theory to be used during the modeling stage is also of great importance. In the present work, an analytical solution of the free vibration of the beam composed of functionally graded materials (FGMs) is presented utilizing different beam theories. The comparison of supposed beam theory for free vibration of functionally graded (FG) beam is examined. For this aim, Euler-Bernoulli, Rayleigh, Shear, and Timoshenko beam theories are employed. The functionally graded material properties are assumed to vary continuously through the thickness direction of the beam with respect to the volume fraction of constituents. The governing equations of free vibration of FG beams are derived in the frameworks of four beam theories. Resulting equations are solved versus simply supported boundary conditions, analytically. To verify the results, comparisons are carried out with the available results. Parametrical studies are performed for discussing the effects of supposed beam theory, the variation of beam characteristics, and FGM properties on the free vibration of beams. In conclusion, it is found that the interaction between FGM properties and the supposed beam theory is of significance in terms of free vibration of the beams and that different beam theories need to be used depending on the characteristics of the beam in question.

• 전산구조공학
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• 제10권1호
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• pp.135-148
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• 1997

본 논문은 면내휨을 받는 2변 탄성지지 2변 단순지지 보강장방형판에 대한 유한요소법을 이용하고, 비보강장방형판에 대해 고전적 해석법에 의해 좌굴해석한 것이다. 4변 단순지지, 2변 단순지지 및 2변 고정 장방형 판에 대해 기존해와 고전적 해석해 및 유한요소해을 비교하여 고전적 해석방법 및 유한요소법의 신뢰도를 입증하였다. 장방형 보강재의 뒤틀림 강성은 무시될 수 있으므로 탄성지지변의 보강재는 뒤틀림의 영향을 파악하기 위해 I형을 사용하였다. 탄성지지변을 갖는 장방형 판의 좌굴강도가 비틀림 강성 및 뒤틀림 강성에 따라 유한요소법 및 고전적 해석법에 의해 계산되고 비교되었다. 판의 지지변 사이에 보강재가 있는 경우 4변 단순지지, 2변 단순지지 및 2변 고정 보강장방형판에 대해 유한요소법에 의한 좌굴강도는 장방형판요소와 비틀림 및 뒤틀림을 고려한 보요소의 강성매트릭스를 조합하여 고유치 문제를 풀므로써 계산될 수 있다. 유한요소법에 의해 지지변 사이의 장방형 보강재 위치와 지지변 상의 I형 보강재의 비틀림(J) 및 뒤틀림 상수 (I/sub W/)에 따른 보강장방형판의 좌굴강도를 구하여 비교하고 효율적인 보강재의 위치를 결정하였다.

• Structural Engineering and Mechanics
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• 제52권5호
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• pp.997-1017
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• 2014

According to the structure characteristics of the non-uniform beam bridge, a practical model for calculating the vibration equation of the non-uniform beam bridge is given and the application scope of the model includes not only the beam bridge structure but also the non-uniform beam with added masses and elastic supports. Based on the Bernoulli-Euler beam theory, extending the application of the modal perturbation method and establishment of a semi-analytical method for solving the vibration equation of the non-uniform beam with added masses and elastic supports based is able to be made. In the modal subspace of the uniform beam with the elastic supports, the variable coefficient differential equation that describes the dynamic behavior of the non-uniform beam is converted to nonlinear algebraic equations. Extending the application of the modal perturbation method is suitable for solving the vibration equation of the simply supported and continuous non-uniform beam with its arbitrary added masses and elastic supports. The examples, that are analyzed, demonstrate the high precision and fast convergence speed of the method. Further study of the timesaving method for the dynamic characteristics of symmetrical beam and the symmetry of mode shape should be developed. Eventually, the effects of elastic supports and added masses on dynamic characteristics of the three-span non-uniform beam bridge are reported.

• Steel and Composite Structures
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• 제27권1호
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• pp.1-12
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• 2018

This paper presents a semi-analytical solution of simply supported horizontally composite curved I-beam by trigonometric series. The flexibility of the interlayer connectors between layers both in the tangential direction and in the radial direction is taken into account in the proposed formulation. The governing differential equations and the boundary conditions are established by applying the variational approach, which are solved by applying the Fourier series expansion method. The accuracy and efficiency of the proposed formulation are validated by comparing its results with both experimental results reported in the literature and FEM results.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 추계학술대회
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• pp.673-677
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• 2004

The sensitivities of eigenvalues to the change of element thickness have been calculated for beams in the paper. For a cantilever beam the sensitivities fluctuate more for higher modes. When the thickness of the element near the fixed end increases, the eigenvalues for all modes increase. On the other hand, increasing of the thickness of the element at the tip decreases the eigenvalues for all modes. For a simply supported beam the sensitivities fluctuate more for higher modes, which is the same phenomenon as for a cantilever beam. The sensitivities are always positive for all modes

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2004년도 춘계 학술발표회 제16권1호
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• pp.60-63
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• 2004

The paper deals with the damage assessment of the concrete beam using static displacements and the flexural stiffness reduction of the beam was evaluated. Simply supported concrete beams were loaded at the mid-span, and the applied load level ranged $20\%,\;40\%,\;80\%$ of the flexural strength of the beam. When the displacements from the tests were increased more than $10\%$ of the initial values, flexural cracks occured. Judging from the observed cracks, damaged area of the beams were assumed and the stiffness reduction using the smeared-cracking concept was estimated to minimize the error between the test results and analytical results. Four stages of the behavior of a RC beam, which are uncracked, initial cracking, stabilized cracking and post-yielding, can be considered to assess the damage of RC beams. Main parameters for the assessment were cracking area and the stiffness reduction ratio. In each stage, damaged elements and their stiffness reduction were estimated to minimized the error.

• Steel and Composite Structures
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• 제23권3호
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• pp.339-350
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• 2017

In this paper, various nonlocal higher-order shear deformation beam theories that consider the size dependent effects in Functionally Graded Material (FGM) beam are examined. The presented theories fulfill the zero traction boundary conditions on the top and bottom surface of the beam and a shear correction factor is not required. Hamilton's principle is used to derive equation of motion as well as related boundary condition. The Navier solution is applied to solve the simply supported boundary conditions and exact formulas are proposed for the bending and static buckling. A parametric study is also included to investigate the effect of gradient index, length scale parameter and length-to-thickness ratio (aspect ratio) on the bending and the static buckling characteristics of FG nanobeams.