• 한국소음진동공학회논문집
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• 제12권2호
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• pp.97-107
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• 2002

The continuous circular cylindrical shells are widely used for the high performance structures of aircraft, spacecraft, missile, nuclear fuel rod shell and so on. In this paper, a method for the vibrational analysis of the continuous circular cylindrical shells with the clamped-clamped supports at two end edges is developed by using the modal expansion method. Forces and/or moments acting on the shell surface are expressed in terms of the Dirac Delta Function. Frequency equation of the continuous shell is also derided by the application of the equilibrium of forces and the continuity of displacements at the boundary. Natural frequencies of the continuous shell are calculated numerically with mathematica 3.0 and they are compared with FEM results from the ANSYS 5.3 to improve the reliability of analytic solutions. Mode shares obtained by the FEM are Presented in this paper.

• Smart Structures and Systems
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• 제19권3호
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• pp.299-307
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• 2017

The magneto-electro-elastic (MEE) material under thermal environment exhibits pyroelectric and pyromagnetic coefficients resulting in pyroelectric and pyromagnetic effects. The pyroelectric and pyromagnetic effects on the behavior of multiphase MEE sensors bonded on top surface of a mild steel beam under thermal environment is presented in this paper. The aim of the study is to find out how samples having different volume fractions of the multiphase MEE composite behave in sensor applications. This is studied at optimal location on the beam, where the maximum electric and magnetic potentials are induced due to pyroelectric and pyromagnetic effects under clamped-free and clamped-clamped boundary conditions. The sensor which is bonded on the top surface of the beam is modeled using 8-node brick element. The MEE sensor bonded on mild steel beam is subjected to uniform temperature rise of 50K. It is assumed that beam and sensor is perfectly bonded to each other. The maximum pyroelectric and pyromagnetic effects on electric and magnetic potentials are observed when volume fraction is ${\nu}_f=0.2$. The boundary conditions significantly influence the pyroelectric and pyromagnetic effects on electric and magnetic potentials.

• Steel and Composite Structures
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• 제46권4호
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• pp.565-575
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• 2023

This study represents a numerical research in vibration and buckling of functionally graded material (FGM) beam comprising edge crack by using finite element method (FEM) and multilayer perceptron (MLP). It is assumed that the material properties change only according to the exponential distributions along the beam thickness. FEM and MLP solutions of the natural frequencies and critical buckling load are obtained of the cracked FGM beam for clamped-free (C-F), hinged-hinged (H-H), and clamped-clamped (C-C) boundary conditions. Numerical results are obtained to show the effects of crack location (c/L), material properties (E₂/E₁), slenderness ratio (L/h) and end supports on the bending vibration and buckling properties of cracked FGM beam. The FEM analysis used in this paper was verified with the literature, and the fundamental frequency ratio ($\overline{P_{cr}}$) and critical buckling load ratio ($\overline{{\omega}}$) results obtained were compared with FEM and MLP. The results obtained are quite compatible with each other.

• 한국산업융합학회 논문집
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• 제3권1호
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• pp.43-51
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• 2000

The response statistics of a hinged-clamped beam under broad-band random excitation is investigated. The random excitation is applied at the nodal point of the second mode. By using Galerkin's method the governing equation is reduced to a system of nonautonomous nonlinear ordinary differential equations. A method based upon the Markov vector approach is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian and non-Gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The case of two mode interaction is considered in order to compare it with the case of three mode interaction. The analytical results for two and three mode interactions are also compared with results obtained by Monte Carlo simulation.

• 소음진동
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• 제9권6호
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• pp.1193-1199
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• 1999

This paper deals with the free vibrations of circular curved beams with thin-walled cross-section. The differential equation for the coupled flexural-torsional vibrations of such beams with warping is solved numerically to obtain natural frequencies and mode shapes. The Runge-Kutta and determinant search methods, respectively, are used to solve the governing differential equation and to compute the eigenvalues. The lowest three natural frequencies and corresponding mode shapes are calculated for the thin-walled horizontally curved beams with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. A wide range of opening angle of beam, warping parameter, and two different values of slenderness ratios are considered. Numerical results are compared with existing exact and numerical solutions by other methods.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2003년도 가을 학술발표회 논문집
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• pp.29-36
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• 2003

This paper deals with the free vibration analysis of horizontally circular mea beams with variable cross sectional width on elastic foundations. Taking into account the effects of rotatory inertia and shear deformation differential equations governing the free vibrations of such beams are derived, in which the Whlkler foundation model is considered as the elastic foundation. The variable width of beam is chosen as the linear equation. The differential equations are solved numerically to calculate natural frequencies. In numerical examples, the curved beam with the hinged-hinged, hinged-clamped, clamped-hinged and damped-clamped end constraints are considered The parametric studies are conducted and the lowest four frequency parameters are reported in figures as the non-dimensional forms.

• 소음진동
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• 제6권1호
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• pp.45-56
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• 1996

Frequency equation for clamped-free circular cylindrical thin shell is derived by the application of Rayleigh-Ritz method using the Sanders shell equation. The cubic frequency equation is solved for each axial and circumferential mode number. Integration of the beam characteristic funcitions was performed via Mathematica which results in more accurate integration of the beam functions that affect the accuracy of the frequency. The natural frequencies from this calculation are compared with existing results. It shows that this calculation predicts natural frequencies closer to the test results than existing results.

• 소음진동
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• 제6권5호
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• pp.587-594
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• 1996

이 논문에서는 일정체적의 정다각형 단면을 갖는 보-기둥의 자유진동 및 좌굴하중을 지배하는 비분방정식을 유도하고 이를 수치해석하였다. 정다각형 단면의 단면깊이 변화식으로는 포물선식과 정현식을 채택하였고, 고정-고정, 회전-고정 및 회전-회전의 단부조건에 대하여 고유진동수 및 좌굴하중을 산출하였다. 수치해석의 결과로 무차원 고유진동수와 무차원변들 사이의 관계 및 무차원 좌굴하중과 단면비 사이의 관계를 그림에 나타내었다. 또한, 최강기둥의 단면비와 좌국하중을 산출 하였다.

• 전산구조공학
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• 제9권3호
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• pp.135-143
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• 1996

일정체적의 원형단면을 갖는 변단면 보-기둥의 자유진동 및 좌굴하중을 지배하는 미분방정식을 유도하고 이를 수치해석하였다. 미분방정식에는 축하중효과를 고려하였다. 원형단면의 반경변화는 포물선식을 채택하였고, 고정-고정, 고정-회전 및 회전-회전 보-기둥의 고유진동수 및 좌굴하중을 산출하였다. 수치해석의 결과로 무차원 고유진동수와 무차원 변수들 사이의 관계 및 무차원 좌굴하중과 단면비 사이의 관계를 그림에 나타내었고, 최강기둥의 단면비와 좌굴하중을 구하였다.

• 대한기계학회논문집
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• 제15권1호
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• pp.366-375
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• 1991

본 연구에서는 보 이론(beam theory)의 변위함수(displacement function)를 도입하고 전달행렬법을 이용하여 각 배관요소의 경계조건에 대한 고유 진동수와 배관 의 불안정성을 일으키는 유체의 임계속도(critical velocity)를 계산 평가하고, 실험 으로 입증된 Blevins의 결과치와 비교하였다.