• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.4
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• pp.595-603
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• 1989

Free vibration of orthotropic laminated composite conical shells with constant thickness are considered. Governing frequency equations are derived based on the Flugge theory and Galerkin method is applied for the numerical analysis. Comparisons are made between present results and others for the isotropic conical shells and numerical results are obtained based on these results for the specially orthotropic laminated composite conical shells with simply supported edges. Variations of frequency parameter on the change of material properties, stacking sequences, stacking number, geometrical parameters and orthotropic parameters are considered in the analysis.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.4 s.97
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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.

• Journal of Power System Engineering
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• v.12 no.2
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• pp.35-40
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• 2008

This paper deals with the free vibrations of conical shells with linearly variable thickness by the transfer influence coefficient method. The classical thin shell theory based upon the Flugge theory is assumed and the governing equations of a conical shell are written as a coupled set of first order matrix differential equations using the transfer matrix. The Runge-Kutta-Gill integration method is used to solve the governing differential equation. The natural frequencies and corresponding mode shapes are calculated numerically for the conical shells with linearly variable thickness and various boundary conditions at the edges. The present method is applied to conical shells with linearly varying thickness, and the effects of the semi-vertex angle, the number of circumferential waves and thickness ratio on vibration are studied.

• Journal of Power System Engineering
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• v.9 no.3
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• pp.58-65
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• 2005

This paper deals with the free vibrations of truncated conical shell with uniform thickness by the transfer influence coefficient method. The classical thin shell theory based upon the $Fl\ddot{u}gge$ theory is assumed and the governing equations of a conical shell are written as a coupled set of first order differential equations using the transfer matrix. The Runge-Kutta-Gill integration and bisection method are used to solve the governing differential equations and to compute the eigenvalues respectively. The natural frequencies and corresponding mode shapes are calculated numerically for the truncated conical shell with any combination of boundary conditions at the edges. And all boundary conditions and the intermediate supports between conical shell and foundation could be treated only by adequately varying the values of the spring constants. Numerical results are compared with existing exact and numerical solutions of other methods.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.6
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• pp.1203-1214
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• 1989

본 연구에서는 화이버각도, 경계조건 및 하중형태의 변화에 따라 적층 복합재료원통 셸 구조물의 수치예를 제시하고, NASTRAN수치결과 및 기존 문헌들과 비교하여 구하여진 결과의 타당성을 입증하였다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.6
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• pp.1273-1281
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• 1988

In this study, the dynamic characteristics of Bellows, used for expansion joint, were investigate by F.E.M. Using the axisymmetric conical frustum element, the natural frequencies, modevectors and the parameters governing the dynamic characteristics of Bellows were also investigated. Through the experiment, it was shown that the results calculated by finite element method and measured experimental values were in good agreement.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.6
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• pp.1439-1450
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• 1995

Bellows is a familiar component in piping systems as it provides a relatively simple means of absorbing thermal expansion and providing system flexibility. In routine piping flexibility analysis by finite element methods, bellows is usually considered to be straight pipe runs modified by an appropriate flexibility factor; maximum stresses are evaluated using a corresponding stress concentration factor. The aim of this study is to develop a bellows finite element, which similarly includes more complex shell type deformation patterns. This element also does not require flexibility or stress factors, but evaluates more detailed deformation and stress patterns. The proposed bellows element is a 3-D, 2-noded line element, with three degrees of freedom per node and no bending. It is formulated by including additional 'internal' degrees of freedom to account for the deformation of the bellows corrugation; specifically a quarter toroidal section of the bellows, loaded by axial force, is considered and the shell type deformation of this is include by way of an approximating trigonometric series. The stiffness of each half bellows section may be found by minimising the potential energy of the section for a chosen deformation shape function. An experiment on the flexibility is performed to verify the reliability for bellows finite element.

• Journal of Power System Engineering
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• v.19 no.5
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• pp.52-59
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• 2015

This paper is presented for the free vibration of a conical shell with annular plates or circular plate using the transfer of influence coefficient. The governing equations of vibration of a conical shell, including annular plate, are written as a coupled set of first order differential equations by using the transfer matrix of the shell. Once the transfer matrix of a single component has been determined, the entire structure matrix is obtained by the product of each component matrix and the joining matrix. The natural frequencies and the modes of vibration were calculated numerically for joined conical-annular plates. The validity of the present method is demonstrated through simple numerical examples, and through comparison with the results of finite element method, transfer matrix method and ANSYS. The conclusion show that the present method can accurately obtain natural vibration characteristics of the conical shell with annular or circle end plates.

• Journal of Power System Engineering
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• v.19 no.1
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• pp.38-44
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• 2015

Various finite elements have been studied and developed to analyze a variety of structures in the finite element method(FEM). The transfer stiffness coefficient method(TSCM) is an effective algorithm for structural analysis but the structures which can be applied were limited. In this paper, a computational algorithm for the structural analysis of axisymmetric conical shells under axisymmetric loading is formulated using the finite element-transfer stiffness coefficient method(FE-TSCM). The basic concept of FE-TSCM is the combination of the modeling technique of FEM and the transfer technique of TSCM. The FE-TSCM has all the advantages of both FEM and TSCM. After carrying out the structural analysis of axisymmetric conical shells using FEM, FE-TSCM, and analytical method we compare the computational results of FE-TSCM with those of the other methods in terms of computational accuracy.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.8
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• pp.1195-1208
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• 1997

Bellows is a component in piping systems which absorbs mechanical deformation with flexibility. Its geometry is an axial symmetric shell which consists of two toroidal shells and one annular plate or conical shell. In order to analyze bellows, this study presents the finite element analysis using a conical frustum shell element. A finite element analysis is developed to analyze various bellows. The validity of the developed program is verified by the experimental results for axial and lateral stiffness. The formula for calculating the natural frequency of bellows is made by the simple beam theory. The formula for fatigue life is also derived by experiments. The shape optimal design problem is formulated using multiple objective optimization. The multiple objective functions are transformed to a scalar function by weighting factors. The stiffness, strength and specified stiffness are considered as the multiple objective function. The formulation has inequality constraints imposed on the fatigue limit, the natural frequencies, and the manufacturing conditions. Geometric parameters of bellows are the design variables. The recursive quadratic programming algorithm is selected to solve the problem. The results are compared to existing bellows, and the characteristics of bellows is investigated through optimal design process. The optimized shape of bellows is expected to give quite a good guideline to practical design.