• Structural Engineering and Mechanics
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• v.4 no.3
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• pp.209-226
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• 1996

One of the major divisions in the mathematical modelling of a tubular structure is to include the effect of the transverse shear stress and rotary inertia in vibration of members. During the past three decades, problems of vibration of tubular structures have been considered by some authors, and special attention has been devoted to the Timoshenko theory. There have been considerable efforts, also, to apply the method of spectral analysis to vibration of a structure with rectangular section beams. The purpose of this paper is to compare the results of the spectrally formulated finite element analyses for the Timoshenko theory with those derived from the conventional finite element method for a tubular structure. The spectrally formulated finite element starts at the same starting point as the conventional finite element formulation. However, it works in the frequency domain. Using a computer program, the proposed formulation has been extended to derive the dynamic response of a tubular structure under an impact load.

• The Journal of the Acoustical Society of Korea
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• v.28 no.1
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• pp.25-31
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• 2009

This paper introduces a spectrally formulated element method (SEM) for the beams treated with passive constrained layer damping (PCLD). The viscoelastic core of the beams has a complex modulus that varies with frequency. The SEM is formulated in the frequency domain using dynamic shape functions based on the exact displacement solutions from progressive wave methods, which implicitly account for the frequency-dependent complex modulus of the viscoelastic core. The frequency response function and dynamic responses obtained by the SEM and the conventional finite element method (CFEM) are compared to evaluate the validity and accuracy of the present spectral PCLD beam element model. The spectral PCLD beam element model is found to provide very reliable results when compared with the conventional finite element model.

• The Journal of the Acoustical Society of Korea
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• v.29 no.5
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• pp.314-324
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• 2010

In waveguide structures, waves may be partially reflected by local non-uniformities. The effects of local non-uniformities has been previously investigated by means of a combined spectral element and finite element (SE/FE) method at relatively low frequencies. However, since the SE is formulated based on a beam theory, the SE/FE method is not appropriated for analysis at higher frequencies where complex deformation of the waveguide occurs. So it is necessary to extend this approach for high frequencies. For the wave propagation at higher frequencies, a combined spectral super element and finite element (SSE/FE) method is introduced in this paper. As an example of the application of this method, wave reflection and transmission due to a local defect in a rail are simulated at frequencies between 20kHz and 30kHz. Also numerical errors are evaluated by means of the conservation of the incident power.

• Journal of the Korean Society for Railway
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• v.7 no.3
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• pp.239-244
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• 2004

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics may provide very accurate solutions, together with drastically reducing the number of degrees of freedom to improve the computation efficiency and cost problems. Thus, this paper develops a spectral element model for the coupled thermoelastic beam which axially moves with constant speed under a uniform tension. The accuracy of the spectral element model is then evaluated by comparing the natural frequencies obtained by the present element model with those obtained by the conventional finite element model.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.595-612
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• 2014

The spectral collocation method for a second order elliptic boundary value problem on a domain ${\Omega}$ with curved boundaries is studied using the Gordon and Hall transformation which enables us to have a transformed elliptic problem and a square domain S = [0, h] ${\times}$ [0, h], h > 0. The preconditioned system of the spectral collocation approximation based on Legendre-Gauss-Lobatto points by the matrix based on piecewise bilinear finite element discretizations is shown to have the high order accuracy of convergence and the efficiency of the finite element preconditioner.

• Journal of the Society of Naval Architects of Korea
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• v.46 no.2
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• pp.155-164
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• 2009

In this paper, a spectral finite element method for a rectangular sandwich plate with viscoelastic core having the Levy-type boundary conditions has been plated. The sandwich plate consists of two isotropic and elastic face plates with a surfaced-bonded viscoelastic core. For the analysis, the in-plane and transverse energy in the face plates and only shear energy in the core are considered, respectively. To account for the frequency dependent complex shear modulus of the viscoelastic core, the Golla-Hughes-McTavish model is adopted. To evaluate the validity and accuracy of the proposed method, the frequency response function and dynamic responses of the sandwich plate with all edges simply supported subject to an impact load are calculated and compared with those calculated by a finite element method. Though these calculations, it is confirmed that the proposed method is very reliable and efficient one for vibration analysis of a rectangular sandwich plate with viscoelastic core having the Levy-type boundary conditions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.10
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• pp.1653-1660
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• 2003

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics is known to provide very accurate solutions, while reducing the number of degrees-of-freedom to resolve the computational and cost problems. Thus, in the present paper, the spectral element model is formulated for the axially moving Timoshenko beam under a uniform axial tension. The high accuracy of the present spectral element is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions. The effects of the moving speed and axial tension on the vibration characteristics, the dispersion relation, and the stability of a moving Timoshenko beam are investigated, analytically and numerically.

• Journal of Mechanical Science and Technology
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• v.18 no.3
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• pp.395-406
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• 2004

The spectral element model is known to provide very accurate structural dynamic characteristics, while reducing the number of degree-of-freedom to resolve the computational and cost problems. Thus, the spectral element model for an axially moving Bernoulli-Euler beam subjected to axial tension is developed in the present paper. The high accuracy of the spectral element model is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions. The effects of the moving speed and axial tension on the vibration characteristics, wave characteristics, and the static and dynamic stabilities of a moving beam are investigated.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.2
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• pp.294-301
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• 2003

It is of often important to accurately predict the flow-induced vibration or dynamic instability of a pipeline conveying internal high speed flow in advance, which requires a very accurate solution method. In this study, first the dynamic equations for the axial and transverse vibrations of a pipeline are reduced from a set of pipe-dynamic equations derived in the previous study and then the spectral element model is formulated. The accuracy of the spectral element method (SEM) is then verified by comparing its results with the results obtained by finite element method (FEM). It is shown that the present spectral element model provides very accurate solutions by using an extremely small number of degrees-of-freedom when compared with FEM. The dynamics of a sample pipeline is investigated with varying the axial tension and the speed of internal flow.

• Journal of Mechanical Science and Technology
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• v.18 no.7
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• pp.1159-1168
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• 2004

In this paper, a spectral element model is derived for the axially moving viscoelastic beams subject to axial tension. The viscoelastic material is represented in a general form by using the one-dimensional constitutive equation of hereditary integral type. The high accuracy of the present spectral element model is verified first by comparing the eigenvalues obtained by the present spectral element model with those obtained by using the conventional finite element model as well as with the exact analytical solutions. The effects of viscoelasticity and moving speed on the dynamics of moving beams are then numerically investigated.