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1

Spectral element modelling of the thermally induced vibration of an axially moving plate

Lee U., Kwon K.

Journal of Achievements in Materials and Manufacturing Engineering

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2008

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Vol. 26, nr 1

65-72

EN

Purpose: To develop a spectral element model for accurate prediction of the dynamic characteristics of an axially moving thin uniform plate subjected to sudden thermal loadings on its surfaces. Design/methodology/approach: First, we have derived the governing equations of motion by using the Hamilton's principle. Secondly, we have used the wave solutions, which satisfy the governing equations of motion in the frequency domain, as the frequency-dependent shape functions to formulate the spectral element matrix by using the variational approach. Thirdly, the extremely high accuracy of the spectral element model has been evaluated by comparing the dynamic responses obtained by the spectral element analysis with the results obtained by using the conventional finite element analysis. Findings: It has been numerically shown that the present spectral element model provides very accurate dynamic responses of an axially moving uniform plate by treating the whole plate as a single finite element, regardless of its length. Practical implications: Numerical investigations have shown that the thermally induced vibration characteristics of an axially moving plate depends on the duration and frequency characteristics of externally applied thermal loadings as well as its moving speed. Originality/value: The paper is the first to develop the spectral element model for the axially moving plates subjected to thermal loadings. The present spectral element model can be applied to the galvanized steel strip passing through a hot zinc tank, for instance.

2

FFT-based spectral dynamic analysis for linear discrete dynamic systems

Lee U., Cho J.

Journal of Achievements in Materials and Manufacturing Engineering

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2007

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Vol. 25, nr 1

95-102

EN

Purpose: An FFT-based spectral dynamic analysis method is developed for the viscously damped, linear discrete dynamic systems subjected to nonzero initial conditions. Design/methodology/approach: The discrete Fourier transform (DFT) theory is used to develop a spectral dynamic analysis method. The dynamic response of a linear system is assumed as the sum of the forced and free vibration response parts. The forced vibration response part is obtained by convolving the dynamic stiffness matrix and Fourier components of excitation force through the Duhamel's integral, and the free vibration response part is obtained by determining its integral constants so as to satisfy initial conditions in frequency-domain. Findings: It is shown through some numeral examples that the proposed FFT-based spectral dynamic analysis method provides the solutions which accurately satisfy all initial conditions. Practical implications: This analysis method is applicable to viscously damped, linear discrete dynamic systems subjected to nonzero arbitrary initial conditions. In this study, two types of viscous damping are considered: proportional damping and non-proportional damping. Originality/value: The FFT-based spectral dynamic analysis method proposed in this paper is unique because the pseudo-force concept or the superposition of corrective free vibration solution used by other researchers is not used to take into account non-zero initial conditions.

3

Thermally induced vibration of an axially-traveling strip: spectral element analysis

Lee U., Kwon K.

Journal of Achievements in Materials and Manufacturing Engineering

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2006

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Vol. 17, nr 1-2

261--264

EN

Purpose: A spectral element model is developed for accurate prediction of the dynamic characteristics of an axially-traveling strip subjected to a sudden thermal loading. Design/methodology/approach: The spectral element model is formulated from the frequency-dependent dynamic shape functions which satisfy the governing equations in the frequency-domain and its extremely high accuracy is evaluated by comparing with the conventional finite element model in which simple polynomials are used as the shape functions. Also some numerical studies are conducted to investigate the vibration characteristics of an example axially-traveling strip subjected to a sudden thermal loading on its upper surface. Findings: The present spectral element model is shown to provide very accurate dynamic characteristics by treating a whole uniform strip between two boundary supports as a single finite element, regardless of its length, when compared with the conventional finite element model. Practical implications: Numerical studies for the typical example problem show that the dynamic characteristics of an axially-traveling strip may depend on the traveling speed and the duration and frequency characteristics of the externally applied thermal loading. Originality/value: The spectral element model presented in this paper is the first one for the axially-traveling strips subjected to thermal loadings and is applicable to the engineering problems such as the galvanized steel strip passing through a hot zinc tank, for instance.

4

Dynamic response with arbitrary initial conditions using the FFT

Lee U., Cho J.

Journal of Achievements in Materials and Manufacturing Engineering

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2006

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Vol. 18, nr 1-2

299--302

EN

Purpose: An FFT-based dynamic analysis method is proposed for damped linear discrete dynamic systems subjected to arbitrary nonzero initial conditions. Design/methodology/approach: The DFT theory is used to develop an FFT-based spectral analysis method. The total dynamic response is considered as the sum of the forced vibration response part and the free vibration response part. The forced vibration response part is obtained from the dynamic stiffness matrix and the Fourier components of excitation force based on the concept of Duhamel’s integral, and the free vibration response part is obtained by determining its integral constant to satisfy arbitrary initial conditions in the frequency-domain. Findings: Through some numeral examples, the proposed FFT-based dynamic analysis method is shown to provide very successful solutions which satisfy all arbitrary non-zero initial conditions. Research limitations/implications: (not applicable). Practical implications: (not applicable). Originality/value: The present FFT-based method is unique because it does not use the superposition of corrective free vibration solution or the pseudo-force concept used by other researchers to take into account the non-zero initial conditions.