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2 Journal of Achievements in Materials and Manufacturing Engineering

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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

2008

Vol. 26, nr 1

65-72

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.

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

Lee U., Kwon K.

Journal of Achievements in Materials and Manufacturing Engineering

2006

Vol. 17, nr 1-2

261--264

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.