For analysis of framed structure, the use of beam elements can reduce the number of degrees of freedom and can improve the efficiency of the analysis compared with the use of the continuum elements. However, for members where the cross-sectional deformation cannot be neglected, such as thin-walled or composite cross-sections, the use of beam elements based on elementary beam theory deteriorates the accuracy of the analysis because of its assumption that the cross-section remains plane. For the dynamic problems, when the wave-length of bending vibration becomes shorter according to an increase of the order of vibration modes, the effect of shear deformation on the dynamic property of the beam becomes relatively large. Although the cross-sectional deformation caused by the shear of the beam, its effect on the dynamic property of the beam has not been studied enough so far. In this study, the dynamic problems of a beam with cross-sectional deformation are formulated. With the proposed beam, the effect of the cross-sectional deformation on the dynamic property of the beam is clarified by comparing the results with those obtained by the conventional beam theory through a series of numerical analyses.

Key Words : shear lag, deformation of cross-section, periodic boundary condition, finite element method, natural vibration analysis

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