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本文以工字梁为对象,同时考虑梁截面的不均匀翘曲、剪切变形影响和腹板的柔度,用变分原理推导得一组基本方程,提出了扭转振动的高阶理论。正如文中所讨论的,如果忽略掉一些因素,按本文的理论即可得到H.R.AGGARWAL和E.T.CRANCH等文的结果。因此,本文在考虑工字梁截面内诸变形因素对扭转振动的影响方面就更全面,更统一。本文得出工字梁扭转振动波的传播,应有三种不同的型式。文中分析了各自的特征,并在扭转波的相速度的水平上与其他理论,特别是与H.R.AGGARWAL和E.T.CRANCH的结果作了比较。
In this paper, the I-beam is taken as the object, considering the non-uniform warping of the beam cross-section, the influence of shear deformation and the web flexibility, a set of basic equations are derived from the variational principle, and the high-order theory of torsional vibration is proposed. As discussed in the article, if omitted some of the factors, according to the theory of this article H.R.AGGARWAL and E.T.CRANCH other results. Therefore, this article is more comprehensive and more unified in considering the influence of deformation factors on torsional vibration in I-beam cross section. This paper concludes that I-beam torsional vibration wave propagation, there should be three different types. In this paper, the respective characteristics are analyzed and compared with other theories, especially those of H.R.AGGARWAL and E.T.CRANCH, at the phase velocity of torsional waves.