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采用四个独立的广义位移w(x,t)、θ(x,t)、u1(x,t)和u2(x,t)对宽翼缘薄壁工字形梁的动位移进行了准确描述,同时考虑剪滞翘曲应力的轴向自平衡条件,提出了一种能对工程中常用的上翼板、下翼板具有不同宽度工字形梁动力反应的分析方法。以能量变分原理为基础,推导出了工字形梁动力反应的控制微分方程和自然边界条件,获得了相应广义动位移的闭和解,据此对薄壁工字梁的动力反应特性进行了研究,揭示了工字形梁动力反应的规律。算例中,该文解析解与有限元数值解进行了比较,证明了该文分析方法的有效性。
The dynamic displacement of wide flanged thin-walled I-beam is accurately described by using four independent generalized displacements w (x, t), θ (x, t), u1 (x, t) and u2 (x, t) , And considering the axial self-balancing condition of shear-lag warpage stress, a method of analyzing the dynamic response of I-shaped beams with different widths, which is commonly used in engineering, is proposed. Based on the principle of energy variation, the governing differential equations and natural boundary conditions of I-beam dynamic response are derived and the corresponding generalized dynamic displacement closure and solution are obtained. The dynamic response of thin-walled I-beam is studied , Revealing the law of I-beam dynamic response. In the example, the analytical solution of the paper is compared with the numerical solution of the finite element method, and the validity of the method is proved.