宽翼薄壁工字形梁动力反应的能量变分法

ENERGY-VARIATIONAL METHOD FOR THE DYNAMIC RESPONSE OF THIN-WALLED I-BEAMS WITH WIDE FLANGE

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。

This paper proposes an approach to analyzing the dynamic response of thin-walled I-beam with wide flange generally used in structural engineering. Four independent generalized dynamic displacement functions w（ x , t ）, θ （ x , t）u1 （ x , t ）, u 2（ x , t ）are employed to reflect the displacement variation of thin-walled I-beams（ b1 ≠ b2）, and a new warping displacement mode of I-beams is used to meet the axial self-equilibrium condition. The minimum potential principle is applied to establish the governing differential equations and corresponding natural boundary conditions, and closed-form solutions of generalized dynamic displacements are obtained. The dynamic characteristics of I-beams are discussed. Through calculation examples, the analytical solutions of this paper are compared with the finite solid element solutions, and the validity of the proposed approach is verified.