双材料单伸臂叠合梁的界面滑移与自振特性分析

Analysis of slip and natural vibration characteristics of bi-material single-stretched beam

将叠合梁划分为接触区和分离区,接触区界面间的摩擦作用会对叠合梁的滑移、刚度和自振频率产生影响。本文给出了单伸臂叠合梁在均布荷载和集中力作用下,考虑叠合界面摩擦作用的滑移应变和滑移分布的表达式;推导了考虑叠合界面间摩擦力及摩擦力产生的抵抗弯矩共同作用下的截面刚度。假设梁按等波长和等刚度两种形式自由振动,运用传递矩阵法推导出了单伸臂叠合梁自振频率的计算公式。最后,基于一个钢-混凝土组合与叠合试验梁的算例分析了滑移沿梁长的分布及自振频率。结果表明:随界面间摩擦系数的增大,接触区界面的滑移值逐渐减小;摩擦效应对叠合梁自振频率的影响随阶次的升高越来越明显。

The laminated beam is divided into contact and separation zones, and the friction between the interfaces of the contact zone affects the slip, stiffness and natural frequency of the beam. The expressions of the slip strain and the slip distribution are given for a single-stretched laminated beam under the action of uniform load or a concentrated force. The section bending stiffness considering the frictional force generated between the interfaces and the frictional moment is derived. The calculation formulas of the natural vibration frequency of the single-stretched beam are derived by the transfer matrix method, under the assumption of a beam vibration in the two forms of equal wavelength and equal stiffness. Finally, based on a steel-concrete composite and laminated test beam, the slip distribution along the length and the natural vibration frequency are analyzed. The results show that:(1) with the increase of the friction coefficient between interfaces, the slip value at the interface of the contact zone gradually decreases;(2) the effect of friction on the natural vibration frequency of the laminated beam is more and more obvious with the increases of the order.