FRP加固含裂纹RC梁的谐振动分析

摘要

裂纹的存在使RC梁的承载性能受到很大影响,基于Euler-Bernoulli梁理论,利用Hamil-ton能量变分法推导,得到了 FRP 加固含裂纹 RC 简支梁的谐振动微分控制方程,并利用Galerkin方法对方程进行数值求解,讨论了在单激励和双激励简谐荷载下,裂纹深度、裂纹位置、钢筋以及FRP对RC简支梁动力响应的影响.结果表明,在外激励荷载作用下,随着裂纹深度的扩展,梁位移响应值增大.裂纹深度相同时,裂纹在梁跨中1/2位置时加固梁的位移响应值最大,靠近梁端时位移响应值逐渐变小;发生共振时,裂纹深度的扩展将使梁的共振频率减小;钢筋对FRP加固含裂纹RC梁的动力响应影响较大,而对FRP的影响较小.%Concrete crack highly affects load-carrying performance of reinforced concrete ( RC) beams.The dy-namic vibration differential equation of the cracked concrete simply-supported beams strengthened by FRP is derived based-on the Euler-Bernoulli beam theory and Hamilton energy variation method.The equation is nu-merically calculated by using Galerkin method.Meanwhile,the effects of crack depth,crack location,steel rein-forcement and FRP on the dynamic performance of RC simply-supported beams under single and multiple har-monic excitation loads were discussed.The results show that under external load excitations,the dynamic dis-placement of the beam increases with the increase of the crack depth.For the same crack depths,the crack lo-cated at the mid-span has larger effect on the beam displacement response than it is located near the beam end.In the case of resonant vibrations,the development of crack depth reduces the resonant vibration frequen-cy.The influence of the steel reinforcement on the dynamic response of FRP repaired cracked beams is larger than that of the FRP.