受损简支梁固有频率变化规律研究

Research on natural frequency characteristics of damaged simply supported beam

以钢筋混凝土梁为研究对象,基于Euler-Bernoulli梁理论和结构动力学理论,通过数值模拟分析,计算得到了不同损伤位置和损伤程度时简支梁单损伤情况下的固有频率.引入损伤因子、频率变化率、频率变化率震荡幅度、频率变化率中值、频率变化率比值等概念,研究了简支梁的固有频率以及频率变化率、频率变化率比值对梁振动响应的变化规律.结果表明,梁的损伤对频率和频率变化率的敏感性与梁的损伤程度和损伤位置相关,而频率变化率比值与梁的损伤位置有关.损伤程度对固有频率的影响大于损伤位置对固有频率的影响.而当损伤位置和损伤程度固定时,梁固有频率的变化率随模态阶数的增加并不是单调变化的.

Taking damaged reinforced concrete beam as the research object, and based on Euler-P, ernoulli beam and structure dy- namics theory and by means of dynamic finite element analysis, the natural frequencies are obtained through calculations in various kinds of damage states. With the concept of damage factor,frequency change rate, frequency change rate oscillation amplitude, frequency change rate mid-value and the ratio of frequency change rate~ the paper researches the natural frequency, frequency change rate and the ratio of frequency change rate characteristics of the simply supported beam. The results show that the sensi- tivities of the damaged beam about natural frequency and frequency change rate relate to damage degree and damage location, and that the sensitivities of the damaged beam about the ratio of frequency change rate relates to damage location only, and that the effect of damage degree on the natural frequency is greater than that of damage location, and that the frequency change rate of the beam is not a monotonic variation with the increase of modes order.