泛函分析在裂缝简支梁损伤检测及参数识别中的应用

利用扭曲弹簧模型，对裂缝简支梁前三阶固有频率的变化与裂缝深度及位置的关系进行了理论分析。对简支梁遭受多种裂缝局部损伤的动力特性进行试验研究，并通过泛函分析及泛函极值定理确定出局部裂缝损伤位置。然后再代入弹簧刚度模型求出裂缝深度参数，识别结果与实际模拟结果平均误差为5．0％。结果表明，用固有频率结合泛函分析方法，获得的裂缝检测方法检测精度较高，裂缝位置识别结果最小误差为2．20％，深度识别结果最小误差为2．10％，并克服了仅仅依靠固有频率难以确定裂缝损伤位置的缺点。

Application of Functional Analysis to Simple-supported-beam Crack Damage Detection and Parameters Verification

Using distortional spring model, theoretic analysis is applied on the relation of natural frequency and crack depth and its location. A dynamic test of simple-supported-beam suffered from a number of crack damage scenarios is carried out to find out local crack damage location by functional analysis and function extremum theorem. Then, crack depth can be extracted from the distortional spring model. It is demonstrated that the crack detection method is satisfactory with its mean error 5.0%, and the minimum error of crack location identification 2.20%,and depth minimum error 2.10%. It overcomes the disadvantage that with only natural frequency,it is difficult to determine crack damage location.