基于均匀荷载面曲率的简支裂纹梁损伤识别

Damage identification of cracked simply supported beam based on uniform load surface curvature

为了采用模态参数对结构裂纹进行定位与定量,基于集中柔度模型,采用无质量的扭转弹簧模拟裂纹,建立简支裂纹梁的振动微分方程。针对现有柔度曲率指标仅能判断裂纹的大致范围,基于线性插值理论,建立裂纹位置与相邻测点均匀荷载面曲率差的关系,提出裂纹进一步定位公式,实现裂纹位置的精确定位。针对现有大多数损伤识别方法无法实现裂纹的损伤定量,基于位移曲率与结构刚度和弯矩的关系,理论推导了均匀荷载面曲率的结构刚度损伤程度识别方法,基于弹簧串联原理和线刚度思想,首次提出串联等效线刚度模型,建立裂纹深度与均匀荷载面曲率的关系,实现裂纹深度的定量。通过简支裂纹梁数值算例,考虑多裂纹的损伤情况,验证了新方法对裂纹定位与定量的有效性。

In order to locate and quantify a structural crack by using modal parameters,the vibration differential equation of motion of a cracked simply supported beam was established based on the lumped flexibility model.Massless torsional springs were used to simulate the cracks.Given that the existing flexibility curvature index can only determine the approximate range of cracks,based on the linear interpolation theory,the relationship between the crack location and the change in uniform load surface curvature was established to realize the precise location of the crack.In view of the fact that most of the existing damage identification methods can not realize the damage quantification of cracks,based on the relationship between displacement curvature and structural stiffness and bending moment,a damage quantification method of structural stiffness of uniform load surface curvature was derived.In order to quantify the crack depth,the series equivalent linear stiffness model was proposed for the first time based on the spring series principle and the linear stiffness idea.It could be used to establish the relationship between the crack depth and the change in the uniform load surface curvature.Through the numerical example of a cracked simply supported beam with considering the damage of multiple cracks,the validity of the new method in crack location and quantification is verified.