基于曲率模态与柔度曲率的损伤识别

Structural damage detection based on curvature mode and flexibility curvature

以含两条裂纹的两端固定梁为例,采用曲率模态差和模态柔度曲率差来检测结构的损伤。首先将梁的裂纹模拟为无质量的等效扭转弹簧,推导了裂纹梁的特征微分方程,利用边界条件和裂纹位置的连续性条件推导得到该裂纹梁的振形函数解析表达式。然后用中心差分法分别求解裂纹梁损伤前后的曲率模态值和模态柔度曲率值,利用其差值确定梁的损伤位置,进而确定损伤程度。最后讨论了曲率模态和柔度曲率对结构损伤识别的敏感性。

With an example of a clamped-clamped beam with two cracks,the application of the changes in modal curvatures and flexibility curvatures to detect damage is investigated.First,the crack is modeled as an equivalent massless rotational spring.The characteristic equation of the beam is derived.By using boundary conditions and continuity/jump condition equations at crack loactions,the analytical solution of mode shapes can be obtained.Then the central difference approximation is imposed to obtain curvature mode shapes and flexibility curvatures before and after damage.And the changes in modal curvatures and flexibility curvatures are used to predict the crack locations and crack depth.Finally,the sensitivity of the modal curvatures and flexibility curvatures are discussed in detail.