Study on the self-vibration characteristics of non-circular arches with cracks based on the transfer matrix method

As the span of reinforced concrete arch bridges continues to increase, so does the difficulty of construction. The structure is at risk of cracking. Most of the bridges under construction are non-circular arches, and there are few studies on such arches. The current study tried to investigate the self-vibration characteristics of non-circular arches with existing cracks. A computational approach proposed in the original non-circular arch is substituted with multiple infinitesimal arch segments having different radii of curvature, enabling the determination of natural frequencies and mode shapes of the non-circular arches with cracks. Furthermore, a finite element model (FEM) of the reinforced concrete structure with existing cracks is developed to assess the effects of various factors, including axial location, crack depth, and positions within the same cross-section. The results demonstrate the feasibility of the computational method using multiple infinitesimal arc segments with varied radii of curvature, yielding a maximum error of only 1.58 %, which satisfies engineering application standards. An increase in crack depth leads to a reduction in the natural frequencies of specific modes of the structure, while the effect on others is insignificant. For cracks situated at the top or bottom plates within the same cross-section, the impact differs based on the local deformation being convex or concave. If the deformation is convex, the top plate cracks exhibit a higher rate of change in natural frequencies compared to the bottom plate cracks; conversely, with concave deformation, the bottom plate cracks have a greater influence than the top plate cracks.