Free vibration analysis of in-plane circular curved beams with crack damage: a semi analytical solution

Abstract In this paper, a semi-analytical method for solving circular curved beams is proposed to study the free vibration of in-plane circular curved beams in both undamaged and damaged configurations. The crack damage of the structure is represented by the cross-sectional reduction of the damaged element. Based on the discrete circular curved beam model, the coupling stiffness matrices of shear, compression and bending are derived. Combined with the lumped mass matrix and the dynamic characteristic equation of the multi-degree-of-freedom system, the frequencies and modes of the damaged and undamaged structures are calculated. The results are compared with the finite element method, and the good consistency between them is verified.