Analysis of out-of-plane free vibration of single damaged curved beam based on precise algorithm of structural mechanics

Based on a dynamic discrete model of an out-of-plane curved beam with a constant cur- vature, eigen-properties of the spatial curved beam structure in undamaged and damaged configurations are considered in this paper. In the literature, based on the equivalent sec- tion reduction method, a distributed damage modeling method is proposed. Accoding to Euler-Bernoulli beam theory, the stiffness matrix of shear, bending and torsion coupling is derived. Combined with the lumped mass matrix and the characteristic equation of the multi degree of freedom system, natural frequencies of the undamaged and damaged structures are calculated.