Unified finite-difference-based discrete modelling for in-plane vibration of shear deformable circular arches with arbitrary cross-sections

Based on the first-order shear deformation theory and accounting for axial extension, a unified finite-difference-based discrete model (FDDM) is developed for the in-plane vibration analysis of circular arches with uniform, varying, stepped, and cracked cross-sections. In the proposed FDDM, circular arches with different cross-sectional configurations are represented by a unified discrete system composed of equivalent axial, extensional, and rotational springs, together with end springs and lumped masses, from which the discrete potential and kinetic energy functions are formulated. By applying Lagrange’s equation to these discrete energy expressions, a set of algebraic equations can be obtained for determining the vibration frequencies of circular arches. The unified FDDM is shown to be a well-posed and independent discrete model. To verify its performance, circular arches with different geometric changes and cracks are investigated. The results confirm its effectiveness and applicability as a new computational model for structural analysis.