Free vibration of higher-order sandwich and composite arches, Part I: Formulation

A higher-order refined model with seven degrees of freedom per node is presented in this paper for the free vibration analysis of composite and sandwich arches. The strain field is modeled through cubic axial, cubic transverse shear and linear transverse normal strain components. As the cross-sectional warping is accurately modeled by this theory, it does not require any shear correction factor. The stress–strain relationship is derived from an orthotropic lamina in a three-dimensional state of stress. The proposed higher-order formulation is validated, in this first part, through arches with various curvatures, aspect ratios, boundary conditions and materials.