In-plane Free Vibration Analysis of Laminated Thick Circular Deep Arches

ABSTRACT: In order to accurately determine the natural frequencies of laminated thick circular deep arches, a solution procedure based on the two-dimensional theory of elasticity is presented. The layerwise finite element method is used to discretize the equations of motion and the related boundary conditions through the thickness of the arch. The formulations are general so that the effects of the variation of beam curvature across the cross-section, the transverse shear and normal stresses and rotary inertia can easily be implemented. Exact solutions are obtained for antisymmetric cross-ply laminated thick circular deep arches with simply supported boundary conditions. The convergence of the method is shown against the number of mathematical layers used for modeling the arches. The effects of different parameters such as opening angle, thickness-to-length and orthotropy ratios on the natural frequencies of the arches are outlined. Due to high accuracy of the method, the results can be used as benchmarks for future research. KEY WORDS: layerwise finite element, laminated thick arches, exact solution