Spectral finite element analysis of in-plane free vibration of laminated composite shallow arches

A spectral finite element model is developed for predicting the free vibration characteristics of cross-ply laminated shallow arches vibrating in the in-plane. The exponential shear deformation theory is used to define the arches’ dynamic behavior. The governing differential equations of laminated shallow arches are derived using Hamilton’s principle. The spectral element matrix is formulated using the dynamic shape functions based on the exact analytical solutions of the homogeneous governing equations. The derived spectral element matrix is then used in conjunction with the Wittrick–Williams algorithm to calculate the natural frequencies and mode shapes of the cross-ply laminated shallow arches. Effects of stacking sequence, material orthotropy ratio, curvature ratio and length to thickness ratio, as well as end condition, on the natural frequencies of the laminated arches are thoroughly investigated.