In-plane vibration of laminated curved beams with variable curvature by dynamic stiffness analysis

Based on the Timoshenko-type curved beam theory, the free vibration of composite laminated beams of variable curvature is studied. The effects of shear deformation and rotary inertia are both considered. By incorporating the dynamic stiffness method and the series solution, an analytical solution is developed. The arch is decomposed into as many elements as needed for the accuracy of solution. In each element, a series solution is formulated in terms of polynomials, the coefficients of which are related to each other through recurrence formulas. As a result, in order to obtain an accurate solution, one does not need a lot of terms in series solution and in Taylor expansion series for the variable coefficients in the governing equations. Compared to the previous literature, the accuracy and efficiency of the present formulation are validated. This methodology can be applied to laminated curved beams of complex arch structures without any difficulty