Free Vibration Analysis of Non-uniform Thin Curved Arches and Rings Using Adomian Modified Decomposition Method

摘要

Differential equation governing free in-plane vibration of non-prismatic thin circular curved beams is a sixth-order differential equation with variable coefficients for which no closed-form solution is reported. For the first time, Adomian modified decomposition method, an efficient analytical tool in solution of ODEs and PDEs, is employed to solve the governing differential equation of motion of thin curved beams and the corresponding recursive relation is obtained. Imposing the boundary conditions, the characteristic equation of the structure is obtained, the roots of which are the eigenfrequencies of the system. The method is then employed to determine natural frequencies of uniform rings, stepped and non-prismatic curved arches. The results are shown to be compatible with those in the literature. Finally, a detailed discussion over the convergence of the method is presented.