In-plane vibrations of nonuniform circular beams

The dependence of in-plane vibrations of nonuniform curved beams on the radius of the beam was studied. Different approximation methods were used to determine exact solutions and coefficients of the two-coupled differential equations. The relation between the inplane flexural and longitudinal displacements of the beam was also derived. The analysis showed that the introduction of two physical parameters helped to obtain the exact vibration solutions of the system.