In-plane free vibration analysis of multi-span curved beams with elastic support and connecting boundary conditions

According to the vibration problem of a curved beam with elastic support boundary conditions,the in-plane free vibration characteristics of multi-span curved beams were analyzed using an improved Fourier series method.The transverse and tangential displacement functions were sought as a Fourier cosine series,and an auxiliary polynomial function was introduced to take all the relevant discontinuities of the elastic boundaries.The Rayleigh-Ritz method was used to solve Hamilton's equation,which is based on the energy principle,and a standard eigenvalue problem concerning the unknown displacement amplitudes was derived from which the natural frequencies and mode shapes can be solved.The results of single-span and two-span curved beams with free,simple supported,clamped,and elastic supported boundary conditions were obtained and compared with the results acquired from the finite element method(FEM) to validate the correctness of the presented method.Furthermore,the effect of the connecting stiffnesses between two-span curved beams on the first four frequencies was described.