Isogeometric Free Vibration Analysis of Curved Euler-Bernoulli Beams with Particular Emphasis on Accuracy Study

An isogeometric free vibration analysis is presented for curved Euler-Bernoulli beams, where the theoretical study of frequency accuracy is particularly emphasized. Firstly, the isogeometric formulation for general curved Euler-Bernoulli beams is elaborated, which fully takes the advantages of geometry exactness and basis function smoothness provided by isogeometric analysis. Subsequently, in order to enable an analytical frequency accuracy study, the general curved beam formulation is particularized to the circular arch problem with constant radius. Under this circumstance, explicit mass and stiffness matrices are derived for quadratic and cubic isogeometric formulations. Accordingly, the coupled stencil equations associated with the axial and deflectional displacements of circular arches are established. By further invoking the harmonic wave assumption, a frequency accuracy measure is rationally attained for isogeometric free analysis of curved Euler-Bernoulli beams, which theoretically reveals that the isogeometric curved beam formulation with pth degree basis functions is 2(p - 1)th order accurate regarding the frequency computation. Numerical results well confirm the proposed theoretical convergence rates for both circular arches and general curved beams.