On the effect of shear coefficients in free vibration analysis of curved beams

We did a comparative study of shear coefficients in free vibration analysis of curved beams having circular and rectangular crosssections. Until recently, the shear coefficient k in Timoshenko beam theory has been studied by many researchers to include transverse shear deformation effect. To obtain more reliable numerical results, a higher-order hybrid-mixed curved beam element is formulated and programmed in MATLAB. The present numerical experiments show that k = 6(1 + v)(2) / (7 + 12v + 4v (2)) is the best expression both for circular and rectangular cross-sections in the flexural vibration of curved beams.