GENERALIZED ANALYSIS OF SHEAR DEFORMABLE RINGS AND CURVED BEAMS

An accurate shear deformable theory for the analysis of the complete dynamic response of curved beams of constant curvature is presented. The equations presented here are very general in the sense that any problem of curved beam and circular ring can be addressed. It is indicated that the classical thin beam theory and the Timoshenko-type shear deformation theory are obtainable from the present theory as special cases. The present formulation accounts for shear deformation and rotary inertia and hence is applicable to the analysis of thick curved beams and rings. The theory assumes parabolic variation for shear strains (hence obviates the use of shear correction factors as usually done in the case of Timoshenko-type theory) and involves six displacement parameters of the center-line-three translations and three rotations. It is pointed out that for certain composite curved beams and rings the in-plane and out-of-plane vibrations are coupled.