ANALYTICAL AND NUMERICAL STUDY ON SPATIAL FREE VIBRATION OF NON-SYMMETRIC THIN-WALLED CURVED BEAMS

For spatial free vibration of non-symmetric thin-walled circular curved beams, an accurate displacement field is introduced by defining all displacement parameters at the centroidal axis and three total potential energy functionals are consistently derived by degenerating the potential energy for the elastic continuum to that for thin-walled curved beams. The closed-form solutions are newly obtained for in-plane and out-of-plane free vibration analysis of monosymmetric curved beams respectively. Also, two thin-walled curved beam elements are developed using the third and fifth order Hermitian polynomials. In order to illustrate the accuracy and the practical usefulness of the present method, analytical and numerical solutions by this study are presented and compared with previously published results or solutions by ABAQUSʹ the shell element. Particularly, effects of the thickness curvature as well as the inextensional condition are investigated on free vibration of curved beams with monosymmetric and non-symmetric cross-sections.