Nonlinear free vibration analysis of asymmetric thin-walled circularly curved beams with open cross section

A finite element formulation is present for the nonlinear free vibration of thin-walled curved beams with non-symmetric open across section. The kinetic and potential energies are derived by the virtual principle. The energy functional includes the effect of flexural–torsional coupling, the torsion warping and the shear center location. For finite element analysis, cubic polynomials are utilized as the shape functions of the two nodal thin-walled curved elements. Each node possesses seven degrees freedom including the warping degree of freedom. The nonlinear eigenvalue problem has been solved by the direct iteration technique. The results are compared with those for straight beams as available in the literature. The results for nonlinear free vibration analysis of curved beams for various radii and subtended angle are presented.