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

Higher-Order Hierarchical Models for the Free Vibration Analysis of Thin-Walled Beams

“…By substitution of the geometrical relations, (7), the material constitutive equations, (11), and the unified hierarchical…”

“…The same authors presented in [10] a finite element formulation for the coupled free vibration analysis of thin-walled beams with generic open cross sections. Duan [11] studied the nonlinear free vibrations of thin-walled curved beams with unsymmetric open cross sections via the finite element method. Vörös [12] accounted for the coupling between different vibration modes due to the eccentricity of the cross section as well as to steadystate lateral loads and internal stress resultants.…”

Free vibration of horizontally curved thin-walled beams with rectangular hollow sections considering two compatible displacement fields

“…Involved with the power series method, Kim, Fu, and Kim (2007) presented a dynamic stiffness matrix for the spatially coupled free vibration analysis of thin-walled curved beam with non-symmetric cross-section on two types of elastic foundation. For the nonlinear free vibration of thin-walled curved beams with non-symmetric open sections, a finite element with seven degrees of freedom was presented by Duan (2008), with the flexural-torsional coupling effect, the torsion warping and the shear center Mechanics Based Design of Structures and Machines 4 location taken into consideration. Yu, Yang, and Nie (2010) carried out an analytical study of the free vibration analysis for naturally curved and twisted beams based on Washizu's static model, where all displacement functions were defined at the centroid axis and the effects of rotary inertia, transverse shear deformations and torsion-related warping were included.…”

Non-linear flexural–torsional dynamic analysis of beams of arbitrary cross section by BEM

“…Lopes and Ribeiro [16] studied also the nonlinear flexural-torsional free vibrations of beams employing a FEM solution and neglecting the longitudinal and rotary inertia as well as the cross-section warping. Duan [17] presented a FEM formulation for the nonlinear free vibration problem of thin-walled curved beams of asymmetric crosssection based on a simplified displacement field. Finally, the boundary element method has also been used for the nonlinear flexural [18][19][20] and torsional [21] dynamic analysis of only doubly symmetric beams.…”