Bo Yeon Kim
The Journal of Mechanical Science and Technology, vol. 23, no. 5, pp.1396-1405, 2009

Abstract : A finite thin circular beam element for the out-of-plane vibration analysis of curved beams is presented in this paper. Its stiffness matrix and mass matrix are derived, respectively, from the strain energy and the kinetic energy by using the natural shape functions derived from an integration of the differential equations in static equilibrium. The matrices are formulated with respect to the local polar coordinate system or to the global Cartesian coordinate system in consideration of the effects of shear deformation and rotary inertias. Some numerical examples are analyzed to confirm the validity of the element. It is shown that this kind of finite element can describe quite efficiently and accurately the out-ofplane motion of thin curved beams.

Keyword : Finite element; Mass matrix; Natural shape function; Out-of-plane vibration; Rotary inertia; Shear deformation; Stiffness