Out of plane vibration of curved beams

Abstract

A very thin circular curved beam is analyzed for its natural frequency in this project.Only out of plane vibrations are considered in this project. The stiffness matrix and mass matrix are derived from the strain energy and kinetic energy. This is done with the help
of natural shape functions. The derivations are done in local coordinate system or Global Cartesian coordinate system. The out of plane deformations considered are the rigid body displacement of the centre of curvature in the axial direction, the rigid body rotation about the centre of curvature in the radial direction, and the rigid body rotation about the centre of curvature in the circumferential direction at the mid cross section.