VIBRATIONS OF HETEROGENEOUS CURVED BEAMS SUBJECTED TO A RADIAL FORCE AT HE CROWN POINT

Abstract

This paper is concerned with the vibrations of heterogenous curved beams under the assumption that the load on the beam is perpendicular to the centerline. It is assumed that (a) the radius of curvature is constant and (b) the Young modulus and Poisson number depend on the cross sectional coordinates only. We have the following objectives: (1) to determine the Green function matrices for pinned beams, fixed beams and beams fixed at one end and pinned at the other end provided that the beam is subjected to a radial load; (2) to clarify how the load affects the natural frequencies if the beam is subjected to a radial force (a vertical force) at the crown point; (3) to develop such a numerical model which makes possible to determine how the natural frequencies are related to the load. We shall present the computational results in a graphical format.