Vibrations of fixed-fixed heterogeneous curved beams loaded by a central force at the crown point

Abstract

This paper addresses the vibrations of heterogeneous curved beams under the assumption that the load of the beam is a dead one and is perpendicular to the centroidal axis. It is assumed that: (a) the radius of curvature is constant, and (b) Young’s modulus and the Poisson’s number depend on the cross-sectional coordinates. As for the issue of fixed-fixed beams, the objectives are the following: (1) to determine the Green’s function matrices provided that the beam is under radial load; (2) to examine how the load affects the natural frequencies given that the beam is subjected to a vertical force at the crown point; (3) to develop a numerical model which makes it possible to determine how the natural frequencies are related to the load. The computational results are presented graphically