IN-PLANE VIBRATIONS OF PINNED-FIXED HETEROGENEOUS CURVED BEAMS UNDER A CONCENTRATED FORCE

Abstract

Abstract: The paper deals with the vibrations of loaded heterogeneous curved beams when a centra load (a constant force) is exerted at the crown point of the beam. The effect of the loading is accounted by the strain it causes. It is assumed that the radius of curvature is constant and the Young’s modulus and the Poisson’s number are functions of the cross-sectional coordinates. The paper presents the determination of the Green function matrices for loads directed upwards and downwards. An appropriate numerical model is also provided, which makes possible to determine how the natural frequencies are related to the load. It is also shown that when the strain is zero, the corresponding formulae yield results valid for the free vibrations of curved beams.