On the eigenfrequencies of preloaded rotationally restrained extensible circular beams by Green’s functions

Abstract

The article is devoted to the vibrations of heterogeneous curved beams with centerline extensibility accounted for. The end supports are rotationally restrained pins, and the effect of a central, either compressive or tensile, force (preload) is incorporated into the model. The coupled differential equations that govern the problem are derived from the principle of virtual work. These are replaced by a system of homogeneous Fredholm integral equations. The kernel of the integral equation system is the Green’s function matrix, which is given in closed form. The eigenvalue problem determined by the homogeneous Fredholm integral equation system is solved numerically, and the results obtained are presented graphically. If the spring stiffness tends to (zero) [infinity], the beam behaves as if it were (pinned–pinned) [fixed–fixed]. When the external force tends to zero, the model returns the eigenfrequencies of the free vibrations.