In-Plane Free Vibrations of Curved Beams by Rayleigh-Ritz Method

Abstract

Curved beams are frequently used structural elements in traditional and emerging fields of civil and mechanical engineering with usual requirements of vibration and deformation analyses utilizing the beam theory. There are challenges in such analyses due to complex equations with curved arcs and numerical methods in case analytical solutions are not available. In this study, curved beams with commonly encountered arcs are studied for free vibrations with featured frequencies and mode shapes as the objectives of calculations. The Rayleigh-Ritz method is used with polynomial functions as the deformation, and accurate frequencies and mode shapes are obtained from convergent and verified solutions. It is the objective of this study that the method will be extended to a long, curved, and periodic beam for its free vibrations for in-depth understanding of vibrations of such unusual but ubiquitous structures from recent technological advances.