Free Vibration Analysis of Curved Beams With Variable Radii of Curvature on Elastic Foundations

Abstract

Free out of plane vibration characteristics of curved beams with variable curvature on elastic foundation are studied by Finite Difference Method (FDM) since the mathematical model of the present system based on the coupled differential eigenvalue problem with variable coefficients. Firstly, vibrations of beams on different elastic foundations are reviewed. Then, out of plane vibrations of curved beams on different elastic foundations are investigated. FDM is detailed for this study. To solve the coupled differential eigenvalue problem, FDM is examined with several computer programs developed in Mathematica. The effects of curvature of the curved beams and elastic foundation parameters on natural frequencies are investigated. The accuracy of the present results obtained from the developed program is evaluated by comparing with FEM results found from model created in ANSYS.