The vibration of initially curved simply supported and clamped beams with sliding end masses

Abstract

The object of this study is to investigate the free vibration behaviour of slightly curved simply supported beams and clamped beams connected to axially sliding end masses. For the simply supported beam, two formulas for the natural frequencies are derived from the theoretical analysis. One is obtained by neglecting the effect of axial inertial force of the beam and the other formula is derived by considering this effect, approximately, using Galerkin's method. For the clamped beam, an approximate formula is derived using Galerkin's method. The results of the theoretical analysis of simply supported and clamped beams are described in chapter 2 and show that there are two different natural frequencies having the same fundamental transverse mode for each case and the ratio of the longitudinal motion to transverse motion are different for modes In order to verify the theoretical results of simply supported and clamped beams some experiments were conducted. Beams of various curvatures under different end masses are tested in this experimental work. The effects of the beam curvatures and axial inertial force of the curved simply supported beams on the natural frequencies also were investigated. The results of the experimental analysis of tested beams are described in chapter 3 and are compared with theoretical results in figures in chapter 4.