RJAV vol V no 2/2008 57 ISSN 1584-7284 Aspects concerning the influence of the self weight over the fundamental eigenfrequency of a slender beam Cristian DRAGOMIRESCU Department of Mechanics, University “Politehnica” of Bucharest dragom@cat.mec.pub.ro, cristian_dragomirescu@yahoo.com Andrei CRAIFALEANU Department of Mechanics, University “Politehnica” of Bucharest craifaleanu@cat.mec.pub.ro, ycraif@yahoo.com Valentin CEAUŞU Department of Mechanics, University “Politehnica” of Bucharest ceausu@cat.mec.pub.ro (Received 19 August 2008; accepted in revised form 28 November 2008) Abstract: - The paper studies the influence of the self weight over the fundamental eigenfrequency, of a beam rigidly fixed at one end and free at the other, situated in a vertical plane. Rayleigh approximate method is applied in order to determine, for different values of the slenderness coefficient, the fundamental eigenfrequency when the self weight is considered and when the self weight is neglected. The ratio of the two quantities is represented versus the length of the beam, as well as with respect to the geometrical and material characteristics. Keywords: vibration, beam 1. INTRODUCTION Slender beams with circular or annular cross-section are used in several technical applications, like, for instance, in the reservoirs of chemical reactors. O A’ A B B’ z y v(z) dz -w(z) l Figure 1. Bending vibration of a vertical beam The paper studies the bending vibration of such a beam, situated in the vertical plane, with the upper end rigidly fixed and the lower one free (Fig. 1). The beam has the length l (with relatively large value: l∈[10,40] m). The ratio of the fundamental eigenfrequency when the self weight is considered, 1 ω , and the one determined when the self weight is neglected, 1 ~ ω , will be determined. Usual notations are used: v – displacement with respect to Oy axis; w – displacement with respect to Oz axis. A’ A B B’ v(z) dz dv -w(z) Figure 2. Element of the deformed axis of the beam