Engineering Transactions, 43, 1-2, pp. 19-26, 1995

Natural Frequencies of a Cantilever Timoshenko Beam With a Tip Mass

N.M Auciello
Department of Structural Engineering and Soil Mechanics University of Basilicata, Potenza

The aim of the present paper is to deduce the free vibration frequencies of cantilever structures with a tip mass at the free end, by taking into account the rotary inertia and the shear deformation. The analysis is conducted by dividing the beam into rigid bars with elastic constraints, extending a previous work by DE ROSA and FRANCIOSI[1]. The proposed method allows us to analyze beams with arbitrarily varying cross-sections, and numerical comparisons with some previous results found in the literature show the good performances of the approach.

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M.A. DE ROSA and C. FANCIOSI, A new approach to the Timoshenko beam theory, 1994, [to be published].

C.W.S TO, Vibration of a cantilever beam with a base excitation and tip mass, J. Sound and Vibration, 83, 445-460, 1982.

P.A.A. LAURA and R.H. GUTIERREZ, Vibrations of an elastically restrained cantilever beam of varying cross-section with tip mass of finite length, J. Sound and Vibration, 108, 1, 123-131, 1986.

J.G. BRUCH and T.P. MITCHELL, Vibrations of mass-loaded clamped-free Timoshenko beam, J. Sound and Vibration1 114, 2, 341-345, 1987.

H. ABRAMOVICH and O. HAMBURGER, Vibration of a cantilever Timoshenko beam with a tip mass, J. Sound and Vibration, 1481 l, 162-170, 1991.

W.H. LIU and D.S. LIU, Natural frequencies of a restrained Timoshenko beam with a tip body at its free end, J. Sound and Vibration, 128, 1, 167-173, 1989.

J.S. PRZEMIENIECKI, Theory of matrix structural analysis, Mc Graw Hill, New York 1968.

P.A.A. LAURA, R.E. ROSSI and M.J. MAURIZI, Vibrating Timoshenko beams, A Tribute to the 70th Anniversary of the Publication of Professor S. Timoshenko's Epoch-Making Contribution, IMA Publication N.92-15, Bahia Blanca, Argentina 1992.

S.H. FARGHALY, On comments on "Vibration of a cantilever Timoshenko beam with a tip mass”, J. Sound and Vibration, 162, 2, 376-378, 1993.

S.H. FARGHALY, On comments on "Vibration of a mass-loaded clamped-free Timoshenko beam", J. Sound and Vibration, 164, 31 549-552, 1993.

S.H. FARGHALY, On comments on "Vibration of a uniform cantilever Timoshenko beam with translational and rotational springs and with a tip mass", J. Sound and Vibration, 1681 1, 189-192, 1993.

R.E. ROSSI, P.A.A. LAURA and R.H. GUTIERREZ, A note on transverse vibrations of a Timoshenko beam of non-uniform thickness clamped at one end and carrying a concentrated mass at the other, J. Sound and Vibration, 143, 491-502, 1990.

W.H. LIU, Comments on "Vibrations of a mass-loaded clamped-free Timoshenko beam" J. Sound and Vibration, 129, 343-344, 1989.

S.P. TIMOSHENKO, Vibration problems in engineering, D. Van Nostrand, New York 1955.

G.R. COWPER, The shear coefficient in Timoshenko's beam theory, J. Appl. Mech.1 33, 335-340, 1966.

N.M. AUCIELLO, Free vibrations of Timoshenko beams with variable cross-sections: a Lagrangian approach, Developments in Computational Engineering Mechanics. CIVIL-COMP93, Edinburgh, 237-241, 1993.

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