Free beam vibration analysis based on the method of integrodifferential relations
Periodic Control Systems, Volume # 3 | Part# 1
V. V. Saurin; G. V. Kostin
Digital Object Identifier (DOI)
distributed-parameter systems,eigenvalue problems,frequency characteristics,verification
Equations describing small free oscillations of a rectilinear elastic beam with a rectangular cross section have been obtained within the framework of the linear theory of elasticity and solved using the method of integrodifferential relations (IDR). The influence of geometry and elastic characteristics on the frequencies and shapes of free beam oscillations is studied. It is shown that the longitudinal motions admit two types of displacement and internal stress fields. The lateral oscillations obtained are specified by two frequency bands, which correspond to different types of the characteristic equation roots. Numerical examples of free beam oscillations are presented and discussed.
 Donnell, L.H. (1976). Beams, plates and shells. McGraw-Hill, New York.  Kostin, G.V. and V.V. Saurin (2005). Itegro-differential approach to solving problems of linear elasticity. Doklady Physics, 50(10), pp. 535-538.  Kostin, G.V. and V.V. Saurin (2006a) The method of integrodifferential relations for linear elasticity problems // Archive of Applied Mechanics. 76(7-8), pp. 391-402.  Kostin, G.V. and V.V. Saurin (2006b) Variational approaches in the beam theory. Mechanics of Solids. 41(1).  Kostin, G.V. and V.V. Saurin (2006c) Free Beam Oscillations. Doklady Physics, 51(12), pp. 680-684.  Strutt, J.W. (Baron Rayleigh) (1926) Theory of sound. V. 1. MacMillan, London.  Timoshenko, S. (1956) Strength of materials. Pt 1. Elementary theory and problems. D. Van Nostrand Reinhold, Princenton:  Timoshenko, S.P. and J.N. Goodier (1970) Theory of elasticity. McGraw, New York.