Engineering Transactions, 55, 1, pp. 29–41, 2007

Influence of Transverse Shearing and Rotary Inertia on Vibrations of a Fibrous Composite Beams

University of Technology and Life Sciences in Bydgoszcz

The aim of the paper was determination of the influence of transverse shear deformation and rotary inertia on the natural frequencies and on the values of displacements of beams made of fibrous composites reinforced with layers of long fibres. It was assumed that the matrix of the composite beam possesses linear elastic and transversally isotropic properties. Moreover, a reinforcement in the form of layers composed of long fibres symmetrically located in the crosssection was considered. In order to describe the displacement and strain state of the matrix, the Timoshenko theory was applied. Using the complete analytical solutions obtained in the paper, the accuracy analysis of the results was performed and compared with the theory of Bernoulli beams.
Keywords: dynamics of composite beam, transverse shear effect
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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


R.K. Kapania, S. Raciti, Recent advances in analysis of laminated beams and plates, Part I. Shear effects and buckling. AIAA J., 27, 7, 923–934, 1989; Part II. Vibrations and wave propagation. AIAA J., 27, 7, 935–946, 1989.

A.K. Malmeister, V.P. Tamuż, G.A Teters, Strength of polymeric and composite materials [in Russian], Zinatne, Riga 1980.

J.N. Reddy, N.D. Phan, Stability and vibration of isotropic, orthotropic and laminated plates according to a higher – order shear deformation theory, J. Sound and Vibr., 98, 2, 157–170, 1985.

J. Gołaś, On limits of application of Kirchhoff’s hypothesis in the theory of viscoelastic fibrous composite plates, Engineering Transactions, 43, 4, 603–626, 1995.

J. Gołaś, On necessity of making allowance for shear strain in cylindrical bending of fibre composite viscoelastic plates, Archives of Civil Engineering, 43, 2, 121–147, 1997.

J. Gołaś, Solution for Timoshenko beams expressed in terms of Euler-Bernoulli solutions for fibre-reinforced straight composite beams [in Polish], Akademia Techniczno-Rolnicza, Zeszyty Naukowe Nr 228, Mechanika, 47, 111–120, Bydgoszcz 2000.

J. Holnicki-Szulc, Distortions in structural systems. Analysis, control, modelling [in Polish], PWN, Warszawa–Poznań 1990.

R. Świtka, Equations of the fibre composite plates, Engineering Transactions, 40, 2, 187– 201, 1992.

W. Nowacki, Dynamics of elastic systems [in Polish], Arkady, Warszawa 1961.

Z. Kączkowski, Dynamics of bars and bar structures [in Polish], Mechanika Techniczna (Applied Mechanics), Vol. IX, 182–240, PWN, Warszawa 1988.

W. Szcześniak, Free vibrations of viscoelastic Timoshenko beam and shield [in Polish], Engineering Transactions, 22, 4, 669–687, 1974.

W. Szcześniak, Selected problems of dynamics of plates [in Polish], Oficyna Wydawnicza PW, 2000.

G. Jemielita, Problems of dynamics of plates [in Polish], Mechanika Techniczna (Applied Mechanics), Vol. VIII, Cz. Woźniak [Ed.], PWN, Warszawa 296–330, 2001.

DOI: 10.24423/ENGTRANS.229.2007