Engineering Transactions, 54, 4, pp. 329–351, 2006

Vibrations of the three-layer shell with damping

K. Cabańska-Płaczkiewicz
Kazimierz Wielki University in Bydgoszcz

In this paper the analytical method [17–18] has been used for solving the problem of vibrations of the three-layer shell with damping. External layers are modelled as the MINDLIN shells and the internal layer possesses the characteristics of a viscoelastic one-directional WINKLER foundation. Small transverse vibrations of the three-layer shell with damping is excited by the dynamical non-uniform loading moving at the constant velocity $v*$. Numerical results are presented in the diagrams.
Keywords: vibrations; three-layer shell; damping; numerical results
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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


S.P. TIMOSHENKO, S. WOINOWSKY-KRYGIER, Theory of plates and shells, New York, Toronto, London, McGraw-Hill, Book Company, Inc., 1956.

W.T. GRINCZENKO, Equilibrium and determination of vibrations of elastic bodies of the final dimensions, Think Science, Kiev 1978.

A. BORISUK, Modelling of the acoustic properties of the larger human blood vessel, J. Acoustic Wisnik, Institute of Hydromechanics, National Academy of Sciences of Ukraine, 1, 3, 3–13, 1998.

G. JEMIELITA, On the shear coefficients, Theor. Found. in Civil Engng., 6, Faculty of Civil Engng., Warsaw Univ. of Tech., 115–122, Warsaw 1998.

W.G. KARNAUCHOW, I. FI. KIRICZOK, Thermomechanics theory of three-layer isotropic shells with viscoelastic interlayer, Applied Mechanics, 19, 31–37, Kiev 1983.

R. BOGACZ, R. SZOLC, On nonlinear analysis of the geared drive systems by means of the wave method, Journal of Theoretical and Applied Mechanics, 31, 2, 393–401, 1993.

W. SZCZEŚNIAK, The selection of problems of beams and shells subjected to inertial moving load, Building Engineering, 132, Warsaw Univ. of Tech., 1994.

W. SZCZEŚNIAK, Vibrations of the plate with mean thikness under the moving loads, J. Engng. Trans., 35, 3, 37–53, 1985.

N.D. PANKRATOVA, B. NIKOLAEV, E. ŚWITOŃISKI, Non-axisymmetrical deformation of flexible rotational shells in classical and improved statement, Journal of Engineering Mechanics, 3, 2, 89–96, Brno 1996.

JA. M. GRIGORENKO, Solution of problems of theory shells by the methods of numerical analysis, 20, 3–22, Applied Mechanics 1984.

T. LEWIŃKI, J.J. TELEGA, Plates, laminates and shells, Asymptotic analysis and homogenization, World Scientific, Series on Advances in Mathematics for Applied Sciences, 52, Singapore, New Jersey, London, Hong Kong 2000.

R.A. Di TARANTO, J.R. McGRAW, Vibratory bending of damped laminated plates, Journal of Engineering for Industry, 91, 1081–1090, Transactions of the American Society of Mechanical Engineers 1969.

W. KURNIK, A. TYLIKOWSKI, Mechanics of laminated elements, Warsaw Univ. of Tech., Warsaw 1997.

M. WOŹNIAK, Railway embankment as the building foundation, Mathematical Modelling, Scientific Treatises and Monograhs, SGGW-AR, Warsaw 1991.

F. TSE, I. MORSE, R. HINKLE, Mechanical vibrations, theory and applications, Allyn and Bacon, Boston 1978.

NIZIOL, J. SNAMINA, Free vibration of the discrete-continuous system with damping, Journal of Theoretical and Applied Mechanics, 28, 1–2, 149–160, 1990.

K. CABAŃSKA-PŁACZKIEWICZ, Dynamics analysis of sandwich cylindrical shell, International Journal of Strength of Materials, 4, 346, 119–127, National Academy of Sciences of Ukraine, Institute of Problems of Strength, Kiev 2000.

K. CABAŃSKA-PŁACZKIEWICZ, Vibrations of the complex system with damping under dynamical loading, International Journal of Strength of Materials, 2, 356, 82–101, National Academy of Sciences of Ukraine, Institute of Problems of Strength, Kiev 2002.

KL. CREMER, M. HECKEL, E. UNGAR, Structure-borne sound, Structural Vibrations and Sound Radiation at Audio Frequencies, Springer-Verlag, Berlin 1988.

J. CABAŃSKI, Generalized exact method of analysis of free and forced oscillations in the non-conservative physical system, Journal of Technical Physics, 41, 4, 471–481, 2000.

D. NASHIF, D. JONES, J. HENDERSON, Vibration damping, Mir, Moscow 1988.

W. NOWACKI, The Building Dynamics, Arkady, Warsaw 1972.

DOI: 10.24423/engtrans.250.2006