Engineering Transactions, 55, 4, pp. 317–333, 2007

Dynamics of the Complex System With Elastic and Visco-Elastic Inertial Interlayers

Kazimierz Wielki University in Bydgoszcz Faculty of Mathematics, Physics and Technology Institute of Technology

In this paper is given the dynamic analysis of the free and forced vibration problems of a complex system with elastic and visco-elastic inertial interlayers. The analytical method of solving the free and forced vibrations problem of the system is presented in the paper [2]. The external layer of the complex system is treated as the plate made from elastic materials, coupled by visco-elastic inertial interlayers. The plate is described by the Kirchhoff–Love model. The visco-elastic, inertial interlayer possesses the characteristics of a continuous inertial Winkler foundation and has been described by the Voigt-Kelvin model. Small transverse displacements of the complex system are excited by the stationary and non-stationary dynamical loadings. The phenomenon of free and forced vibrations problems has been described using a non-homogeneous system of conjugate, partial differential equations. After separation of variables in the homogeneous system, the boundary value problem has been solved and two sequences have been obtained: the sequences of frequencies and the sequences of free vibrations modes. Then, the property of orthogonality of complex free vibrations has been presented. The free vibrations problem has been solved for some arbitrarily assumed initial conditions. The forced vibrations problem has been considered for different modes of dynamical loading. The solution of the ecological safety problem and protection from exposure to dust, depend much on the equipment and techniques used in quarrying the brown coal. Thus, dynamics of loading the open cast colliery dump trucks which have a load-carrying capacity of hundreds of tons, mass of tens of tons and dimensions of tens of meters, is a very important problem. The numerical results of free and forced vibrations problems of the complex system with the elastic and visco-elastic inertial interlayer, for various parameters and different modes of dynamical loading, are given in this paper.
Keywords: vibrations; two-layer system; damping; numerical results
Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


R. Bogacz, R. Szolc, On non-linear analysis of the geared drive systems by means of the wave method, Journal of Theoretical and Applied Mechanics, 31, 2, 393–401, 1993.

K. Cabanska–Płaczkiewicz, Vibrations of the sandwich plate with a viscoelastic inertial interlayer, The International Journal of Strength of Materials, 103–115, National Academy of Sciences of Ukraine, Institute of Problems of Strength, Kiev 2001.

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

J. Cabanski, 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.

Kl. Cremer, M. Heckel, E. Ungar, Structure-Borne Sound, Structural Vibrations and Sound Radiation at Audio Frequencies, Springer-Verlag, Berlin 1988.

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.

G. Jemielita, The technical theory of a plate of anaverage thickness, Journal of Engineering Transactions, 199–220, 1974.

G. Kirchhoff, Über das Gleichgewicht und die Bewegung einer elastichen Scheibe, Journal fur die Reine und Angewandte Math., 40, 1, 55–88, 1850.

S. Kukla, Dynamic Green’s functions in free vibration analysis of continuous and discrete-continuous mechanical systems, Pub. of the Czestochowa Univ. of Tech., Czestochowa 1999.

W. Kurnik, A. Tylikowski, Mechanics of laminated elements, Pub. of the Warsaw Univ. of Tech., Warsaw 1997.

R.D. Mindlin, A. Schacknow, H. Deresewicz, Flexural vibrations of rectangular plates, Journal of Applied Mechanics, 23, 3, 430–436, 1956.

D. Nashif, D. Jones, J. Henderson, Vibration damping, Mir, Moskva 1988.

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

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

Z. Oniszczuk, Free vibrations of elastically connected rectangular double-plate compound system, Building Engineering, Pub. of the Warsaw Univ. of Tech., 132, 183–109, Warsaw 1998.

Z. Oniszczuk, Vibration analysis of the compound continuous systems with elastic constraints, Pub. of the Rzeszow Univ. of Tech., Rzeszów 1997.

Z. Osinski, Damping of the mechanical vibration, PWN, Warsaw 1979.

J. Osiowski, A draft of the operator calculus, Warsaw: WNT, 1981.

N.D. Pankratova, B. Nikolaev, E. Switonski, Nonaxisymmetrical deformation of flexible rotational shells in classical and improved statement, Journal of Engineering Mechanics, 3, 2, 89–96, 1996.

N.D. Pankratova, A. A. Mukoed, Deformation of the thick laminated orthotropic plate, XXXIV Symposium of Model. in Mech., Silesian Univ. of Tech., 122, 251–256, Gliwice 1995.

E. Reissner, On transverse bending of plates, including the effect of transverse shear deformation, Int. Journal of Solid Structures, 11, 569–573, 1975.

M. Renaudot, Etude de l’influence des charges en mouvement sur la resistance des ponts metallique, Annales des Ponts et Chausses, 1, 145–204, 1861.

Cz. Rymarz, Mechanics of continua, PWN, Warsaw 1993.

W. Szczesniak, The problems of vibrations of dynamical plates under moving inertial loads, Building Engineering, Pub. of the Warsaw Univ. of Tech., 119, 1–112, Warsaw 1992.

W. Szczesniak, Vibrations of plates. Theoretical fundamentals of the mechanics of trackairfield structure, Research Institute of Track and Bridges, Warsaw 2000.

S.P. Timoshenko, S. Woinowsky-Krygier, Theory of plates and shells, Arkady, New York, Toronto, London 1956.

F. Tse, I. Morse, R. Hinkle, Mechanical vibrations theory and applications, Allyn and Bacon, Boston 1978.

A. Tylikowski, Influence of bonding layer on piezoelectric actuators of an axisymmetrical annular plate, Journal of Theoretical and Applied Mechanics, 38, 3, 607–621, 2000.

T.M. Wang, Natural frequencies of continuous Timoshenko beams, Journal of Sound and Vibration, 13, 409–414, 1970.

E. Winkler, Die Lehre von der Elastizität und Festigkeit, Dominicus, Prag 1867.

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

DOI: 10.24423/engtrans.214.2007