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

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

K. CABANSKA–PŁACZKIEWICZ
The 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
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