Engineering Transactions, 55, 4, pp. 317–333, 2007
10.24423/engtrans.214.2007

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

K. CABANSKA-PŁACZKIEWICZ
Kazimierz Wielki University in Bydgoszcz Faculty of Mathematics, Physics and Technology Institute of Technology
Poland

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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DOI: 10.24423/engtrans.214.2007