Authors: Hedrih, Katica (Stevanović) 
Title: Double plate system with a discontinuity in the elastic bonding layer
Journal: Acta Mechanica Sinica/Lixue Xuebao
Volume: 23
Issue: 2
First page: 221
Last page: 229
Issue Date: 1-Jul-2007
Rank: M22
ISSN: 0567-7718
DOI: 10.1007/s10409-007-0061-x
Abstract: 
The double plate system with a discontinuity in the elastic bonding layer of Winker type is studied in this paper. When the discontinuity is small, it can be taken as an interface crack between the bi-materials or two bodies (plates or beams). By comparison between the number of multifrequencies of analytical solutions of the double plate system free transversal vibrations for the case when the system is with and without discontinuity in elastic layer we obtain a theory for experimental vibration method for identification of the presence of an interface crack in the double plate system. The analytical analysis of free transversal vibrations of an elastically connected double plate systems with discontinuity in the elastic layer of Winkler type is presented. The analytical solutions of the coupled partial differential equations for dynamical free and forced vibration processes are obtained by using method of Bernoulli's particular integral and Lagrange's method of variation constants. It is shown that one mode vibration corresponds an infinite or finite multi-frequency regime for free and forced vibrations induced by initial conditions and one-frequency or corresponding number of multi-frequency regime depending on external excitations. It is shown for every shape of vibrations. The analytical solutions show that the discontinuity affects the appearance of multi-frequency regime of time function corresponding to one eigen amplitude function of one mode, and also that time functions of different vibration basic modes are coupled. From final expression we can separate the new generalized eigen amplitude functions with corresponding time eigen functions of one frequency and multi-frequency regime of vibrations.
Keywords: Analytical solution | Discontinuity | Double plate system | Interface crack | Multifrequency transversal vibrations
Publisher: Springer Link
Project: Theoretical and Applied Mechanics of the Rigid and Solid Bodies. Mechanics of Materials 

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