02-64 S.B. Karavashkin and O.N. Karavashkina Special Laboratory for Fundamental Elaboration SELF E-mail: [email protected] http://angelfire.lycos.com/la3/SELFlab http://angelfire.lycos.com/la3/selftrans

On complex resonance systems vibration (845K, Postscript) Feb 9, 02

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Abstract. Basing on exact analytical solutions obtained for semi-finite elastic lines with resonance subsystems having the form of linear elastic lines with rigidly connected end elements, we will analyse the vibration pattern in systems having such structure. We will find that between the first boundary frequency for the system as a whole and that for the subsystem, the resonance peaks arise, and their number is equal to the integer part of [(n 1)/2] , where n is the number of subsystem elements. These resonance peaks arise at the bound between the aperiodical and complex aperiodical vibration regimes. This last regime is inherent namely in elastic systems having resonance subsystems and impossible in simple elastic lines. We will explain the reasons of resonance peaks bifurcation. We will show that the phenomenon of negative measure of subsystems inertia arising in such type of lines agrees with the conservation laws. So we will corroborate and substantiate Professor Skudrzyk s concept. We will obtain a good qualitative agreement of our theoretical results with Professor Skudrzyk s experimental results.

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