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S.B. Karavashkin and O.N. Karavashkina Special Laboratory for Fundamental Elaboration SELF E-mail: email@example.com http://angelfire.lycos.com/la3/SELFlab http://angelfire.lycos.com/la3/selftrans
Exact analytical solutions for an ideal elastic infinite line having one heterogeneity transition
ABSTRACT. In this paper we will present some results of investigation of an infinite 1D elastic lumped line having one section of heterogeneity. We have obtained these results, using the original non-matrix method to find exact analytical solutions of the infinite system of differential equations. We will present few features important for the practical use, conditioned by the transition of an elastic line section to the anti-phase damping regime. We also will consider the conditions of solutions transformation, when transiting to the models related to basic, as well as to the related elastic distributed line. The results of this investigation can be extended to the rotary vibrations of lumped and distributed elastic lines, as well as with the help of original dynamical electromechanical analogy (DEMA) they can be applied to the electrical filters calculation.