Abstract
An analysis of steady-state vibration of linear dynamical systems subjected to harmonic force and/or kinematic exposure can be reduced to analysis of mechanical two-term networks (M2TN), also known as replacement schemes, which are equivalent to the original scheme. The two representations of the system are equivalent in the sense that both representations can be described by the same differential equations. The theory of analogy [1–4] is what makes such an interchange possible. The advantage of representing a dynamical system as a replacement scheme is that its construction for multi-element dynamical systems is fairly simple and consists in analyzing M2TN by algebraic methods [5], whereas analysis of the original design diagram must be performed by solutions to differential equations. Another advantage of representing systems through M2TN is that theorems often used to analyze electrical circuits (Kirchhoff’s rule, Thevenin and Norton’s theorem, principle of superposition, etc.) can also be applied to replacement schemes.
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Karnovsky, I.A., Lebed, E. (2016). Mechanical Two-Terminal Networks for a System with Lumped Parameters. In: Theory of Vibration Protection. Springer, Cham. https://doi.org/10.1007/978-3-319-28020-2_2
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DOI: https://doi.org/10.1007/978-3-319-28020-2_2
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