On the equivalent systems for concurrent springs and dampers – Part 1: Small in-plane oscillations

In this work, concurrent linear springs placed in the system that performs small in-plane oscillations around the stable equilibrium position are considered. New theorems defining how they can be replaced by two mutually orthogonal springs are provided. The same concept is applied to find two mutual...

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Bibliographic Details
Published in:Proceedings of the Institution of Mechanical Engineers. Part C, Journal of mechanical engineering science Journal of mechanical engineering science, 2014-10, Vol.228 (14), p.2520-2531
Main Authors: Radomirovic, Dragi, Kovacic, Ivana
Format: Article
Language:English
Subjects:
Dampers
Damping
Equivalence
Invariants
Mechanical engineers
Mechanical properties
Oscillations
Springs (elastic)
Stiffness
Theorems
Viscosity
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Summary:In this work, concurrent linear springs placed in the system that performs small in-plane oscillations around the stable equilibrium position are considered. New theorems defining how they can be replaced by two mutually orthogonal springs are provided. The same concept is applied to find two mutually orthogonal linear viscous dampers that can replace a system of concurrent linear viscous dampers. The directions of such springs and dampers correspond to the principal stiffness and damping axes, respectively. So far unknown invariants related to the sum of stiffness coefficients and damping coefficient of the original and equivalent systems are presented. A few examples are given to illustrate the use and benefits of this approach. In addition, it is shown how the concept of two mutually orthogonal springs can be beneficially used for analysing problems concerned with oscillations of a particle on elastic frames.
ISSN:0954-4062
2041-2983
DOI:10.1177/0954406213519616