Complete results for free and forced vibrations of inerter-added one-degree-of-freedom systems

César A. Morales1

1Facultad de Ingeniería, Universidad Peruana de Ciencias Aplicadas, Lima, Perú

Journal of Vibroengineering, Vol. 21, Issue 6, 2019, p. 1564-1573. https://doi.org/10.21595/jve.2019.20554
Received 28 January 2019; received in revised form 26 March 2019; accepted 3 April 2019; published 30 September 2019

Copyright © 2019 César A. Morales. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Abstract.

A comprehensive study on the influence of an inerter on the response of single-degree-of-freedom systems is presented; therefore, complete and thorough results for free and forced vibrations of linear SDOF systems with inerter are obtained. The free response results are for damped and undamped systems; moreover, the forced response solutions are for harmonic and arbitrary excitations. The classical problems of rotating unbalanced mass and support vibration isolation are solved.

Graphical Abstract

Highlights
  • Complete and thorough results for free and forced vibrations of linear single-degree-of-freedom systems with inerter
  • The classical problems of rotating unbalanced mass and support vibration isolation are presented, with inerter
  • New definitions for natural and damped frequencies, damping factor, amplification factor, transmissibility and transfer function
  • Comprehensive study on the influence of an inerter on the response of SDOF systems

Keywords: inerter, vibrations, free response, forced response.

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