Modal localisation in a beam modelled as a continuous system: A discussion on the use of auxiliary oscillators

In this work, we show that perfectly localised modal vibrations can be obtained in continuous linear elastic structures, provided that, in addition to the regular boundary and continuity/jump conditions, extra (admissibility) conditions are met. They are derived with the aid of: (i) new parameters a...

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Bibliographic Details
Published in:Journal of sound and vibration 2020-10, Vol.485, p.115595, Article 115595
Main Authors: Ribeiro, Eduardo A.R., Lenci, Stefano, Mazzilli, Carlos E.N.
Format: Article
Language:English
Subjects:
Auxiliary tuning oscillators
Beamforming
Cantilever beams
Continuous system
Finite-length localisation
Localization
Materials elasticity
Modal asynchronicity
Modal localisation
Oscillators
Parameters
Vibration
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Summary:In this work, we show that perfectly localised modal vibrations can be obtained in continuous linear elastic structures, provided that, in addition to the regular boundary and continuity/jump conditions, extra (admissibility) conditions are met. They are derived with the aid of: (i) new parameters and/or DOFs of auxiliary systems, and/or (ii) admissible relationships amongst the original structural parameters. In both cases, however, the solution resorts to a fine-tuning problem. To illustrate the main ideas, we discuss three examples: two simply-supported beams with cantilever extensions and attached lumped oscillators, and a “tuning-fork-like” structure. Finally, to show that there are also systems in which fine-tuning is not possible, we discuss the case of two lumped oscillators attached to the free end of a cantilever beam.
ISSN:0022-460X
1095-8568
DOI:10.1016/j.jsv.2020.115595