Vol. 11, No. 3, 2016

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On low-frequency vibrations of a composite string with contrast properties for energy scavenging fabric devices

Askar Kudaibergenov, Andrea Nobili and Ludmilla Prikazchikova

Vol. 11 (2016), No. 3, 231–243

Free vibrations of a two-component string with high-contrast material parameters are considered at different boundary conditions to illustrate the very low-frequency energy harvesting capability of fabric devices. It is revealed that, only for the case of mixed boundary conditions, low-frequency (locally) almost rigid-body vibrations are admissible, provided that material parameter ratios lie in some well defined interval. A low-frequency perturbation procedure is carried out to determine the eigenfrequencies as well as the eigenforms. The analysis is extended to a piecewise inhomogeneous string and to a string supported on an elastic foundation. It is shown that both situations may still admit low-frequency vibrations, under certain restrictions on the material properties. This is particularly remarkable given that the situation of elastic support normally possesses two nonzero cutoff frequencies. The results may be especially relevant for energy scavenging fabric devices, where very low-frequency ( < 10 Hz) mechanical vibrations of textile fibers are harvested through friction.

low-frequency vibration, energy scavenging, contrast properties, strings
Received: 20 November 2015
Revised: 29 January 2016
Accepted: 7 February 2016
Published: 29 March 2016
Askar Kudaibergenov
Department of Mathematical and Computer Modelling
al-Farabi Kazakh National University
71 al-Farabi Avenue
Andrea Nobili
DIEF - Dipartimento di Ingegneria “Enzo Ferrari”
Università di Modena e Reggio Emilia
Via Vignolese 905
I-41125 Modena
Ludmilla Prikazchikova
School of Computing and Mathematics
Keele University
Keele, Staffordshire
United Kingdom