# A mathematical description of the acoustic coupling of the mass/spring model

Kao, David, Graham, Deryn, Knight, Brian and Pericleous, Koulis A.
(2007)
*A mathematical description of the acoustic coupling of the mass/spring model.*
Applied Mathematical Modelling, 31 (12).
pp. 2684-2695.
ISSN 0307-904X
(doi:10.1016/j.apm.2006.10.016)

## Abstract

This paper describes hybrid mathematical model which couples the mechanics of the mass/spring model to the acoustic wave propagation model for use in generating the acoustic signal emitted by complex structures of paper fibres under strain. A discussion of the coupling method is presented including remarks on the errors encountered intrinsic to the discretisation scheme. The numerical results of a vibrating rubber band and a vibrating paper fibre are compared to their experimental counterparts. The fundamental frequencies of the acoustic signals are compared showing a close agreement between the experimental and numerical results

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