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A chirp excitation for focussing flexural waves

A chirp excitation for focussing flexural waves
A chirp excitation for focussing flexural waves
In this paper, the dispersive nature of flexural waves is exploited to generate a shock response at an arbitrary location on a waveguide. The input waveform is an up-chirp whose instantaneous frequency is chosen to ensure synchronous arrival at an arbitrary focal point. An analytical expression is derived for the required chirp waveform as a function of bandwidth and focal point location given prior knowledge of the dispersion relation.

The principle is illustrated for an analytical model of a uniform beam. Simulated results show that it is possible, in theory, to achieve peak responses that are at least an order of magnitude larger than steady state response due to harmonic excitation. Further, the peak response increases with approximately the square root of distance from the point of excitation when damping is negligible. Velocity, acceleration, normal strain and shear stress exhibit qualitatively similar results which differ quantitatively owing to their different frequency responses with respect to the input.

A single degree-of-freedom model of an electrodynamic shaker is coupled to the analytical beam model in order to predict peak mechanical responses per peak input voltage of the chirp waveform. The coupled electromechanical model is then validated experimentally through both frequency response and transient measurements. The technique is potentially
applicable to situations where a large and reasonably localised transient response is required on a beam or plate-like structure using minimal instrumentation.
chirp, flexural wave, dispersion, shock, accretion removal, ice
0022-460X
113-128
Waters, Timothy
348d22f5-dba1-4384-87ac-04fe5d603c2f
Waters, Timothy
348d22f5-dba1-4384-87ac-04fe5d603c2f

Waters, Timothy (2019) A chirp excitation for focussing flexural waves. Journal of Sound and Vibration, 439, 113-128. (doi:10.1016/j.jsv.2018.07.028).

Record type: Article

Abstract

In this paper, the dispersive nature of flexural waves is exploited to generate a shock response at an arbitrary location on a waveguide. The input waveform is an up-chirp whose instantaneous frequency is chosen to ensure synchronous arrival at an arbitrary focal point. An analytical expression is derived for the required chirp waveform as a function of bandwidth and focal point location given prior knowledge of the dispersion relation.

The principle is illustrated for an analytical model of a uniform beam. Simulated results show that it is possible, in theory, to achieve peak responses that are at least an order of magnitude larger than steady state response due to harmonic excitation. Further, the peak response increases with approximately the square root of distance from the point of excitation when damping is negligible. Velocity, acceleration, normal strain and shear stress exhibit qualitatively similar results which differ quantitatively owing to their different frequency responses with respect to the input.

A single degree-of-freedom model of an electrodynamic shaker is coupled to the analytical beam model in order to predict peak mechanical responses per peak input voltage of the chirp waveform. The coupled electromechanical model is then validated experimentally through both frequency response and transient measurements. The technique is potentially
applicable to situations where a large and reasonably localised transient response is required on a beam or plate-like structure using minimal instrumentation.

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JSV paper 23Jul 18 post acceptance - Author's Original
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More information

Submitted date: July 2017
Accepted/In Press date: 15 July 2018
e-pub ahead of print date: 11 September 2018
Published date: 20 January 2019
Keywords: chirp, flexural wave, dispersion, shock, accretion removal, ice

Identifiers

Local EPrints ID: 423574
URI: http://eprints.soton.ac.uk/id/eprint/423574
ISSN: 0022-460X
PURE UUID: 6aa0b856-a1a4-4b83-ae5b-d70e2214c392

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Date deposited: 26 Sep 2018 16:30
Last modified: 09 Jan 2022 06:43

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