Chladni-like patterns in pillared plates
Chladni-like patterns in pillared plates
Nominally identical rods mounted on stiff plates appear in many industrial contexts such as heat exchangers. Here we report the modal behaviour of a plate coupled with flexible pillars that serves as an abstraction to the commonly encountered tube-plate assemblies frequently found in engineering. We develop an analytical model to describe the modal characteristics of a stiff plate attached to an array of cantilevered resonators. The model is able to capture accurately the intricate “spatial phase”, resembling Chladni patterns formed by the tips of the resonators. We also describe how the problem of matching the modes obtained from analysis with those obtained from FE simulations can be posed as one of rearrangement, which can be solved efficiently using the Hungarian algorithm [1], a celebrated result from combinatorial mathematics. We show that the analytical model developed here can predict many modes with a high degree of accuracy, as characterized by the MAC number [2] with respect to modes obtained from finite element analysis. Frequencies appear in clusters that resemble the pass-bands of a periodic structure. The phase of the resonators is interpreted and its physical origins are brought out. Modal density shows spikes at locations close to the natural frequencies of the resonators, which is consistent with the band structure.
Chladni patterns, periodic structures, flexural resonators
Jose, Kevin
f4b1bda1-3c49-4c48-82cc-f7456e65ee22
Ferguson, Neil
8cb67e30-48e2-491c-9390-d444fa786ac8
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e
Jose, Kevin
f4b1bda1-3c49-4c48-82cc-f7456e65ee22
Ferguson, Neil
8cb67e30-48e2-491c-9390-d444fa786ac8
Bhaskar, Atul
d4122e7c-5bf3-415f-9846-5b0fed645f3e
Jose, Kevin, Ferguson, Neil and Bhaskar, Atul
(2022)
Chladni-like patterns in pillared plates.
ESMC 2022: 11th European Solid Mechanics Conference, , Galway, Ireland.
04 - 08 Jul 2022.
(Submitted)
Record type:
Conference or Workshop Item
(Other)
Abstract
Nominally identical rods mounted on stiff plates appear in many industrial contexts such as heat exchangers. Here we report the modal behaviour of a plate coupled with flexible pillars that serves as an abstraction to the commonly encountered tube-plate assemblies frequently found in engineering. We develop an analytical model to describe the modal characteristics of a stiff plate attached to an array of cantilevered resonators. The model is able to capture accurately the intricate “spatial phase”, resembling Chladni patterns formed by the tips of the resonators. We also describe how the problem of matching the modes obtained from analysis with those obtained from FE simulations can be posed as one of rearrangement, which can be solved efficiently using the Hungarian algorithm [1], a celebrated result from combinatorial mathematics. We show that the analytical model developed here can predict many modes with a high degree of accuracy, as characterized by the MAC number [2] with respect to modes obtained from finite element analysis. Frequencies appear in clusters that resemble the pass-bands of a periodic structure. The phase of the resonators is interpreted and its physical origins are brought out. Modal density shows spikes at locations close to the natural frequencies of the resonators, which is consistent with the band structure.
Text
Chladni-like patterns in pillared plates
- Other
Restricted to Repository staff only
Request a copy
More information
Submitted date: 2022
Venue - Dates:
ESMC 2022: 11th European Solid Mechanics Conference, , Galway, Ireland, 2022-07-04 - 2022-07-08
Keywords:
Chladni patterns, periodic structures, flexural resonators
Identifiers
Local EPrints ID: 470727
URI: http://eprints.soton.ac.uk/id/eprint/470727
PURE UUID: 41fcb309-0d34-4e7d-8fca-5f062276c760
Catalogue record
Date deposited: 18 Oct 2022 17:15
Last modified: 17 Mar 2024 02:32
Export record
Contributors
Author:
Kevin Jose
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics