Helical spring mode grouping

Jacob McQuillan*, Maarten Van Walstijn

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Abstract

The main vibrational elements of a spring reverb tank are helical springs. The coupling between bending, longitudinal, and torsional oscillations in a single spring gives rise to complex vibrational behaviour characterised by several distinct echo patterns in measured impulse responses. For modelling purposes, a reduced representation that covers only the hearing range can be obtained by casting the equations in modal form. Previous attempts to explain the various features of measured impulse responses have largely focused on dispersion relation analysis. However, addressing open questions on driving, pick-up, and damping mechanisms requires also considering modal amplitudes. This work applies a pseudospectral method to a thin spring version of Wittrick’s twelve equations, framing an eigenvalue problem from which modal parameters are extracted. To investigate the influence of model parameters on the system response, we propose grouping modes across the wave number axis, which requires extracting wave numbers from mode shapes. This allows separate visualisation and analysis of the various echo patterns in the modelled impulse response. Preliminary results give new perspectives on how transition frequencies arise, and on the significance of specific mode groups.

Original languageEnglish
Title of host publicationProceedings of the Stockholm Music Acoustics Conference, SMAC 2023
EditorsSara D’Amario, Anders Friberg, Sten Ternström
Pages43-50
Number of pages8
Publication statusPublished - 14 Jun 2023
Event5th Stockholm Music Acoustics Conference 2023 - Stockholm, Sweden
Duration: 14 Jun 202315 Jun 2023
https://smcnetwork.org/smc2023/SMAC_2023_All_papers.pdf

Publication series

NameProceedings of the Sound and Music Computing Conferences
ISSN (Print)2518-3672

Conference

Conference5th Stockholm Music Acoustics Conference 2023
Abbreviated titleSMAC 2023
Country/TerritorySweden
CityStockholm
Period14/06/202315/06/2023
Internet address

Keywords

  • Helical springs
  • Physical modelling
  • Pseudospectral method
  • Spring reverberation
  • modal analysis

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