A superconvergent convolution quadrature method for time-dependent dynamical energy analysis

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Chappell, D ORCID: https://orcid.org/0000-0001-5819-0271, 2024. A superconvergent convolution quadrature method for time-dependent dynamical energy analysis. In: Proceedings of ISMA2024 including USD2024. Leuven: Katholieke Universiteit Leuven, pp. 4014-4019.

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Abstract

Dynamical Energy Analysis (DEA) was introduced in 2009 as a novel method for predicting high-frequency acoustic and vibrational energy distributions [1]. In this work we detail how DEA can be reformulated in the time-domain by means of a convolution integral operator and apply a modified multistep-based Convolution Quadrature (CQ) method to discretise in time. Stable time-stepping based on multistep CQ schemes has typically been limited to second-order convergence as a consequence of the second Dahlquist barrier. In this work we apply a simple modification to the traditional second-order backward-difference multistep scheme, which leads to third-order convergence of the time discretisation in time-dependent DEA. The final result is a fully time-dependent DEA method that can accurately track the propagation of high-frequency transient signals through phase-space.

Item Type:	Chapter in book
Creators:	Chappell, D.
Publisher:	Katholieke Universiteit Leuven
Place of Publication:	Leuven
Date:	9 September 2024
Identifiers:	Number Type 2291194 Other
Divisions:	Schools > School of Science and Technology
Record created by:	Jonathan Gallacher
Date Added:	20 Nov 2024 13:53
Last Modified:	20 Nov 2024 13:53
URI:	https://irep.ntu.ac.uk/id/eprint/52625