The University of Southampton
University of Southampton Institutional Repository
Warning ePrints Soton is experiencing an issue with some file downloads not being available. We are working hard to fix this. Please bear with us.

Variational principles of liquid-porous material interactions with applications to approximate solutions and finite element modelling

Variational principles of liquid-porous material interactions with applications to approximate solutions and finite element modelling
Variational principles of liquid-porous material interactions with applications to approximate solutions and finite element modelling
For liquid-porous material interactions (LPMI), three variational principles are developed in Biot’s theory of porous materials in association with Darcy’s law. First one takes solid-acceleration, and fluid velocity, acceleration, pressure with time derivative as five variables, while second and third respectively have three and two variables when Darcy’s law used as variational constrain reducing variables. These principles provide a means to derive approximate solutions and finite element (FE) models for LPMI. Each LPMI element includes fluid and solid together with no longer necessarily to distinguish fluid domain from solid. Examples illustrate applications to establish FE model for numerical solutions of LPMI. Solution of a 1-D problem reveals that LPMI behaves a coupled-frequency separation measured by a defined-coupling factor. Dynamic response explores coupled-dynamic absorber mechanism in LPMI system, from which it is found that the external force at fluid does not contribute to fluid response but fully absorbed by solid local-resonance if the force frequency equals the solid natural frequency; while in the reverse case when the force frequency equals the fluid one, the force at solid does not produce the solid response but fully absorbed by fluid local-resonance. New findings with defined LPMI coupling-factor provide guidelines designing LPMI-system with expected dynamic behaviour meeting engineering requirements.
Biot’s theory with Darcy’s law, Coupled-dynamic absorbers, Coupled-frequency separation, Liquid-porous material coupling factors, Variational principles of LPMI, X_d Q_n LPMI-element.
1364-5021
Xing, Jing
d4fe7ae0-2668-422a-8d89-9e66527835ce
Qin, Hongling
3639d591-fa71-4738-b1d2-e846890d18cf
Xing, Jing
d4fe7ae0-2668-422a-8d89-9e66527835ce
Qin, Hongling
3639d591-fa71-4738-b1d2-e846890d18cf

Xing, Jing and Qin, Hongling (2021) Variational principles of liquid-porous material interactions with applications to approximate solutions and finite element modelling. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477 (2248), [20200678]. (doi:10.1098/rspa.2020.0678). (In Press)

Record type: Article

Abstract

For liquid-porous material interactions (LPMI), three variational principles are developed in Biot’s theory of porous materials in association with Darcy’s law. First one takes solid-acceleration, and fluid velocity, acceleration, pressure with time derivative as five variables, while second and third respectively have three and two variables when Darcy’s law used as variational constrain reducing variables. These principles provide a means to derive approximate solutions and finite element (FE) models for LPMI. Each LPMI element includes fluid and solid together with no longer necessarily to distinguish fluid domain from solid. Examples illustrate applications to establish FE model for numerical solutions of LPMI. Solution of a 1-D problem reveals that LPMI behaves a coupled-frequency separation measured by a defined-coupling factor. Dynamic response explores coupled-dynamic absorber mechanism in LPMI system, from which it is found that the external force at fluid does not contribute to fluid response but fully absorbed by solid local-resonance if the force frequency equals the solid natural frequency; while in the reverse case when the force frequency equals the fluid one, the force at solid does not produce the solid response but fully absorbed by fluid local-resonance. New findings with defined LPMI coupling-factor provide guidelines designing LPMI-system with expected dynamic behaviour meeting engineering requirements.

Text
RSPA-2020-0678R1 - Accepted Manuscript
Restricted to Repository staff only
Available under License Creative Commons Attribution.
Request a copy
Text
rspa.2020.0678 - Version of Record
Restricted to Repository staff only
Request a copy

More information

Accepted/In Press date: 23 March 2021
Keywords: Biot’s theory with Darcy’s law, Coupled-dynamic absorbers, Coupled-frequency separation, Liquid-porous material coupling factors, Variational principles of LPMI, X_d Q_n LPMI-element.

Identifiers

Local EPrints ID: 448860
URI: http://eprints.soton.ac.uk/id/eprint/448860
ISSN: 1364-5021
PURE UUID: 255155ef-d1ed-4ad7-a307-a35d2b090c66

Catalogue record

Date deposited: 07 May 2021 16:30
Last modified: 25 Nov 2021 17:48

Export record

Altmetrics

Contributors

Author: Jing Xing
Author: Hongling Qin

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

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×