Mixed finite elements applied to acoustic wave problems in compressible viscous fluids under piezoelectric actuation

In the present contribution, we develop a mixed finite element method capable of the coupled multi-field simulation of a viscous fluid actuated by a piezoelectric resonator. Several challenges are met with in this setting, among which are the necessity of correct interface coupling, near incompressi...

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Vydané v:	Acta mechanica Ročník 233; číslo 5; s. 1967 - 1986
Hlavní autori:	Meindlhumer, Martin, Pechstein, Astrid, Jakoby, Bernhard
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Vienna Springer Vienna 01.05.2022 Springer Springer Nature B.V
Predmet:	Acoustic waves Acoustics Actuation Approximation Classical and Continuum Physics Compressibility Control Coupling Decay rate Deformation Dynamical Systems Elastic waves Engineering Engineering Fluid Dynamics Engineering Thermodynamics Finite element analysis Finite element method Fluids Geometry Heat and Mass Transfer Incompressibility Locking Methods Original Paper Partial differential equations Piezoelectric transducers Resonators Shear Simulation Solid Mechanics Tensors Theoretical and Applied Mechanics Vibration Viscous fluids
ISSN:	0001-5970, 1619-6937
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Abstract	In the present contribution, we develop a mixed finite element method capable of the coupled multi-field simulation of a viscous fluid actuated by a piezoelectric resonator. Several challenges are met with in this setting, among which are the necessity of correct interface coupling, near incompressibility of the fluid, adverse geometric dimensions of flat piezoelectric transducers and different length scales of shear and pressure wave. Assuming small deformations and velocities, we present a mixed variational formulation with consistent interface coupling conditions in (mechanic) frequency domain. Both fluid and piezoelectric solid domain are discretized using Tangential-Displacement Normal-Normal-Stress elements. These elements model not only the deformation, but add an independent tensor-valued stress approximation. The method has been rigorously proven to be free from shear locking for flat prismatic or hexahedral elements. Thus, modeling of the flat geometry of piezoelectric resonators as well as resolution of the fastly decaying shear wave are facilitated. To circumvent the problem of volume locking due to the near incompressibility of the fluid, an additional independent pressure field is introduced. We present computational results indicating the capability of the method.
AbstractList	In the present contribution, we develop a mixed finite element method capable of the coupled multi-field simulation of a viscous fluid actuated by a piezoelectric resonator. Several challenges are met with in this setting, among which are the necessity of correct interface coupling, near incompressibility of the fluid, adverse geometric dimensions of flat piezoelectric transducers and different length scales of shear and pressure wave. Assuming small deformations and velocities, we present a mixed variational formulation with consistent interface coupling conditions in (mechanic) frequency domain. Both fluid and piezoelectric solid domain are discretized using Tangential-Displacement Normal-Normal-Stress elements. These elements model not only the deformation, but add an independent tensor-valued stress approximation. The method has been rigorously proven to be free from shear locking for flat prismatic or hexahedral elements. Thus, modeling of the flat geometry of piezoelectric resonators as well as resolution of the fastly decaying shear wave are facilitated. To circumvent the problem of volume locking due to the near incompressibility of the fluid, an additional independent pressure field is introduced. We present computational results indicating the capability of the method. In the present contribution, we develop a mixed finite element method capable of the coupled multi-field simulation of a viscous fluid actuated by a piezoelectric resonator. Several challenges are met with in this setting, among which are the necessity of correct interface coupling, near incompressibility of the fluid, adverse geometric dimensions of flat piezoelectric transducers and different length scales of shear and pressure wave. Assuming small deformations and velocities, we present a mixed variational formulation with consistent interface coupling conditions in (mechanic) frequency domain. Both fluid and piezoelectric solid domain are discretized using Tangential-Displacement Normal-Normal-Stress elements. These elements model not only the deformation, but add an independent tensor-valued stress approximation. The method has been rigorously proven to be free from shear locking for flat prismatic or hexahedral elements. Thus, modeling of the flat geometry of piezoelectric resonators as well as resolution of the fastly decaying shear wave are facilitated. To circumvent the problem of volume locking due to the near incompressibility of the fluid, an additional independent pressure field is introduced. We present computational results indicating the capability of the method.
Audience	Academic
Author	Jakoby, Bernhard Pechstein, Astrid Meindlhumer, Martin
Author_xml	– sequence: 1 givenname: Martin surname: Meindlhumer fullname: Meindlhumer, Martin organization: Institute for Microelectronics and Microsensorics, Johannes Kepler University Linz – sequence: 2 givenname: Astrid orcidid: 0000-0002-1948-9753 surname: Pechstein fullname: Pechstein, Astrid email: astrid.pechstein@jku.at organization: Institute of Technical Mechanics, Johannes Kepler University Linz – sequence: 3 givenname: Bernhard surname: Jakoby fullname: Jakoby, Bernhard organization: Institute for Microelectronics and Microsensorics, Johannes Kepler University Linz
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Cites_doi	10.1016/S0003-2670(00)82721-X 10.1190/1.1441945 10.1007/s00211-017-0933-3 10.1201/9781420057881 10.1142/S0218202511005568 10.1006/jsvi.1999.2308 10.1177/1045389X20951252 10.1016/j.sna.2011.03.050 10.1007/BF01337937 10.1002/nme.1447 10.2514/3.2546 10.1002/(SICI)1097-0207(20000610)48:4<565::AID-NME890>3.0.CO;2-U 10.1016/j.cma.2021.113857 10.1007/BF02576171 10.1007/978-3-662-04775-0 10.1016/j.enganabound.2014.08.005 10.1080/19475411.2018.1556186 10.1088/0957-0233/19/5/052001 10.1088/0964-1726/18/6/065015 10.1177/1045389X18781026 10.1088/0957-0233/19/5/055201 10.1007/BF01389668 10.1021/ac00020a015 10.1002/nme.3319 10.1007/BF01396415 10.1007/s11831-016-9202-3 10.1016/0045-7930(73)90027-3 10.1007/978-3-642-36519-5 10.1093/imanum/drz022 10.1063/1.1697637 10.1190/1.1440881 10.1137/20M1338034 10.1007/978-3-7091-6442-6
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References_xml	– reference: NédélecJCMixed finite elements in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{R}^3$$\end{document}Numer. Math.19803531534159216010.1007/BF01396415 – reference: Neunteufel, M.: Mixed finite element methods for nonlinear continuum mechanics and shells. Ph.D. thesis, Wien (2021) – reference: FilippiPBergassoliAHabaultDLefebvreJAcoustics: Basic physics, theory, and methods1999USAAcademic Press – reference: LiEHeZCChenLLiBXuXLiuGRAn ultra-accurate hybrid smoothed finite element method for piezoelectric problemEng. Anal. 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Snippet	In the present contribution, we develop a mixed finite element method capable of the coupled multi-field simulation of a viscous fluid actuated by a...
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SubjectTerms	Acoustic waves Acoustics Actuation Approximation Classical and Continuum Physics Compressibility Control Coupling Decay rate Deformation Dynamical Systems Elastic waves Engineering Engineering Fluid Dynamics Engineering Thermodynamics Finite element analysis Finite element method Fluids Geometry Heat and Mass Transfer Incompressibility Locking Methods Original Paper Partial differential equations Piezoelectric transducers Resonators Shear Simulation Solid Mechanics Tensors Theoretical and Applied Mechanics Vibration Viscous fluids
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Title	Mixed finite elements applied to acoustic wave problems in compressible viscous fluids under piezoelectric actuation
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