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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Bibliographic Details
Published in:Acta mechanica Vol. 233; no. 5; pp. 1967 - 1986
Main Authors: Meindlhumer, Martin, Pechstein, Astrid, Jakoby, Bernhard
Format: Journal Article
Language:English
Published: Vienna Springer Vienna 01.05.2022
Springer
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-022-03195-6