Acoustics on small scales

Tóth, Ferenc L.; Guilvaiee, Hamideh Hassanpour; Jank, Georg

doi:10.1007/s00502-021-00875-4

Cited by 3 publications

(5 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Heat conduction within the fluid is neglected, and thus one does not need to solve for the temperature perturbation. These linearised Navier-Stokes equations are a simplified case of the full linearised Navier-Stokes (compressible flow) equations taking the temperature field into account [4].…”

Section: Governing Equationsmentioning

confidence: 99%

A model order reduction technique for the linearised compressible flow equations

Tóth

Luo

2023

Proc Appl Math and Mech

Self Cite

View full text Add to dashboard Cite

Viscous effects in acoustics are significant if the thickness of the oscillating viscous boundary layer (Stokes boundary layer) becomes comparable to characteristic problem dimensions. For air as an acoustic medium, this is frequently the case in small‐scale devices like micro‐electro‐mechanical systems or micro‐perforated panels for sound absorption. Accurate modelling of viscous effects can be done by the solution of the linearised compressible flow equations by the finite element method, which is computationally demanding due to the high number of unknowns arising in the problem: pressure, velocity and temperature. Furthermore, the discretisation must resolve the thin viscous boundary layers, creating a model with a high number of degrees of freedom. We suggest a projection‐based model order reduction procedure using the system eigenmodes as generalised coordinates. The procedure is tested based on a simple example problem in 2D. Here we show that the derived reduced order model is accurate and computationally highly efficient. The number of degrees of freedom can be reduced by several orders of magnitude, from around 30 000 to 100, thereby dramatically reducing the computation time for harmonic solutions.

show abstract

Section: Governing Equationsmentioning

confidence: 99%

A model order reduction technique for the linearised compressible flow equations

Tóth

Luo

2023

Proc Appl Math and Mech

Self Cite

View full text Add to dashboard Cite

show abstract

“…The coupling between the solid and thermoviscous domains are enforced using non-conforming interfaces [6]. The coupling between thermoviscous and acoustics are applied using Nitsche-type mortaring method [16]. These methods apply the interface conditions in the weak sense; therefore, the non-conforming grids are supported on their interfaces.…”

Section: Finite Element Formulationmentioning

confidence: 99%

“…Air material properties such as density, visosity and etc. at room temperature and under atmopheric pressure of 1 bar are illustrated in [16].…”

Section: Finite Element Formulationmentioning

confidence: 99%

FEM‐Modeling of thermal and viscous effects in piezoelectric MEMS loudspeakers

Guilvaiee

Tóth

2023

Proc Appl Math and Mech

Self Cite

View full text Add to dashboard Cite

Loudspeakers based on piezoelectric micro‐electro‐mechanical system (PMEMS) are attracting an increasing interest due to their small size, low electronic power consumption, and easy assembly. These aspects are particularly advantageous in applications like earphones, mobile phones, and in‐ear hearing aid devices. However, creating sufficiently high sound pressure levels challenges many existing MEMS loudspeakers. Furthermore, their small dimensions require the consideration of additional physical phenomena like thermoviscous losses, which are often negligible in large loudspeakers. We model and characterize a 3D piezoelectric MEMS loudspeaker in this work using our open‐source finite element method (FEM) program openCFS. We use the linearized conservation of mass, momentum, and energy (thermoviscous acoustic PDEs) for a compressible Newtonian fluid (air) and describe the linear elastic solid using the linearized balance of momentum. The coupling between flow and solid fields is then applied using a non‐conforming FEM formulation. The standard acoustic partial differential equation (PDE) is used in the far‐field, where the thermal and viscous effects are negligible. We study the viscous effects on the displacement and the sound pressure levels (SPLs) of the loudspeaker by parameter studies. These results indicate that at a distance of 13 mm, an SPL of 55 dB at 5 kHz is achieved by a single PMEMS loudspeaker with a footprint of 1.7×1.7 mm2 under a low driving voltage of only 1 V, which is promising considering its dimensions.

show abstract

“…Using complex algebra, the acoustic purturbations pressure, velocity and temperuture take the harmonic form of pe ixt , ve ixt , and Te ixt , respectively [19,20]; a time derivative of any quantity n ( on ot ) becomes ixn. The final linearized conservation equations modeling the fluid behavior in the thermoviscous domain for these small perturbations are [18]…”

Section: Fluid Governing Equationsmentioning

confidence: 99%

“…We use the FEM for solving the linearized conservation of mass, momentum and energy to take viscous and thermal effects into account. The formulation allows couplings to the flexible solid and the acoustic wave equation by using non-conforming interfaces [18]. Employing these formulations, we develop a 3D FEM model of a piezoelectric MEMS loudspeaker.…”

Section: Introductionmentioning

confidence: 99%

A validated modeling strategy for piezoelectric MEMS loudspeakers including viscous effects

Guilvaiee

Heyes²,

Novotny³

et al. 2023

Acta Acust.

Self Cite

View full text Add to dashboard Cite

Piezoelectric micro-electro-mechanical system (MEMS) loudspeakers are drawing more interest due to their applications in new-developing audio technologies. MEMS devices’ small dimensions necessitate including thermal and viscous effects in the surrounding air when simulating their behaviors. Thus, the linearized mass, momentum and energy conservation equations are used to describe these effects. These formulations are implemented in our open-source finite element program openCFS. In this article, we model a 3D piezoelectric MEMS loudspeaker in two configurations: open and closed back-volume, which behave differently due to the effects of air viscosity and pressure forces between the cantilever and the closed back-volume. Furthermore, using a customized vacuum chamber, the atmospheric pressure is varied and its effects are studied in these two configurations, numerically and experimentally. Experimental results prove that our model predicts the behavior of the piezoelectric MEMS loudspeaker in various configurations very well. Additional simulations illustrate the effect of the slit thickness and thermal losses.

show abstract

Acoustics on small scales

Cited by 3 publications

References 15 publications

A model order reduction technique for the linearised compressible flow equations

A model order reduction technique for the linearised compressible flow equations

FEM‐Modeling of thermal and viscous effects in piezoelectric MEMS loudspeakers

A validated modeling strategy for piezoelectric MEMS loudspeakers including viscous effects

Contact Info

Product

Resources

About