Modeling and numerical simulations of MEMS shutter devices

We investigate the acoustic behaviour of Micro-Electro-Mechanical-Systems (MEMS) with a focus on shutter devices. These shutter devices can be used for a new method of sound generation ­ which we call Advanced Digital Sound Reconstruction (ADSR) ­ where a redirection mechanism for sound pulses is incorporated [1]. With the help of this redirection mechanism, sound pulses can be generated which are superimposed to form an audio signal. At MEMS-scales viscous effects can play a major role regarding sound transmission. Therefore, we utilize the linearized flow equations in time domain in order to solve for the acoustic pressure while incorporating effects caused by viscous boundary layers. Furthermore, the movement of the shutter itself contributes to the overall generated sound in a negative manner. Since the generation of the sound pulses is in the ultra sound range, the generated noise by the shutter might lead to adverse effects on the human body [2]. Hence, modeling the shutter noise and understanding its generation process can help to improve the design. To model the noise generated by the shutter, we apply the arbitrary LagrangianEulerian (ALE) framework to the linearized flow equations to be able to compute the noise generation on the moving geometry. The geometry update itself is governed by an artificial quasi-static mechanical problem which is solved in each step to get the new element deformation [3]. Assuming that the impact of the acoustic pressure is negligible, a simple forward coupling from the quasistatic mesh-smoothing to the the linearized flow equations is employed. Furthermore, we use a direct coupling approach to couple the acoustic wave equation to the linearized flow equations. The final coupled system is then used to characterize the impact of the shutter movement on the overall system behaviour of a certain embodiment

The comparison of different acoustic approaches in the simulation of human phonation

This contribution deals with mathematical modelling and numerical simula- tion of the human phonation process. This phenomena is described as a coupled problem composed of the three mutually coupled physical fields: the deformation of elastic body, the fluid flow and the acoustics. For the sake of simplicity only a two-dimensional model problems is considered in this paper. The fluid-structure interaction problem is described by the incompressible Navier-Stokes equations, by the linear elasticity theory and by the interface conditions. In order to capture the motion of the fluid domain the arbitrary Lagrangian-Eulerian method is used. The strongly coupled partitioned scheme is used for solution of the coupled fluid-structure problem. For solution of acoustics the acoustic analogies are used. Two analogies are compared - the Lighthill analogy and convected perturbation wave equation. The influence of acoustic field back to fluid as well as to structure is neglected. The numerical approximation of all three physical domains is per- foremd with the aid of the finite element method. The numerical results present sound propagation through the model of the vocal tract

Modelling of air chamber supported floating platforms – coupling free surface flow, compressible air, and flexible structures

Air chamber supported floating platforms can significantly decrease wave induced structural responses. Novel applications, like floating arrays of solar collectors, with low payload requirements allow the design of floating platforms supported by large, cylindrical air chambers made of highly flexible membranes. In order to predict the dynamics of such systems a modelling strategy capturing all important phenomena: incompressible free surface flow, compressible air and flexible structures is presented. The governing partial differential equations and boundary conditions are given in their linearised form, and subsequently solved by the finite element method. A frequency domain formulation is chosen to compute the steady state response to harmonic excitation. In order to handle problems in unbounded domains a perfectly matched layer formulation is used. Thereby, radiating waves are efficiently damped at the edge of the computational domain. For the sake of simplicity we present two-dimensional, test problems used for the validation of the developed modelling strategy. Finally, we present a fully coupled simulation of wave interactions with a flexible, air chamber supported floating platform

Efficient and Higher-Order Accurate Split-Step Methods for Generalised Newtonian Fluid Flow

[EN] In numerous engineering applications, such as polymer or blood flow, the dependence of fluid viscosity on the local shear rate plays an important role. Standard techniques using inf-sup stable finite elements lead to saddle-point systems posing a challenge even for state-ofthe-art solvers and preconditioners. Alternatively, projection schemes or time-splitting methods decouple equations for velocity and pressure, resulting in easier to solve linear systems. Although pressure and velocity correction schemes of high-order accuracy are available for Newtonian fluids, the extension to generalised Newtonian fluids is not a trivial task. Herein, we present a split-step scheme based on an explicit-implicit treatment of pressure, viscosity and convection terms, combined with a pressure Poisson equation with fully consistent boundary conditions. Then, using standard equal-order finite elements becomes possible. Stability, flexibility and efficiency of the splitting scheme is showcased in two challenging applications involving aortic aneurysm flow and human phonation.The authors gratefully acknowledge Graz University of Technology for the financial support of the Lead-project: Mechanics, Modeling and Simulation of Aortic Dissection.Schussnig, R.; Pacheco, D.; Kaltenbacher, M.; Fries, T. (2022). Efficient and Higher-Order Accurate Split-Step Methods for Generalised Newtonian Fluid Flow. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 335-344. https://doi.org/10.4995/YIC2021.2021.12217OCS33534

Semi-implicit fluid–structure interaction in biomedical applications

Fluid–structure interaction (FSI) incorporates effects of fluid flows on deformable solids and vice versa. Complex biomedical problems in clinical applications continue to challenge numerical algorithms, as incorporating the underlying mathematical methods can impair the solvers’ performance drastically. In this regard, we extend a semi-implicit, pressure Poisson-based FSI scheme for non-Newtonian fluids to incorporate several models crucial for biomechanical applications. We consider Windkessel outlets to account for neglected downstream flow regions, realistic material fibre orientation and stressed reference geometries reconstructed from medical image data. Additionally, we incorporate vital numerical aspects, namely, stabilisations to counteract dominant convective effects and instabilities triggered by re-entrant flow, while a major contribution of this work is combining interface quasi-Newton methods with Robin coupling conditions to accelerate the partitioned (semi-)implicit coupling scheme. The numerical examples presented herein aim to finally bridge the gap to real-world applications, considering state-of-the-art modelling aspects and physiological parameters. FSI simulations of blood flow in an iliac bifurcation derived from medical images and vocal folds deforming in the process of human phonation demonstrate the versatility of the framework

Numerical Investigation of Signal Launch Imperfections for Edge Mount RF Connectors

In this paper, common practice RF design guidelines for SMA edge mount connectors are investigated in terms of numerical simulations and VNA measurements. These guidelines are used in a variety of applications for coaxial-to-planar interfaces but often do not provide information regarding the physical origins of increased insertion and transmission losses. The presented results in this work focus on different RF PCB design features and their impact on electromagnetic field distributions in the launching zone. The presented investigations should raise awareness on the issue of electromagnetic field resonances occurring in the RF frequency range and assist PCB design engineers to identify potential issues occurring at an coaxial-to-planar interface. The investigated PCB features facilitate a high performance RF PCB design up to a frequency of 26 GHz

A Validated Finite Element Model for Room Acoustic Treatments with Edge Absorbers

Porous acoustic absorbers have excellent properties in the low-frequency range when positioned in room edges, therefore they are a common method for reducing low-frequency reverberation. However, standard room acoustic simulation methods such as ray tracing and mirror sources are invalid for low frequencies in general which is a consequence of using geometrical methods, yielding a lack of simulation tools for these so-called edge absorbers. In this article, a validated finite element simulation model is presented, which is able to predict the effect of an edge absorber on the acoustic field. With this model, the interaction mechanisms between room and absorber can be studied by high-resolved acoustic field visualizations in both room and absorber. The finite element model is validated against transfer function data computed from impulse response measurements in a reverberation chamber in style of ISO 354. The absorber made of Basotect is modeled using the Johnson-Champoux-Allard-Lafarge model, which is fitted to impedance tube measurements using the four-microphone transfer matrix method. It is shown that the finite element simulation model is able to predict the influence of different edge absorber configurations on the measured transfer functions to a high degree of accuracy. The evaluated third-octave band error exhibits deviations of 3.25dB to 4.11dB computed from third-octave band averaged spectra.Comment: 20 pages, 16 figures, 3 tables, Preprint submitted to Acta Acustic

Flexible Discretization for Computational Aeroacoustics

This contribution discusses the capabilities of non-conforming grid techniques to allow an optimal discretization for each subdomain. In doing so, we derive the Nitsche-type mortaring formulation for the acoustic wave equation, which incorporates the physical transmission condition of continuity of acoustic pressure and its flux being the normal component of the acoustic particle velocity. The Nitschetype mortaring handles the coupling by symmetrizing the bilinear form and adding an appropriate jump term. The simulation of the edge tone demonstrates the applicability and superiority of non-conforming grids for computational aeroacoustics at low Mach numbers compared to conforming finite element methods