ECCOMAS 2024

Vibroacoustic Coupling Including Viscous Boundary Layers

  • Toth, Florian (TU Wien)
  • Ganapathy, Arun Parkash (TU Wien)

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Viscous effects are commonly neglected in vibroacoustic modeling approaches. However, dissipation due to the oscillating viscous and thermal boundary layers can be crucial in many applications. Examples include small compression drivers and many micro-electro-mechanical systems (MEMS). While viscous and thermal effects in such systems can be analyzed accurately using a coupling between solid mechanics and the linearized compressible flow equations[1], this comes at a considerable computational cost. A computationally efficient modeling approach is to use the Helmholtz equation to model the fluid, and account for viscous and thermal effects by impedance-like boundary conditions [2, 3]. We extend the approach by Berggren et.al.[3] which is suitable for stationary walls. By incorporating interface motion into the derivation and making use of the analytically derived viscous forces in the boundary layer we derive an impedance-like coupling condition between solid mechanics and pressure acoustics. The formulation is valid for the frequency domain and an implementation is available in the open-source finite element software openCFS. The formulation is tested based on several validation examples, exploring the range of validity, e.g. in cases where two boundary layers merge. Furthermore, we use the formulation in realistic application examples of a MEMS device, demonstrating its usefulness and extreme computational efficiency in comparison to fully resolved linearized compressible flow equations. [1] H. Hassanpour Guilvaiee, P. Heyes, C. Novotny, M. Kaltenbacher, and F. Toth. A validated modeling strategy for piezoelectric MEMS loudspeakers including viscous effects. Acta Acustica, 7:24, 2023. [2] R. Bossart, N. Joly, and M. Bruneau. Hybrid numerical and analytical solutions for acoustic boundary problems in thermo-viscous fluids. Journal of Sound and Vibration, 263(1):69–84, 2003. [3] M. Berggren, A. Bernland, and D. Noreland. Acoustic boundary layers as boundary conditions. Journal of Computational Physics, 371:633–650, 2018.