We present a modelling strategy based on the finite element method to describe flexible, piezoelectric structures surrounded by a compressible fluid, including viscosity. Non-conforming interfaces based on the Mortar method are used to couple the different physical domains. Finally, we present an application example of a piezoelectrically actuated MEMS structure to illustrate the modeling procedure and the impact of viscous effects.

In modeling fluid–solid interaction (FSI), considering the impact of fluid compressibility is necessary to describe sound propagation. Furthermore, in micro‐scale, fluid viscosity is important. We present a finite element formulation for modeling a flexible solid coupled to a compressible viscous fluid. We use the linearized Navier–Stokes equations for a Newtonian fluid and describe the linear elastic solid using the linearized balance of momentum. For coupling between fluid and solid, we develop a non‐conforming finite element formulation, and propose an estimation for the necessary penalty factor by applying a scaling approach. The formulation is validated based on several test cases for various material combinations and shows good agreement with analytical solutions. Further, Nitsche‐based and symmetrization‐free formulations are compared, and spatial convergence is studied. Finally, we present an application example of a miniature Helmholtz resonator, which depicts a notable impact of the solid interaction on the viscous flow. In sum, our study indicates the potential for widespread use of the presented numerical approach in modeling FSI in miniature systems.

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.

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.