Dynamic behaviour of a planar micro-beam loaded by a fluid-gap: Analytical and numerical approach in a high frequency range, benchmark solutions

Miniaturized vibrating MEMS devices, active (receivers or emitters) or passive devices, and their use for either new applications (hearing, meta-materials, consumer devices,…) or metrological purposes under non-standard conditions, are involved today in several acoustic domains. More in-depth characterisation than the classical ones available until now are needed. In this context, the paper presents analytical and numerical approaches for describing the behaviour of three kinds of planar micro-beams of rectangular shape (suspended rigid or clamped elastic planar beam) loaded by a backing cavity or a fluid-gap, surrounded by very thin slits, and excited by an incident acoustic field. The analytical approach accounts for the coupling between the vibrating structure and the acoustic field in the backing cavity, the thermal and viscous diffusion processes in the boundary layers in the slits and the cavity, the modal behaviour for the vibrating structure, and the non-uniformity of the acoustic field in the backing cavity which is modelled in using an integral formulation with a suitable Green's function. Benchmark solutions are proposed in terms of beam motion (from which the sensitivity, input impedance, and pressure transfer function can be calculated). A numerical implementation (FEM) is handled against which the analytical results are tested.