JSV: Dynamic behaviour of a planar micro-beam loaded by a fluid-gap

JSV: Dynamic behaviour of a planar micro-beam loaded by a fluid-gap

A. Novak, P. Honzik & M. Bruneau (2017), “Dynamic behaviour of a planar micro-beam loaded by a fluid-gap: Analytical and numerical approach in a high frequency range, benchmark solutions”, Journal of Sound and Vibration. Vol. 401(2017), pp. 36-53.

  • In this paper three analytical models for three types of micro-beams surrounded by thin air slits is presented. As the following figure shows, the three micro-mechanical system consist of a rigid planar beam attached to one end of a flat spring (a), a thin elastic one-dimensional planar beam clamped to one end (b), a suspended rigid planar beam (c).

    Visco-thermal losses of the peripheral slit between the beam and the wall (see the following sketch) must be taken into account.

    The following figure shows a comparison of the displacement/pressure sensitivity between the numerical model (dots) and the proposed analytical one (solid line) for a rigid one-dimensional flat beam suspended at both ends on non-rigid walls (spring-like boundaries) when excited with a uniform pressure on the top of the beam.


  • 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.

  • @article{novak2017dynamic,
    author={Novak, A and Honzik, P and Bruneau, M},
        title={Dynamic behaviour of a planar micro-beam loaded by a fluid-gap: Analytical and numerical approach in a high frequency range, benchmark solutions},
        journal={Journal of Sound and Vibration},
        volume={401},
        number={0},
        pages={36-53},
        year={2017},
        publisher={Elsevier}
    }
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