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Fluid Layer Trapped Between a Plane, Circular Membrane and an Axisymmetrically Curved, Smooth Backing Wall: Analytical Model of the Dynamic Behaviour

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Current electrostatic transducers are designed with a planar perforated backing electrode while nowadays some authors suggest that a non planar backing wall would enhance their performances. Accurate analytic results for these new shapes of backing electrode are not available until now whereas current applications (metrology, miniaturisation) arise which need more refined modelling. Therefore the present paper aims at providing an analytical description of the strong coupling between a fluid layer trapped between an axisymmetrically curved smooth backing wall and a circularvibrating membrane (the thickness of the fluid layer depends on the radial coordinate) using modelling wherein viscosity, heat conduction, inertia and compressibility of the fluid are considered, beyond realistic boundary conditions (no slip condition and no temperature variations near the walls). Solutions are given as the sum of an expansion on eigenfunctions of the membrane in vacuo and an extended power series (using Frobenius method) to overcome the limitations of a standard electrical equivalent network analysis in the frequency range of interest (up to 100 kHz for circular membranes approximately one millimetre in diameter). The results obtained provide tools for optimising the design of such small electrostatic transducers.
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Document Type: Research Article

Publication date: May 1, 2008

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  • Acta Acustica united with Acustica, published together with the European Acoustics Association (EAA), is an international, peer-reviewed journal on acoustics. It publishes original articles on all subjects in the field of acoustics, such as general linear acoustics, nonlinear acoustics, macrosonics, flow acoustics, atmospheric sound, underwater sound, ultrasonics, physical acoustics, structural acoustics, noise control, active control, environmental noise, building acoustics, room acoustics, acoustic materials, acoustic signal processing, computational and numerical acoustics, hearing, audiology and psychoacoustics, speech, musical acoustics, electroacoustics, auditory quality of systems. It reports on original scientific research in acoustics and on engineering applications. The journal considers scientific papers, technical and applied papers, book reviews, short communications, doctoral thesis abstracts, etc. In irregular intervals also special issues and review articles are published.
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