Modal radiation patterns of baffled circular plates and membranes

Thomas Lehrmann Christiansen, Ole Hansen, Erik Vilain Thomsen, Jørgen Arendt Jensen

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The far field velocity potential and radiation pattern of baffled circular plates and membranes are found analytically using the full set of modal velocity profiles derived from the corresponding equation of motion. The derivation is valid for a plate or membrane subjected to an external excitation force, which is used as a sound receiver in any medium or as a sound transmitter in a
gaseous medium. A general, concise expression is given for the radiation pattern of any mode of the membrane and the plate with arbitrary boundary conditions. Specific solutions are given for the four special cases of a plate with clamped, simply supported, and free edge boundary conditions as well as for the membrane. For all non-axisymmetric modes, the velocity potential
along the axis of the radiator is found to be strictly zero. In the long wavelength limit, the radiationpattern of all axisymmetric modes approaches that of a monopole, while the non-axisymmetric modes exhibit multipole behavior. Numerical results are also given, demonstrating the implications
of having non-axisymmetric excitation using both a point excitation with varying eccentricity and a homogeneous excitation acting on half of the circular radiator.
Original languageEnglish
JournalJournal of the Acoustical Society of America
Issue number5
Pages (from-to)2523–2533
Publication statusPublished - 2014


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