title: Modal radiation patterns of baffled circular plates and membranes.
abstract: 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 radiation pattern 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.
authors.affiliation: Department of Micro- and Nanotechnology, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark.
authors.forename: Thomas Lehrmann
authors.initials: TL
authors.lastname: Christiansen
authors.affiliation: Department of Micro- and Nanotechnology, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark.
authors.forename: Ole
authors.initials: O
authors.lastname: Hansen
authors.affiliation: Department of Micro- and Nanotechnology, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark.
authors.forename: Erik Vilain
authors.initials: EV
authors.lastname: Thomsen
authors.affiliation: Center for Fast Ultrasound Imaging, Department of Electrical Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark.
authors.forename: Jørgen Arendt
authors.initials: JA
authors.lastname: Jensen
mesh_terms: D000162:Acoustics; D000465:Algorithms; D003198:Computer Simulation; D004867:Equipment Design; D008420:Manufactured Materials; D008567:Membranes, Artificial; D008670:Metals; D008962:Models, Theoretical; D009038:Motion; D013016:Sound; D014732:Vibration
chemical_list: D008567:Membranes, Artificial; D008670:Metals