Christiansen, Thomas Lehrmann1; Hansen, Ole4; Thomsen, Erik Vilain1; Jensen, Jørgen Arendt6
1 Department of Micro- and Nanotechnology, Technical University of Denmark2 MEMS-AppliedSensors, Department of Micro- and Nanotechnology, Technical University of Denmark3 Department of Physics, Technical University of Denmark4 Experimental Surface and Nanomaterials Physics, Department of Physics, Technical University of Denmark5 Silicon Microtechnology, Department of Micro- and Nanotechnology, Technical University of Denmark6 Department of Electrical Engineering, Technical University of Denmark7 Biomedical Engineering, Department of Electrical Engineering, Technical University of Denmark8 Center for Fast Ultrasound Imaging, Center, Technical University of Denmark
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.
Journal of the Acoustical Society of America, 2014, Vol 135, Issue 5