focusedBowlONeil
Compute O'Neil's solution for focused bowl transducer.
Syntax
[p_axial, p_lateral] = focusedBowlONeil(radius, diameter, velocity, ... axial_position, lateral_position, frequency, sound_speed, density)
Description
focusedBowlONeil
calculates O'Neil's solution (O'Neil, H. Theory of focusing radiators. J. Acoust. Soc. Am., 21(5), 516-526, 1949) for the axial and lateral pressure amplitude generated by a focused bowl transducer when uniformly driven by a continuous wave sinusoid at a given frequency and normal surface velocity.
The solution is evaluated at the positions along the beam axis given by axial_position
(where 0 corresponds to the transducer surface), and lateral positions through the geometric focus given by lateral_position
(where 0 corresponds to the beam axis).
Note, O'Neil's formulae are derived under the assumptions of the Rayleigh integral, which are valid when the transducer diameter is large compared to both the transducer height and the acoustic wavelength.
Example:
% define transducer parameters radius = 140e-3; % [m] diameter = 120e-3; % [m] velocity = 100e-3; % [m/s] frequency = 1e6; % [Hz] sound_speed = 1500; % [m/s] density = 1000; % [kg/m^3] % define position vectors axial_position = 0:1e-4:250e-3; % [m] lateral_position = -15e-3:1e-4:15e-3; % [m] % evaluate pressure [p_axial, p_lateral] = focusedBowlONeil(radius, diameter, velocity, ... frequency, sound_speed, density, axial_position, lateral_position); % plot figure; subplot(2, 1, 1); plot(axial_position .* 1e3, p_axial .* 1e-6, 'k-'); xlabel('Axial Position [mm]'); ylabel('Pressure [MPa]'); subplot(2, 1, 2); plot(lateral_position .* 1e3, p_lateral .* 1e-6, 'k-'); xlabel('Lateral Position [mm]'); ylabel('Pressure [MPa]');

Inputs
radius |
transducer radius of curvature [m] |
diameter |
diameter of the circular transducer aperture [m] |
velocity |
normal surface velocity [m/s] |
frequency |
driving frequency [Hz] |
sound_speed |
speed of sound in the propagating medium [m/s] |
density |
density in the propagating medium [kg/m^3] |
axial_position |
vector of positions along the beam axis where the pressure amplitude is calculated [m] |
lateral_position |
vector of positions along the lateral direction where the pressure amplitude is calculated [m] |
Outputs
p_axial |
pressure amplitude at the positions specified by axial_position [Pa] |
p_lateral |
pressure amplitude at the positions specified by lateral_position [Pa] |
See Also
mendousse