Ultrasonic beam models: An edge element approach

Abstract

A new method, the edge element method, has been developed to numerically evaluate a variety of ultrasonic transducer beam models. The edge element technique divides the transducer surface into a web of sources consisting of radiating straight line elements whose individual contributions can be evaluated analytically. When all of these edge elements are summed, the wave field of the transducer can be obtained at any field point in the surrounding medium for a given ultrasonic frequency. To demonstrate the versatility of this approach, it is shown that edge elements can accurately model the wave fields radiated into a fluid by focused and unfocused transducers of circular and noncircular apertures.

Modeling the Ultrasonic Radiation of a Planar Transducer Through a Plane Fluid–Solid Interface

“…This model has been previously described [22] for incident wave fields in a single medium. To obtain the edge element model for a planar interface problem, the transducer surface is divided into a discrete number of small area elements.…”

“…Another method we consider, called the edge element method [22], divides the transducer surface into small area elements and makes a first-order approximation on the phase term of the original surface integral model. Through this phase approximation and Stokes' theorem, the two-dimensional surface integration of the surface integral expression can be reduced to two finite summations involving terms associated with the edges of the area elements.…”

Ultrasonic field modeling for immersed components using Gaussian beam superposition

“…Refs. [1][2][3][4][5][6]. Many of these approaches are based on the mathematical formulation of Huygens' principle [7], the Rayleigh-Sommerfield integral being a well-known outcome of this formulation.…”

Family of Quantum Sources for Improving Near Field Accuracy in Transducer Modeling by the Distributed Point Source Method

“…A list of more recent developments is given by Sha et al [6]. The pressure field in front of a planar transducer in a homogeneous isotropic fluid has been computed both in the time domain [5,7,8] and in the frequency domain [9][10][11][12][13][14]. In the frequency domain analysis, which is more popular, the transducers are assumed to be vibrating with constant amplitudes at certain frequencies, and the pressure fields in front of the transducers are computed.…”