TY - JOUR
T1 - Ultrasonic field modeling
T2 - A comparison of analytical, semi-analytical, and numerical techniques
AU - Kundu, Tribikram
AU - Placko, Dominique
AU - Rahani, Ehsan Kabiri
AU - Yanagita, Tamaki
AU - Dao, Cac Minh
N1 - Funding Information:
manuscript received april 24, 2010; accepted august 30, 2010. Grant sponsor: aFosr: Fa9550-08-1-0318. This research was partially supported by the air Force office of scientific research (aFosr) grant (#Fa9550-08-1-0318), program manager is dr. david stargel. The results and conclusions presented here are those of the authors and do not represent the views of aFosr.
PY - 2010/12
Y1 - 2010/12
N2 - Modeling ultrasonic fields in front of a transducer in the presence and absence of a scatterer is a fundamental problem that has been attempted by different techniques: analytical, semi-analytical, and numerical. However, a comprehensive comparison study among these techniques is currently missing in the literature. The objective of this paper is to make this comparison for different ultrasonic field modeling problems with various degrees of difficulty. Four fundamental problems are considered: a flat circular transducer, a flat square transducer, a circular concave transducer, and a point focused transducer (concave lens) in the presence of a cavity. The ultrasonic field in front of a finite-sized transducer can be obtained by Huygens-Fresnel superposition principle that integrates the contributions of several point sources distributed on the transducer face. This integral which is also known as the Rayleigh integral or Rayleigh-Sommerfeld integral (RSI) can be evaluated analytically for obtaining the pressure field variation along the central axis of the transducer for simple geometries, such as a flat circular transducer. The semi-analytical solution is a newly developed mesh-free technique called the distributed point source method (DPSM). The numerical solution is obtained from finite element analysis. Note that the first three problems study the effect of the transducer size and shape, whereas the fourth problem computes the field in presence of a scatterer.
AB - Modeling ultrasonic fields in front of a transducer in the presence and absence of a scatterer is a fundamental problem that has been attempted by different techniques: analytical, semi-analytical, and numerical. However, a comprehensive comparison study among these techniques is currently missing in the literature. The objective of this paper is to make this comparison for different ultrasonic field modeling problems with various degrees of difficulty. Four fundamental problems are considered: a flat circular transducer, a flat square transducer, a circular concave transducer, and a point focused transducer (concave lens) in the presence of a cavity. The ultrasonic field in front of a finite-sized transducer can be obtained by Huygens-Fresnel superposition principle that integrates the contributions of several point sources distributed on the transducer face. This integral which is also known as the Rayleigh integral or Rayleigh-Sommerfeld integral (RSI) can be evaluated analytically for obtaining the pressure field variation along the central axis of the transducer for simple geometries, such as a flat circular transducer. The semi-analytical solution is a newly developed mesh-free technique called the distributed point source method (DPSM). The numerical solution is obtained from finite element analysis. Note that the first three problems study the effect of the transducer size and shape, whereas the fourth problem computes the field in presence of a scatterer.
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U2 - 10.1109/TUFFC.2010.1753
DO - 10.1109/TUFFC.2010.1753
M3 - Article
C2 - 21156375
AN - SCOPUS:78650399761
SN - 0885-3010
VL - 57
SP - 2795
EP - 2807
JO - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
JF - IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control
IS - 12
M1 - 5610565
ER -