Simulation of self-focusing by an array on a crack in an immersed specimen

Ming Zhang, Jan D. Achenbach*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


An ultrasonic measurement model is developed to simulate self-focusing by a curved array of transducers on an interior crack. The far field radiated by each transducer element is modeled by rays with a Gaussian distribution of amplitudes over the beam width. The ray tracing method is used to determine the focused wave field in the immersed specimen and the travel times from each array element to the crack. The self-focusing array is modeled for both sonification and reception focusing. The transducers in the array are excited with the appropriate time delays to achieve sonification focusing. After the incident wave field on the crack has been obtained, the crack opening volume is calculated. For a pair of transducers, a reciprocal identity for two media in contact is used to determine the amplitudes of signals scattered back from the crack. The field transmitted and received by the entire array is obtained by superposition. Reception focusing is used to adjust the differences in signal arrival times for in-phase signal summation. Considerable signal amplification can be achieved by the self-focusing procedure, as has been shown by comparison of scattered fields.

Original languageEnglish (US)
Pages (from-to)9-18
Number of pages10
Issue number1
StatePublished - 1999


  • Array
  • Crack
  • Scattering
  • Self-focusing

ASJC Scopus subject areas

  • Acoustics and Ultrasonics


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