Transient Wave Field Calculation for Ultrasonic Transducers Using Integral Transform Methods

Kuehnicke, Elfgard; Voelz, Uwe

doi:10.1007/978-1-4419-8588-0_55

Cited by 10 publications

(6 citation statements)

References 7 publications

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“…The results are spherical waves and a directivity function of the point source. Already in a distance of about one wavelength, such an approximation agrees with an exact calculation [8,9] and thus it is much more practicable than a far-field approximation. The asymptotic approximation of the stress component r zz due to any source and receiver functions is described in general by the following equation:…”

Section: Calculation Of the Single Array-element Fieldmentioning

confidence: 90%

“…Therefore, even a small number of harmonic sound fields yields sufficient results. In [8,9], this optimized approximation method was introduced and evaluated for a solid half-space by means of an exact method basing on transient Green's functions. …”

Section: Calculation Of the Transient Field For The Whole Arraymentioning

confidence: 99%

“…Calculations by this approach are given for the sound field of angle beam probes in [6] and for the sound field in the eye, which is a natural multi-layered problem, in [7]. In [8,9], an optimized approximation method to calculate the transient sound field was introduced. For a solid half-space, the approach was evaluated by an exact calculation of a transient field by means of the generalized ray theory.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Plane arrays – Fundamental investigations for correct steering by means of sound field calculations

Kühnicke

2007

Wave Motion

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Section: Calculation Of the Single Array-element Fieldmentioning

confidence: 90%

Section: Calculation Of the Transient Field For The Whole Arraymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Plane arrays – Fundamental investigations for correct steering by means of sound field calculations

Kühnicke

2007

Wave Motion

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“…Two main theoretical methods have been proposed to evaluate the effects of excitation sources on guided wave excitation: the classical integral transform method [17][18][19] and the normal mode expansion (NME) method [20][21][22]. The integral transform methods, such as the Fourier transform, have been developed to solve partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Source Influence on Guided Wave Excitation in Cylindrical Structures Using Spatial Fourier Transform Method

et al. 2020

Journal of Sensors

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Guided wave transducers, such as electromagnetic acoustic transducers and piezoelectric transducers, generate multimode waves at a given excitation frequency in a cylindrical structure, making it difficult to detect flaws in such structures. To accurately identify the flaws, the transducers must be well designed to suppress the nonaxisymmetric modes. Instead of using the normal mode expansion (NME) method, a spatial Fourier transform (SFT) method is proposed to analyze source influence on the guided wave excitation in a cylindrical structure. A two-dimensional SFT is performed on the spatial distribution function of the surface loading applied to the cylindrical structure. The spatial distribution function is represented in a cylindrical coordinate system. The circumferential-direction SFT is carried out from the angular coordinate to the circumferential orders of the guided wave modes. The axial-direction SFT is carried out from the axial coordinate to the wavenumbers of the guided wave modes. The results of the two-dimensional SFT represent guided wave excitation capabilities for different circumferential orders and wavenumbers. The specific surface loading conditions on the outer surface of a pipe are analyzed to predict source influence on the guided wave excitation. The results are consistent with those obtained using the NME method. Experiments corresponding to the specific surface loading conditions are carried out on a stainless steel pipe. The results confirm the effectiveness of the SFT method.

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“…Several mathematical models describe the sound field of a point source on the surface of a half-space (e.g. [3] & [4]). The dynamic Green's functions describe the transient time function of the complete displacement field of a point force with all excited wave modes considered.…”

Section: Introductionmentioning

confidence: 99%

Four-dimensional directivity pattern for fast calculation of the sound field of a phased array transducer

Voelz

2012

2012 IEEE International Ultrasonics Symposium

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A new approach is presented for an efficient calculation of the complete four-dimensional wave propagation in a transversely isotropic elastic half-space excited by a normal oriented impulsive point force. The sound field will be represented by the dynamic Green's functions for the particle displacement. The Green's functions will be derived by a solution of the elastodynamic wave equation with integral transform methods applying the Cagniard-de Hoop-method.We transform the Green's functions into a four-dimensional directivity pattern by normalizing the time axis. The formulation of the directivity pattern provides a very short calculation time for the complete four-dimensional sound field of a rectangular transducer element of a phased array probe using a point source synthesis. The calculation results in a complete transient time function for the three spatial directions of the particle movement in each point of the half-space. The complete time function of the three-dimensional sound field of a phased array transducer can be calculated by a convolution with the measured time function of the probe and the superposition of the delayed sound fields of multiple transducer elements. This approach provides an efficient method for optimizing the delay laws in phased array applications with consideration of all excited wave modes.We present the derivation of the four-dimensional directivity pattern and calculate sample simulations for the sound field of a phased array probe. Further we compare the modeling with the wave propagation in solids measured by an electrodynamic probe.

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Transient Wave Field Calculation for Ultrasonic Transducers Using Integral Transform Methods

Cited by 10 publications

References 7 publications

Plane arrays – Fundamental investigations for correct steering by means of sound field calculations

Plane arrays – Fundamental investigations for correct steering by means of sound field calculations

Analysis of Source Influence on Guided Wave Excitation in Cylindrical Structures Using Spatial Fourier Transform Method

Four-dimensional directivity pattern for fast calculation of the sound field of a phased array transducer

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