**Optimization of curved broadband arrays for pipe inspection** E. Kühnicke^{14}
^{}Institute for Solid-State Electronics; Dresden University of Technology (TU Dresden)^{76}, Dresden, Germany Ultrasonic Testing (UT), phased array, transducer, controlling mode, grating lobes, time harmonic sound field, transient field, modeling simulation, focusing
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In this paper a convex broadband array for pipe inspection is optimized in respect to size and shape and controlling mode by means of calculating the time harmonic and transient fields. The sound fields are calculated in water and in pipe wall. Since the middle element distance is about a half wavelength regarding to steel and about two wavelengths regarding to water, grating lobes exist in water delay. The angle of grating lobes depends on the middle distance of the elements and on excitation function. The magnitude of the grating lobes depends additionally on steering angle and on element width. It is demonstrated that grating lobes do not transfer into the pipe wall. However there is an energy loss for the sound field in the pipe wall that depends on the magnitude of the grating lobes in water. The comparison of time harmonic sound fields for different controlling modes yields to a good approximation value of the energy loss caused by the water side lobes. Further it is demonstrated that on the one hand, geometrical calculations are often not sufficient to determine the right controlling mode. (That means in this case an effective placing of the focus is impossible by means of a geometrical calculation.) On the other hand, the time harmonic field generally yields to an appropriate controlling mode. Hence, the optimization by means of the transient field is redundant. As a general conclusion, it is demonstrated that there is only a small difference between the transient sound field and the time harmonic sound field at center frequency of the broadband array. Thus the optimization of array parameters and of controlling mode can be done by means of the time harmonic sound field only.
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| Modelling and Signal Processing |

**Optimization of ultrasound broadband transducers for complex testing problems by means of transient and time harmonic sound fields** E. Kühnicke^{14} Dresden University of Technology (TU Dresden)^{76}, Dresden, Germany
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In previous works, two fast approaches are introduced to optimize the parameters of broadband transducers for multilayered complex structures; one is applied to simulate the time harmonic sound field while the other one is used to simulate the transient sound field for broadband excitation. The calculation of time harmonic sound field is based on Green's functions in a steepest descent approximation, a superposition of the fields of all point sources to get the field of the entire element and a separate calculation in each layer. The transient field is calculated by means of a harmonic synthesis - a superposition of the time harmonic fields for selected partial frequencies and a convolution with the excitation function. On examples, the optimization of the transducer parameters and of the measurement setup is demonstrated. The fitting procedure of the setup is done by calculating the time harmonic sound field. For this purpose, the relation between transient and time harmonic sound field has to be investigated. It is shown that there is a good agreement between the transient fields for different excitation functions and the time harmonic field at center frequency in case of transmission through one interface only. After the transmission through more interfaces, the higher frequencies are damped so that the center frequency shifts to a lower range. This is valid especially for transducers of high center frequencies. Therefore this frequency shift has to be determined by calculating the transient field before starting the optimization. The later optimization can be done by calculating the time harmonic sound field at the calculated center frequency. Thus the calculation of the time harmonic sound field is an efficient tool to optimize probe parameters and the measurement setup in each case.
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| Modelling and Signal Processing |