A spacing compensation factor for the optimization of guided wave annular array transducers

Transducer arrays can be utilized in ultrasonic guided wave applications to achieve preferential excitation of particular points on a dispersion curve. These arrays are designed according to the principles of wave interference and the influence of the wavelength excitation spectrum. This paper develops the relationships between the peak wavelength in the excitation spectra and the element spacing of linear comb and annular arrays. The excitation spectra are developed by applying Fourier and Hankel transforms to the spatial loading distribution functions of the comb and annular arrays, respectively. Although the peak wavelength of excitation of a comb array is typically assumed to be equal to the element spacing, it is shown that this can be an inaccurate assumption for annular arrays. The ratio of element spacing to the peak wavelength in the excitation spectrum is termed the spacing compensation factor, and is dependent on the number of array elements and the inner radius. It is determined that the compensation factor is negligible for comb arrays but is crucial for annular arrays in order to achieve optimal mode selection. Finite element analyses and experimental data are used to verify the calculations and demonstrate the significance of the compensation factor.