Analysis of annular phased array transducers for ultrasonic guided wave mode control

Exact and asymptotic analyses of annular phased array transducers (PAT) for elastic guided wave mode selection are presented. For the purpose of analysis, the transducer-substrate interaction is formulated in terms of a three-dimensional analogy to filters as applied one-dimensionally in areas such as signal processing and control theory. This enables the deduction of most of the properties of the annular array purely from the Fourier analysis of any actuating function that represents the loading due to the transducer. A generalized mathematical model of the actuating function due to the annular PAT is constructed. The Fourier spectrum is analyzed for resonances in the wavenumber domain. Formulas for phase and time delays are presented. The phenomena of outgoing and incoming waves are also studied. Numerical analysis of the wavenumber spectrum for the annular PAT with a finite number of elements is performed to further illustrate the results deduced from exact and asymptotic analyses. Finite element simulations are presented to further verify the phenomena predicted through the wavenumber spectrum analysis.