Dual Element Transducer Approach for Second Harmonic Generation and Material Nonlinearity Measurement of Solids in the Pulse-Echo Method

A planar stress-free boundary is known to destructively alter the nonlinear wave generation process including the second harmonic component. This is the reason why the harmonic generation measurements in the study of nonlinear fluids and solids have been limited to the through-transmission setup. Recently, we have found through acoustic modeling and simulation that a dual element transducer composed of the annular ring emitter and the inner disk receiver improves the second harmonic generation in the pulse-echo mode with the stress-free boundary. This paper utilizes a dual element transducer for nonlinearity parameter ( β ) measurements of solid specimens in the pulse-echo testing configuration. The theoretical derivation provides the received beam fields and the formula for β determination with all necessary corrections incorporating diffraction, attenuation and boundary reflection. The dual element transducer is applied to pulse-echo β measurements of aluminum alloy samples, and the results are found to be in good agreement with the through-transmission method.