Inversion of acoustic nonlinearity parameter (beta) from nonlinear resonance ultrasound spectroscopy measurements

Abstract

The acoustic nonlinearity parameter (beta) is well known to be sensitive to lattice parameters and defects. There are several techniques which can measure this parameter such as laser interferometry, capacitance microphone, piezoelectric methods, dynamic acoustoelastic methods, etc. However, the instrumentation required is expensive and complex for some of these techniques. There are also limitations on geometry and surface finish of the samples. Nonlinear resonance ultrasound spectroscopy has been previously used to measure the classic and non-classical nonlinearity of materials. The current work presents a model which can be used to invert the acoustic nonlinearity parameter from nonlinear resonance measurements. A diverse group of solids including metals, and composites were chosen, and nonlinear resonance experiments were conducted to measure the frequency shift. A nonlinear vibration model built from first principles was used to relate the frequency shift to the acoustic nonlinearity parameter. It was also observed that the sign or phase of the parameter can also be measured using this technique. The measured acoustic nonlinearity parameters were found to be in good agreement with reference values obtained from literature.