Detection of material nonlinearity using nonlinear ultrasonic three-wave mixing technique

Abstract

This paper proposes a new nonlinear ultrasonic technique based on three-wave mixing to generate and measure third-order combined harmonics (TOCH) for detecting material nonlinearity in plate-like structures. This technique introduces three input ultrasonic waves with distinct frequencies to a nonlinear structure (e.g., Lattice-anharmonicity). The mutual interaction of these waves generates TOCH at mixing frequencies of input frequency components. The amplitudes of the generated TOCH and the input frequency components are used to estimate the cubic nonlinearity parameter and thereby based on it the associated the material nonlinearity. Here, the cubic nonlinearity parameter is defined as the third- and fourth-order elastic constants of the material. A theoretical model to predict the TOCH due to the mutual interaction of input waves in a nonlinear structure is developed. Further, the experimentally evaluated material nonlinearity of the aluminum specimen is compared with the material nonlinearity estimated by the theoretical model. When the phase matching and non-zero power flux conditions are satisfied, the amplitude of the third-order harmonics was observed to increases steeply with the propagation distance. Because material nonlinearity alters the third- and fourth-order elastic constants of the material, the proposed technique for measuring the TOCH can be used to identify the material nonlinearity more effectively. Attributable to the fact that the material nonlinearity alters the third- and fourth-order elastic constants of the material, the proposed nonlinear three-wave mixing technique is more effective in identifying the material nonlinearity.