Session: Nonlinear Ultrasonic Techniques for NDE

Paper Number: 170240

170240 - Second Harmonic Surface Waves in a Hyperelastic Half Space With Quadratic Nonlinearity 

Abstract: 

            This paper considers a half-space made of a hyperelastic solid with quadratic nonlinearity. As a time-harmonic surface wave of fundamental frequency propagates along the free surface of the half-space, it generates a resonant second harmonic surface wave whose amplitude grows with the propagation distance. By using the method of multi-scale expansion, an explicit solution to the second harmonic surface wave is obtained. It is seen from this solution that amplitude of the resonant second harmonic surface wave is at least one order of magnitude smaller than that of the fundamental frequency. Further, the second harmonic surface wave propagates in the same direction and with the same Rayleigh surface wave speed  as the fundamental surface wave. On the free surface, these two waves also have the same polarization. However, the second harmonic surface wave decays away from the free surface twice as fast as the primary surface wave does. Finally, amplitude of the second harmonic surface wave is proportional to a linear combination of three acoustic nonlinear acoustic parameters, which clarifies the long outstanding question of which acoustic nonlinearity parameter is being measured in surface wave experiments. These results can be used to interpret experimental measurement results when conducting surface wave experiments in nonlinear elastic materials.

Presenting Author: Jianmin Qu Stevens Institute of Technology

Presenting Author Biography: Dr. Jianmin Qu is professor at Stevens Institute of Technology

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