Investigation of stress effect on combinational harmonics generation of low-frequency S0 Lamb wave

This study experimentally and numerically explores the effect of initial stresses on the generation of combinational harmonics due to the nonlinear mixing of low-frequency <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>S</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> Lamb waves. The experimental study considers different levels of uniaxial tensile stress. The results indicate that the sum combinational harmonic has a much higher sensitivity to the prestress level, compared to the corresponding acoustoelastic effect. In the numerical study, material nonlinearity is modelled through a 5-constant hyperelastic constitutive equation derived from Murnaghan’s strain energy function. The finite element (FE) simulation results for a quasi-one-dimensional FE model agree with analytical results for bulk-wave mixing, thereby validating the two-step computational procedure for simulating wave propagation in the presence of a prestress. The same procedure is applied to a three-dimensional FE model to investigate different biaxial prestress conditions. The results indicate the feasibility of using the nonlinearity parameter derived from measurements of combinational harmonics to identify the principal stress directions and magnitudes in biaxially prestressed structures, provided that measurements are carried out for a sufficient sampling of wave propagation directions.