The Second Harmonic Generation in Reflection Mode: An Analytical, Numerical and Experimental Study

  • Anne Romer
  • Jin-Yeon Kim
  • Jianmin Qu
  • Laurence J. Jacobs


The procedure to measure the second harmonic generation has typically been restricted to relatively simple setups such as through transmission of longitudinal waves or Rayleigh surface waves on one side of a component. Since these types of setups are not always applicable for in-service components, this research investigates the second harmonic wave generation in longitudinal and shear waves reflected from a stress-free surface. This particular measurement setup potentially provides information about the local damage state in an in-service component with only single-sided access. Therefore, this measurement setup is evaluated analytically, numerically and experimentally with an aluminum specimen as an example. The setup being considered proposes two possible measurement positions, where the second harmonic and the fundamental wave amplitude can be measured to determine the nonlinearity parameter of the specimen. This proposed “reflection mode” setup is first analyzed analytically, and then is implemented in a commercial finite element code, using increasing fundamental wave amplitudes to calculate the different values of the nonlinearity parameters. The results of the simulations verify the analytical results, when taking into account assumptions and approximations of the analytical solution procedure. Furthermore, these numerical finite element results provide further insights into the intricacies of the setup, including the need to avoid interaction with the diffracted waves. On the basis of these numerical results, a recommendation for the measurement position and angle is given. Finally, the nonlinearity parameters of two similar specimens with different levels of nonlinearity are experimentally measured with the proposed measurement setup, and the results show the potential of the single-sided determination of a change in acoustic nonlinearity using reflected bulk waves.


Nonlinear acoustics Second harmonic generation Reflection mode FE simulation 



The authors would like to acknowledge funding received from the DOE Office of Nuclear Energys Nuclear Energy University Programs. Anne Romer was supported by the Deutscher Akademischer Austauschdienst (DAAD) and the Studienstiftung des deutschen Volkes.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Anne Romer
    • 1
  • Jin-Yeon Kim
    • 1
  • Jianmin Qu
    • 2
  • Laurence J. Jacobs
    • 3
  1. 1.School of Civil and Environmental EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of Civil EngineeringNorthwestern UniversityEvanstonUSA
  3. 3.G.W. Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA

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