Abstract Nonlinear ultrasonic guided wave has attracted increasing attention for its ultra-sensitive to detect the incipient damages in service material by analyzing the amplitude of second harmonic wave. However, the mainstream method of simulating the second harmonic generation (SHG) in nonlinear material is using finite element method with time-domain solver, which is extremely time-consuming and can hardly simulate the huge and complex structures. In this paper, we propose a flexible finite element method based on frequency solver to simulate the SHG. The primary wave field, the second harmonic wave field and the static component field are separately set. This method is realized in Comsol Multiphysics software, the case of the SHG in plate indicates that the calculation efficiency has been significantly improved in compare with the time domain solver, whereas the results of time-domain solver and frequency domain solver have good agreement with each other. This method can be easily applied in the SHG analysis in huge and complex structures. Moreover, the primary wave field, the second harmonic wave field and the static component field can be respectively presented in the post-processing to help provide more information about physical insight of SHG.
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