# A Feasibility Study for a Nonlinear Guided Wave Mixing Technique
## 5 Conclusions  
The main purpose of this study is the theoretical and experimental verification of a guided wave mixing technique. The biggest advantage of the mixing technique is the reduction of system nonlinearity. Because the system nonlinearity is not what a user wants, it interrupts the evaluation. We can expect clear nonlinearity variation if the measured nonlinearity contains less system nonlinearity. A part of bulk wave mixing theory was applied for simple or assumed guided wave signals. In order to simplify the guided wave mixing theory study, wave structure was considered. In-plane and out-of-plane dominant displacements for each guided wave were considered as longitudinal and transverse waves in a bulk wave.  
It was theoretically and experimentally verified that a certain frequency ratio must be considered for mixing. The guided wave mixing result showed the same tendency as the phase matching mode result, but the guided wave mixing technique had better sensitivity for nonlinear variation, because it has less system nonlinearity. Because of the experimental difficulty, the experimental result contains a large error, so repeated and accurate experiments are necessary. Moreover, nonlinearity variation was only evaluated according to distance. For field applications, experiments with micro-damage, such as that from corrosion, are essential. The significant results in this study are as follows:  
In this study, guided wave mixing equations and terms such as frequency ratio and mode are derived, and calculated successfully.  
The experimental results and the theoretical expectation matched well. The mixing signal only detected the calculated frequency ratio condition.  
Comparison of the results between the conventional technique and guided wave mixing technique indicates that the guided wave mixing technique has less system nonlinearity and more sensitive nonlinear variation.  
The final result of this study is that the guided wave mixing technique is the proper method for nonlinear evaluation, compared with the conventional technique, because less system nonlinearity is included.  
The nonlinear ultrasonic technique used in this study is used by many researchers as an innovative method that can detect micro-defects, but it was used without considering the nonlinearity of the equipment. Analyzing only the nonlinearity of the material without considering the nonlinearity of the system cannot guarantee the reliability of the results. The guided ultrasonic mixing technique that can reduce system nonlinearity is expected to decrease experimental errors and analyze micro-defects in materials more quantitatively.  
[PERSON] and [PERSON] designed and performed the experiments. [PERSON] and [PERSON] conceived the original idea. [PERSON] developed the theory, and performed the computations with support from [PERSON] and [PERSON] verified the analytical methods. [PERSON] wrote the draft study, [PERSON] completed the final study, and [PERSON] made the final review. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2019R1A5A808320112).  
The authors declare no conflict of interest.