## 5 Conclusions and Discussion  
In this paper, a second-order generalized Maxwell viscoelastic model was developed to characterize the behavior of fluororubber in small-strain conditions. This model was extended to high-frequency simple harmonic vibration, allowing for a detailed description of the relationship between mechanical properties and acoustic parameters. The model effectively explained the observed frequency shift and rapid attenuation phenomena that occurred during the propagation of ultrasonic waves through the fluororubber. These insights are crucial for understanding how material degradation in fluororubber affects its ultrasonic properties. Building on this model, a nonlinear fitting-based ultrasonic nondestructive evaluation (NDE) method was proposed to assess the mechanical property degradation of fluororubber. The method was tested through a controlled experiment involving sealing rings used in nuclear power plants, comparing the mechanical properties of both the used and unused sealing rings. Mechanical tensile tests and electron microscopy analysis provided additional validation. The results showed a significant increase in the elastic modulus of the used sealing rings (2.97 \(\pm\) 0.15 GPa) compared with the unused ones (2.75 \(\pm\) 0.22 GPa), in line with the mechanical tensile test findings. Furthermore, the unused sealing rings exhibited a noticeably higher sound attenuation coefficient, corroborating the hypothesis that ultrasonic wave attenuation increases as the material degrades. The proposed model and detection method offer a promising approach for evaluating the mechanical properties of fluororubber through ultrasonic techniques. The tensile strength and elastic modulus of fluororubber can be estimated using its elastic coefficients, while its compressibility can be inferred from the relaxation time and the acoustic attenuation coefficient. This provides a robust framework for the ultrasonic quantitative evaluation of fluororubber degradation. This methodology can be particularly useful in industries where material integrity and longevity are critical such as in nuclear power plants, aerospace, and automotive applications. The investigation of ultrasonic attenuation and frequency shifts due to degradation in fluororubber is a significant contribution to ultrasonic nondestructive evaluation (NDE). Past research has explored similar phenomena in elastomers, but often without the detailed modeling of viscoelastic properties affecting ultrasonic wave propagation. The proposed model allows for a more precise understanding of how material degradation--manifested through changes in the elastic modulus and viscosity--affects ultrasonic wave velocity and attenuation. This advancement is crucial for improving the precision of ultrasonic NDE techniques, particularly in high-risk applications like nuclear power plants, where material failure can lead to severe consequences. The decision to describe the stress-strain behavior of fluororubber using the generalized Hooke's law, as opposed to more complex hyperelastic models, was based on the small-strain condition (\(\varepsilon<5\%\)) encountered in this study. Hyperelastic models, such as Mooney-Rivlin, Yeoh, Ogden, and others, are typically employed for large strains (\(\varepsilon>30\%\)), which are not relevant for ultrasonic wave propagation, where the strain amplitudes are small. At small strains, rubber-like materials behave linearly, and the stress-strain relationship is well-represented by Hooke's law. This is consistent with the well-established understanding that the elastic response of rubber under small strains is essentially Hookean. Additionally, ultrasonic waves, being high-frequency vibrations, induce small deformations that are better captured by linear elasticity, making the use of complex, nonlinear hyperelastic models unnecessary.