## 2 The Effects of Temperature on UGW  
Temperature has an impact on the density, Young's modulus, and Poisson's ratio. Q235 steel pipes are commonly used for transporting low-pressure fluids. They are produced in large quantities and have a wide range of applications. According to the Chinese national standards [38], their chemical composition is shown in Table 1.  
JMatPro, the Java-based Materials Properties software, is a comprehensive simulation tool used to calculate the phase diagrams, physical properties, and thermodynamic properties of metal materials. It includes various built-in modules for materials such as steel, aluminum alloys, magnesium alloys, and titanium alloys. In this paper, JMatPro7.0 is employed to analyze the influence of temperature on the properties of Q235 steel. The specific material parameters should align with those used in the experiment. Based on the Q235 pipeline manufacturer's test report, the chemical composition is primarily Fe = 98.925%, Mn = 0.55%, Si = 0.26%, C = 0.18%, P = 0.040%, and S = 0.045%. These parameters are input into JMatPro, with the upper temperature limit set to 100 \({}^{\circ}\)C and the lower limit to 24 \({}^{\circ}\)C. The resulting temperature-dependent property curves are shown in Figure 1. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Material Grade**} & \multicolumn{4}{c}{**Chemical Composition (Mass Fraction)/\%, Not Exceeding**} \\ \cline{2-6}  & **C** & **Si** & **Mn** & **P** & **S** \\ \hline Q235 & 0.22 & 0.35 & 1.40 & 0.045 & 0.050 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Chemical composition of Q235. Figure 1: Influence of temperature change on various material properties: (**a**) Young’s modulus; (**b**) Poisson’s ratio; (**c**) density. Figure 1 shows the curves of the Young's modulus, Poisson's ratio, and density as they vary with temperature. The Young's modulus and density decrease gradually with increasing temperature, while the Poisson's ratio increases. It is clear that the effects of temperature on these material properties are linear. The propagation behavior of guided waves in pipelines is governed by the Navier equations,  
\[\mu\
abla^{2}\mathbf{u}+(\lambda+\mu)\
abla\
abla\cdot\mathbf{u}=\rho\frac{\partial^{2} \mathbf{u}}{\partial t^{2}}. \tag{1}\]  
Considering the boundary conditions of the pipeline,  
\[\sigma_{rr}=\sigma_{r\theta}=\sigma_{rz}=0,\quad r=R_{i},\quad r=R_{o}, \tag{2}\]  
it is possible to derive the dispersion characteristic equation of guided waves in the pipeline:  
\[ \begin{bmatrix}C_{11}&C_{12}&\cdots&C_{16}\\ C_{21}&C_{22}&\cdots&C_{26}\\ \vdots&\vdots&\ddots&\vdots\\ C_{61}&C_{62}&\cdots&C_{66}\end{bmatrix}\begin{bmatrix}A\\ B\\ \vdots\\ B_{3}\end{bmatrix} = \begin{bmatrix}0\\ 0\\ \vdots\\ 0\end{bmatrix} , \tag{3}\]  
where \(C_{ij}\) is a coefficient matrix of \(A,B,A_{1},B_{1},A_{3},B_{3}\). The determinant of the coefficient matrix, \(\|C_{ij}\|=0(i,j=1,2,\cdots,6)\), represents the dispersion equation of guided waves in a free pipe within a vacuum medium [39]. This paper focuses on analyzing the impact of temperature on material properties. As such, only the fully elastic isotropic material model is considered in this analysis. Due to the inability to obtain an analytical solution for the characteristic equation of guided waves, only numerical solutions can be achieved. Therefore, this paper utilizes COMSOL5.6 simulation software to analyze the propagation behavior of UGW across various temperature fields. The cross-sectional dimensions of the pipeline are consistent with those of the experimental pipeline in this study and conform to the Chinese national standards [40]. The pipe diameter is set to \(\phi 219\) mm, with a wall thickness of 6 mm. To minimize simulation time without compromising the analysis, the pipe length is set to 3 m. For the inspection of pipelines, it is optimal to select a mode that is single and exhibits minimal dispersion; thus, the T (0,1) mode, characterized by being single and nondispersive, is the preferred choice.