## 5 Discussions and Numerical Results
### Comparative Analysis of Several Thermoelastic Theories  
In these paragraphs, the outcomes of the mathematical modeling of the problem are presented, and some comparisons with previous research are made to verify the framework that is recommended in this article. Also, the most significant deductions that can be derived from the discussions are presented. If all other effective factors remain constant, then the studied fields along the \(x\)-axis of the beam that is generated on a viscoelastic basis can be investigated if several different thermoelastic theories are used. As indicated in Section 2, some preceding theories of thermoelasticity can be obtained from the current model. First, if the thermal parameters vanish, i.e., \(\tau_{0}=K^{*}=0\), then the coupled theory of conventional thermoplastics (CTE) can be obtained, which predicts the infinite velocities of heat waves. Secondly, if the parameter \(K^{*}=0\) is omitted, [PERSON]'s theory (LS) can be obtained, including the relaxation time. Third, the type III GN-III model of [PERSON] and Naghdi is accessible when the relaxation time parameter \(\tau_{0}\) disappears, while the type II GN-II model is formed when the first term on the right side of the generalized heat equation is omitted (6). Finally, in the case of the thermoelastic model (MGTE), which includes the Moore-Gibson-Thomson equation, the thermal parameters are \(\tau_{0},K^{*}>0\). In addition to Figures 5-8, numerical results will also be shown in Tables 1-4 so that researchers in this field can easily compare their results to them. It is shown how the laser pulse heating changes the thermomechanical behavior of the microbial beams with the change of the thermoelastic model that is used by taking various values of the thermal constants \(\tau_{0}\) and \(K^{*}\) at the same values for time \(t=0.12\). It is clear from the numerical outcomes that the constant thermal factors \(\tau_{0}\) and \(K^{*}\) have a prominent effect on each field of physical journals. the CTE model, thermal waves move at an unlimited speed, in contrast to the considered advanced models, which travel at a restricted rate. At the beginning points, such as for temperature \(\theta\) and deformation \(u\), as well as at the peak places, such as for heat stress \(\sigma_{xx}\) and thermal deflection \(w\), the differences between the models can be observed. The numerical results in Tables 2-5 and Figures 7-10 show the differences between the predictions that were made by the new MGTE theory and those made by other thermoelastic models. According to the numerical analysis results, it is noted that the values of the physical fields that were predicted by the GN-III and CTE theories are much higher than the values that were predicted by the MGTE theory, as well as other generalized models of thermal elasticity. In addition, it is quite clear that the responses of the generalized thermoelastic model of type GN-III converge with the responses of the classical thermoelastic model (CTE), which does not decompose into heat as quickly as other generalized thermoelastic theories do. This shows the shortcomings of the GN-III model, which predicts the spread of thermal waves at unlimited speeds like the traditional model. When one is looking at the tables and figures, it can be seen that the effect of the relaxation coefficient in the MGTE and LS theories show a slight decrease in temperature change behavior. This displays the precision of the suggested MGTE model, which addresses the contradiction in the GN-III thermoelasticity model. The obtained results provide further evidence that the values of different physical domains will converge and behave similarly according to the LS, GN-II, and MGTE theories. The positions and behaviors of viscoelastic materials in response to variations in temperature and other physical variables are illustrated in both the images and the table. These differences were examined in the MGTE and LS models of thermoelasticity.