# Modal Analysis and Optimization of Tractor Exhaust System
## 4 Conclusions  
In this study, the vibration characteristics of the vertical exhaust system of a 90 HP tractor were analyzed using the finite element method. The main steps of the study are as follows: First, vibration measurements were performed on the existing exhaust system using an accelerometer, and regions with permanent deformations were identified. Based on these findings, a 3D model of the exhaust system was created using PTC Creo 3D software and transferred to the ANSYS Workbench environment for finite element modeling. As a result of the modal analysis performed in ANSYS, the natural frequencies and mode shapes of the system were determined. The analyses revealed the following:  
Effect of Geometric Changes: It was determined that changes in the geometry of the exhaust system (pipe diameter, length, bending angles, and connection points) affected the vibration behavior. These changes caused the system to vibrate at higher frequencies and increased its resistance to external forces. As [PERSON] et al. [27] also stated in their research, vibrations in exhaust systems are generally concentrated at low frequencies. This situation is consistent with the results of our study, once again confirming the effect of the geometric properties of the exhaust system on vibration behavior. Mode Shapes: Mode shapes provide information to the designer about which areas of the system undergo more deformation, indicating where to focus attention. In this way, the overall performance of the exhaust system has been improved. Modal Analysis Results: Modal analyses performed with ANSYS simulations showed that the natural frequency increased, especially in the fifth mode, and the deformation in critical regions decreased by 92%. These findings indicate that the exhaust system has been moved away from dangerous resonance frequencies. Experimental Verification: Measurements taken at 1200 rpm showed that some old frequencies disappeared and new frequency components emerged in the modified exhaust system. This situation indicates that the change in the exhaust system has changed the vibration characteristics of the vehicle. Modifications have reduced some vibrations but created new vibration sources. This also shows that the changes in the exhaust system have affected the vibrations of the vehicle. The ANSYS 2023 R1 Workbench software, as verified by experimental studies, provides high accuracy, cost effectiveness, and time savings in the design of exhaust systems. Natural frequency analyses, in particular, are critical for optimizing system performance and preventing failures caused by unwanted vibrations. For these analyses to provide  
Figure 15: Experimental vibration measurement graph for modified exhaust at 1200 rpm. reliable results, a realistic numerical model of the exhaust system is essential. The structural modifications made were verified by computer simulations and experimental measurements on the actual exhaust system. These verifications show that the design changes made are effective not only theoretically but also in practical application. As in the study of [PERSON] et al. [29], a high agreement was observed between the data obtained as a result of two different modal analyses. This result shows that both experimental and numerical methods provide reliable and consistent results for preventing vibration-induced damage in tractor exhaust systems. These findings constitute an important reference point for solutions to vibration problems in other engineering systems with similar structural dynamics. In this context, the findings of the study once again demonstrate the critical importance of vibration analysis and structural improvements in the design of agricultural machinery and other heavy vehicles. It is considered that future studies will contribute to obtaining more comprehensive results by applying similar methods under different exhaust system and vibration conditions. Conceptualization, Writing--Review and Editing, Supervision, A.T.; Methodology, Resources, Analysis, H.S.