1 DYN 201 - ENGINEERING MECHANICS: DYNAMICS PROJECT REPORT “Bridge Prototype Stabilization using a Tuned Mass Damper” Team members: Mustafa Akıllı (042305043) Doğukan Kutlu (042305007) Ali Özkan (042305026) Ahmet Naim Şen (042305030) Emre Gergin (042304023) Umut Can Öztürk (042304020) Instructor: Prof. Dr. Dante Dorantes October 18 st , 2025 2 Table of Contents Project learning objectives ........................................................................................................ 3 Introduction ............................................................................................................................... 3 Frame Design, Construction , and Optimization ...................................................................... 4 Experiment, Measurements , and Calculations ........................................................................ 5 Construction of the Tuned Mass Damper (TMD) ................................................................. 8 Measurements and Calculations ............................................................................................. 10 Team members’ contributions ................................................................................................. 12 Conclusion ............................................................................................................................... 15 References ................................................................................................................................ 17 3 Project learning objectives The students are expected to be able to [1, 2]: 1. apply the concept of tuned mass damper to attenuate earthquake-like simulated vertical oscillations of the middle part of a bridge-like structure; 2. exploit student creativity and develop critical thinking skills by designing and building a wooden or plastic-made frame and their own proposed damping device at home conditions; 3. learn how to use a simple pixel-tracking software, and apply it in a video to track a point of the frame to generate an exponential decay-like graph from initial horizontal displacements; 4. Use the logarithmic decrement method to calculate basic vibration parameters for a single degree of freedom damped beam model, as well as analyze the results, and conclude on their findings and impressions on the experimental process 5. improve time management, teamwork, and proper experiment report writing skills. Introduction Bridges are flexible structures that can vibrate due to wind, traffic, or other external forces. Excessive vibrations can compromise stability, safety, and comfort. One of the most effective methods for reducing such vibrations is the use of Tuned Mass Dampers (TMDs). “The TMD is used as a mechanical absorber tuned for an explicit resonant frequency of the civil - like structure. The movement of the structure can be reduced by controlling the mechanical vibrations in the system”. (Enríquez-Zárate et al., 2019) A tuned mass damper (TMD) is a dynamic vibration control device added to a structure (e.g. building, tower, bridge) to reduce unwanted oscillations. It typically comprises: ● A secondary mass (a “damper mass”) ● A spring or elastic element ● A damping (energy dissipation) mechanism The idea is that the TMD is “tuned” such that its natural frequency is close (or equal) to one of the dominant vibration modes of the host structure. When the structure vibrates (due to wind, earthquake, or another dynamic excitation), the TMD moves (oscillates) in a controlled manner that counteracts the motion of the main structure, thereby reducing the amplitude of that vibration. In effect, the TMD introduces additional damping into the system by converting part of the vibrational energy into internal friction or other dissipative mechanisms in the damper. ( TMD Principles - ESM GmbH , 2020) 4 Frame Design, Construction, and Optimization Fig. 1. Photos of the team with the beam frame. The bridge frame is made of a 1.6 m (long) x 20 cm (wide) piece of poplar MDF, with two wheels securely fastened at one end, one at the top, and one at the bottom, allowing the beam to flex freely but preventing it from bouncing (see Figure 2 and Figure 3). The bridge frame is positioned 50 cm above the ground, allowing for the placement of a Tuned Mass Damper (TMD) device under the beam in the future, thereby providing space for coupling the beam-TMD oscillations. 5 Fig. 2. Bridge frame sketch. (basic design in SolidWorks) We initially assembled the fixed side of the beam using two wooden strips, securing them with nails and screws to ensure the stability of the structure and prevent any collapse. Next, we installed four 60 cm long supporting feet on the opposite side to provide balanced support for the beam. The wheels were carefully mounted at the center of the 20 x 25 cm pieces, and precise measurements were taken to ensure that the wheel clearance was exactly 50 cm from the ground, allowing smooth oscillation. During the assembly process, we encountered technical challenges, such as aligning the wheels and ensuring the stability of the supporting feet, which were promptly addressed with practical solutions. By resolving these issues, we successfully completed the construction while maintaining both structural integrity and functionality. This careful planning and problem-solving approach ensured that the bridge prototype was stable, fully functional, and ready for the next stage of testing and experimentation. The beam section was made from a sturdy material of our choice. The beam material, length, and cross-sectional area were chosen to allow the beam to be vertically deflected approximately 10 cm from its midpoint with one hand. Fig. 3. supported beam end. 6 Experiment, Measurements, and Calculations without TMD When using tracking software, we placed a black dot at the midpoint of the beam to track the oscillation, allowing the tracking software to easily follow it. During the video, the viewer plotted the data on the graph by following this black dot. We also displayed all the data below the graph as x and y coordinates. X represents the time period, and Y represents the beam's displacement. We selected the starting location and took 3 videos with different displacements. ( x = 11, x = 9 cm, x = 8 cm) Fig. 4. Applying “Tracker” software to track the red dot’s pixel in the structure and plot its graph. 7 Fig. 5. Close-up of the displacement plot for one initial displacement is 11 cm. Fig. 6. Close-up of the displacement plot for one initial displacement is 9 cm. 8 Fig. 7. Close-up of the displacement plot for one initial displacement is 8 cm. Equations: δ = ln x 1 x 2 ζ = δ / √ ❑ ω n = 2 π τ k = m beam ω n 2 c = 2 m beam ζ ω n Table 1. Measured parameters and calculation results without TMD. Beam’s mass: m beam = 1.7 kg x 0 [m] x 1 [m] x 2 [m] τ [s] δ ζ ω n [s -1 ] k [N/m] c [Ns/m] 0.11 0.056 0.038 0.133 0.39 0.062 47.2 3794 9.930 0.09 0.067 0.041 0.150 0.49 0.078 42.02 3000 11.14 0.08 0.062 0.040 0.152 0.44 0.070 41.44 2919 9.80 averaged values 0.070 43.56 3238 10.29 Choose two masses so that the base of the metal strip would be high enough for the end masses to oscillate freely. If we had used only one end mass, it might have touched the beam. We produced the weights ourselves on a lathe and chose 130 grams for each . We selected this value to make the TMD work close to the system’s critical point. Construction of the Tuned Mass Damper (TMD) At the beginning, we decided on the weights and the type of metal to use. For the metal strip, we used a stainless steel ruler about 50 cm long, but we changed the location of the weights and placed them 25 cm away from each other . The other parts of the damper were made of wood . We also planned to use a TMD (Tuned Mass Damper) with two end masses. We also planned to use a TMD (Tuned Mass Damper) with two end 9 masses. We chose two masses so that the base of the metal strip would be high enough for the end masses to oscillate freely. If we had used only one end mass, it might have touched the beam. Fig. 8. Photos of the construction and team while building TMD. The masses of all TMD components were as follows: each mass located 12.5 cm away from the center was 0.130 kg (total 0.260 kg), the metal strip with its base was 0.330 kg, and the bar and piston together were 0.175 kg. We also included the weight of screws and nails, because even small weights can affect the results. The total mass of the damper was _G = 0.765 kg. 𝑚 We decided to use liquid soap as the viscous damper because it was cheaper and had a more suitable viscosity. The whole setup process took us about a week . Choosing the right liquid for the damper and carefully making measurements took a lot of effort. We also faced several unexpected problems along the way that we had to solve immediately. 10 Fig. 9. a) TMD with two end masses, and b) Design in SolidWorks Table 2. Cost Table of Construction Bridge and TMD No. Component/material (and place where you acquired it) Cost 11 BRIDGE 1 MDF 104.7 TL 2 Fixed Wheels 60 TL 3 Felt 20 TL 4 (Frame Wood) 1219 TL 5 Poplar Plywood 306.88 TL 6 Drill bit 23.76 TL 7 Screws 20 TL TMD 8 Liquid Soap 84.95 TL 9 Oil 105 TL 10 Double-Sided Tape 150 TL 11 Plastic Container 80 TL 12 Balance Weights 350 TL 13 Steel Ruler 350 TL Total Cost 2.874,29 TL Measurements and Calculations with TMD We applied three different initial displacements, which are 𝑥 = 10 𝑐𝑚, 𝑥= 9 𝑐𝑚, 𝑥 = 8 𝑐𝑚, with a tuned mass damper (TMD). Fig.10. Close-up of the displacement plot with TMD for one initial displacement is 10 cm. 12 Fig.11. Close-up of the displacement plot with TMD for one initial displacement is 9 cm. Fig.12. Close-up of the displacement plot with TMD for one initial displacement is 8 cm. 13 When we examined these graphs, we saw that the time period increased as the wavelengths attenuated rapidly. The viscous damper also affected our graph, applying resistance to the beam from the bottom up. Consequently, we found that the Tuned Mass Damper (TMD) made a significant difference in reducing vibration during oscillation. Equations: δ = ln x 1 x 2 ζ = δ / √ ❑ ω n = 2 π τ k = m ω n 2 c = 2 m ζ ω n Table 3. Measured parameters and calculation results with TMD. Beam’s mass: m beam = 1.7 kg TMD’s mass: m TMD = 0.765 kg Total system mass: m = m beam 2 + m TMD = 1.615 kg x 0 [m] x 1 [m] x 2 [m] τ [s] δ ζ TMD ω n [s -1 ] k [N/m] c [Ns/m] 0.09 0.078 0.035 0.266 0.789 0.1250 23.65 902.9 9.638 0.11 0.092 0.045 0.267 0.714 0.1132 23.56 896.7 8.636 0.08 0.070 0.030 0.266 0.847 0.1340 23.64 902.9 10.339 averaged values with TMD 0.1241 23.62 900.8 9.538 averaged values without TMD (stage 2, Table 1) 0.070 43.56 3238 10.29 TMD performance efficiency (percent of attenuation) η = ζ TMD − ζ ζ ∙ 100 % = ¿ %77.3 Team members’ contributions During the first stage of the project, we held a total of six meetings, including two online sessions and four face-to-face meetings at MEF University. These meetings played a crucial role in coordinating the work and ensuring that each stage of the project was carefully planned and executed. During our discussions, we focused on design, material selection to build the frame, and the step-by-step construction process of the prototype. During the second stage of the project, we had 1 online and 5 face-to-face meetings. These meetings were really helpful for us because they allowed us to plan our work properly and stay in constant communication as a team. In the meetings, we focused on topics such as the overall design, material selection to build a Tuned Mass Damper, and the step-by-step construction process of the prototype. All team members actively participated in the second stage of the project, and the whole process was a great example of teamwork. Everyone took responsibility for specific tasks, supported each other, and shared the workload fairly. This helped us move faster, stay organized, and find solutions to any problems we encountered together. 14 During our meetings, we constantly shared ideas, discussed possible improvements, and made collective decisions about both technical and practical aspects of the project. Overall, 3 online meetings and 9 face-to-face meetings made the project much more efficient. The active participation and cooperation of every team member greatly improved our communication, collaboration, and project management skills. Fig. 13. Photo of all the team members during a video meeting. 15 Fig. 14. Photo of all the team members. Stage 1: ● Mustafa Akıllı: Responsible for report writing and doing research for design. ● Doğukan Kutlu: Responsible for process management, helping design, providing equipment, building structure, and report writing as the team leader. ● Ali Özkan: Responsible for designing, providing equipment, building structure, and report writing. ● Ahmet Naim Şen: Responsible for designing, providing equipment, and building structure. ● Emre Gergin: Responsible for report writing and doing research for design. ● Umut Can Öztürk: Responsible for report writing and doing research for design. 16 Stage 2: ● Mustafa Akıllı: Responsible for report writing and doing research for design, building structures. Working with the entire team. Effort to work together at every stage. ● Doğukan Kutlu: Responsible for project process management, helping design, providing equipment, helping teammates to use Tracker and obtaining data, building structure, and report writing as the team leader. Working with the entire team. Effort to work together at every stage. ● Ali Özkan: Responsible for designing, providing equipment, helping teammates to use Tracker and obtaining data, building structure, and report writing. Working with the entire team. Effort to work together at every stage. ● Ahmet Naim Şen: Responsible for designing, providing equipment, producing weights on a lathe, building structure, and report writing. Using the Tracker program and obtaining data. Working with the entire team. Effort to work together at every stage. ● Emre Gergin: Responsible for report writing and doing research for design, building structures. Helping design.Working with the entire team. Effort to work together at every stage. ● Umut Can Öztürk: Responsible for designing and building structures, responsible for report writing, helping design and teammates ,the measurement part of the construction and working with the entire team. Effort to work together at every stage. Stage 3: ● Mustafa Akıllı: Responsible for making research to optimize the prototype, report writing and making improvements on the prototype. Effort to work together at every stage. ● Doğukan Kutlu: Responsible for making research to optimize the prototype, report writing and making improvements on the prototype. Editing the final video. Effort to work together at every stage. ● Ali Özkan: Responsible for making research to optimize the prototype, report writing and making improvements on the prototype. Effort to work together at every stage. ● Ahmet Naim Şen: Responsible for making research to optimize the prototype, report writing and making improvements on the prototype. Tracking new videos of the prototype. Effort to work together at every stage. ● Emre Gergin: Responsible for making research to optimize the prototype, report writing and making improvements on the prototype. Effort to work together at every stage. ● Umut Can Öztürk: Responsible for making research to optimize the prototype, report writing and making improvements on the prototype. Effort to work together at every stage. Conclusions Stage 1: 17 In the first stage of the project, we focused on learning the basic skills needed to build a simple prototype using wooden parts and contour plates. This stage gave us our first real experience in turning theoretical knowledge into something practical. Building something with our own hands helped us understand that engineering design is not just about calculations on paper. During this process, we learned more about vibration and structural balance. Seeing how a real structure reacts to different forces helped us better understand the concepts of stability and damping. We also realized how important teamwork, communication, and collaboration are for the success of an engineering project. The construction process was both fun and educational. Taking part in every step—from measuring to assembling—kept us motivated and made learning more meaningful. By combining the measurement of existing structures with hands-on construction, we gained valuable practical experience. We think this first stage was really useful for us. We improved our technical skills and understood better how creative and solution-oriented engineering actually is. We also learned what to pay attention to during the design process and realized how even small mistakes can make a big difference. Through this project, we started to learn how to work as a team and how to think like engineers. Overall, it was a fun, educational, and valuable experience that helped us grow. Stage 2: During this project, we could not achieve a smooth oscillation when dropping the beam by hand. Our hands were vibrating slightly, so the initial position wasn't completely stationary. Moreover, the Tracker software employed approximate values in drawing the graphs, and hence our results were not 100% precise. Our system turned out to be underdamped as the damping ratio was less than the first prototype. From the experiment, we learned how to sense vibrations and read graphs with the Tracker program. We also learned about different types of wood, such as poplar plywood and hardwood, and compared their elasticity. After these experiments, we learned how important the tuned mass damper (TMD) is in reducing structural vibrations. During the first phase of the project, we chose which beam to use for the bridge. We built the ends of the beam with hardwood and fastened the structure tightly to prevent collapse. During the second phase, we added a bearing support on one side. This side had a certain amount of movement, preventing the beam from deforming. Throughout the experiment, we learned new physics concepts such as the spring constant, viscous damping coefficient, damping ratio, and damped natural frequency. We used all these concepts in calculations as well as when analyzing data acquired from Tracker. We also realized just how much we need accurate measurements. A slight miscalculation would definitely affect the result. It was enjoyable and interesting to complete this project.We had a lot of challenges, but we worked very well as our team. We all had a part to do, and we completed the work in collaboration and enthusiasm. It was a completely new and valuable experience for us since it was our initial physical prototype project. We faced a few issues while building the vibration damper. First of all, we had to determine which metal strip to use and how to attach the masses. Spending some time to position them so as to attain the optimum balance. The initial piston did not fit the beaker properly when setting up the viscous damper, and hence, we substituted both of them. We used soft soap gel initially, but found that its density wasn't satisfactory. We later switched to the sunflower oil, and this produced much better results with the measurements. 18 It wasn't difficult to tune the TMD itself, but finding materials and lining everything up proved difficult. We moved the positions of the masses a couple of times and learned what worked by trial and error. We also made several videos so we could more clearly observe the motion. After a couple of tries, we managed to get clear graphs showing that the vibration had been minimized by the TMD. If we were to improve the system, we might try using a denser liquid or larger masses in order to produce more damping. Overall, this project helped us a lot as engineering students. We were able to apply concepts of physics in real experiments and learn how to solve problems sequentially. Seeing the vibration of the beam decrease after inserting the TMD was rewarding because it proved that our design worked. We also knew that good communication skills, patience, and cooperation are just as important as technical skills. Stage 3: Our third stage was entirely focused on solving the problems we encountered in the second stage. In our initial measurements, we realized that the Tuned Mass Damper (TMD) we built wasn't very successful at reducing the oscillations. The graphs we got from the Tracker program were also very inconsistent and erroneous. Because of this, we thought about how we could make the system more efficient and decided to make some fundamental changes. We started with the masses to increase the damping. We increased the weights to 130 grams and repositioned them closer together to intensify the effect. On the viscous damper side, we took more drastic steps; we found a new container that was both wider and taller so the piston could move freely without getting stuck. We also tried liquid soap instead of the old fluid, hoping its higher viscosity would increase the damping. After these changes, the new measurements we took showed that the system worked more efficiently, just as we expected. The liquid soap, in particular, created a better resistance against the piston's movement, and we saw that the oscillations were significantly reduced. With this new, positive data, we reorganized our report and added the clear graphs we obtained. This optimization process taught us, in a practical way, how important it is to try different parameters and make adjustments when solving an engineering problem. We experienced firsthand that making a system efficient requires a constant cycle of trial and error and analysis. References 1) J. J. Connor and S. Laflamme, Structural motion engineering . Cham, Switzerland: Springer, 2014. 19 2)D. Dorantes, "Instructions for Project Stage 2 'Bridge Prototype Stabilization using a Tuned Mass Damper'," MEF University, 2025. 3)D. Dorantes, "Lecture notes from the course DYN 201 'Engineering Mechanics: Dynamics'," MEF University, 2025. 4)J. Enríquez-Zárate, H. F. Abundis-Fong, R. Velázquez, and S. Gutiérrez, "Passive vibration control in a civil structure: Experimental results," Measurement and Control , vol. 52, no. 7–8, pp. 938–946, Sep. 2019, doi: 10.1177/0020294019847715. 5)D. J. Inman, Engineering vibration , 5th ed. Hoboken, NJ: Pearson Education, 2017. 6)ESM GmbH, "TMD Principles," ESM GmbH , Feb. 21, 2020. [Online]. Available: https://www.esm- gmbh.de/en/products/tmd-principles/ . (Accessed: Oct. 2, 2025). 7)Webtekno, “Windows İçin En İyi 15 Ekran Kaydedici Program - 2021,” Webtekno , Jul. 27, 2021. [Online]. Available: https://www.webtekno.com/ekran-kaydedici-windows-h88734.html . (Accessed: Oct. 2, 2025).