Akıllı Kirişlerin Dinamik Özelliklerinin Araştırılması

Abstract

Sağlık sektöründe, robotik sistemlerde ve endüstride kullanılan cihazların kullanım ömrü ve performansı dinamik yüklemelere maruz kaldıklarında verdikleri tepkilerle doğrudan ilişkilidir. Dinamik yüklemeler sonucunda ortaya çıkan titreşimler stabilitesi ve mekanik performansı üzerinde kritik etkilere sahiptir. Bu nedenle, dinamik yükleme altındaki titreşim davranışının analiz edilmesi, özellikle biyomekanik uygulamalar kapsamında önem taşımaktadır. Özellikle biyolojik doku simülasyonları üzerinde gerçekleştirilen titreşim analizleri, sistemlerin dinamik yanıtlarının belirlenmesi ve güvenilirliğinin artırılmasına yönelik temel bir adımdır. Polilaktik asit (PLA), hem yapay biyolojik doku üretiminde hem de üç boyutlu yazıcı filamenti için yaygın olarak tercih edilen bir malzeme olarak öne çıkmaktadır. Bu çalışmada yapılan deneysel ve nümerik çalışmalarda, motor tahriki ile harmonik yük uygulanmış kirişler üzerinde konuma göre dinamik analizler gerçekleştirilmiştir. Kirişler üzerinde konum olarak üç düğüm noktası belirlenmiş ve bu noktalar arasına piezo sensörler yerleştirilerek analizler yapılmıştır. PLA kutu içerisine yerleştirilen kirişli sistemin sönümlü ve sönümsüz titreşimine bağlı olarak zaman analizi, doğal frekansı, sönümleme oranı incelenmiştir. Kirişlerin üretiminde iki farklı malzeme seçilmiştir. Metal malzeme olarak geleneksel yöntem ile imal edilmiş A366/CQ siyah çelik levha (Soğuk haddelenmiş sac-DKP) ve polimer malzeme olarak PLA filament kullanılmıştır. Deneysel ve nümerik çalışmalarımız sonucunda, her iki sistemin kararlı olma durumu serbest uç bölgesinde tespit edilmiştir. Çelik ve PLA kiriş için bahsedilen bölgedeki sönüm oranları deneysel olarak sırasıyla 0,227 ve 0,755 bulunmuştur. Sayısal sonuçlara göre ise çelik kirişli sistemin sönüm oranları [0,93; 0,93; 0,55; 0,55; 0,76; 0,76], PLA kirişli sistemin ise [1; 0,98; 0,98; 0,97; 0,97; 0,94; 0,94] olarak elde edilmiştir. Çalışma, malzeme ve sistem dinamiklerinin optimize edilmesi, titreşim kontrolü ve kararlılık artırmaya yönelik mühendislik uygulamalarına katkı sağlayabilecek bir referans niteliği taşımaktadır.

Keywords

• Akıllı kirişler
• Harmonik yükleme
• Sönümleme
• Piezo sensör
• PLA

Supporting Institution

Süleyman Demirel Üniversitesi Bilimsel Araştırma Projeleri Koordinasyon Birimi

Project Number

FDK-2022-8789

Thanks

Bu çalışma, FDK-2022-8789 proje numarası ile Süleyman Demirel Üniversitesi Bilimsel Araştırma Projeleri Koordinasyon Birimi tarafından desteklenmektedir.

Investigation of Dynamic Characteristics of Smart Beams

Abstract

The service life and performance of devices used in the healthcare sector, robotic systems, and industry are closely associated with their response under dynamic loading conditions. Vibrations resulting from dynamic loads have a significant impact on stability and mechanical performance. Consequently, the analysis of vibration behavior under dynamic loading is of critical importance, particularly in biomechanical applications. Vibration analyses conducted on biological tissue simulations play a fundamental role in determining the dynamic responses of systems and improving their reliability. Polylactic acid (PLA) is widely utilized as a material for the production of artificial biological tissues and as a filament in 3D printing applications. In this study, experimental and numerical investigations were carried out on beams subjected to harmonic loading via motor excitation, with dynamic analyses performed at specific positions. Three nodal points were identified on the beams, and piezoelectric sensors were placed between these points for analysis. The damped and undamped vibration responses of the beam system housed in a PLA box were analyzed in terms of time response, natural frequency, and damping ratio. Two different materials were used in beam production: A366/CQ black steel sheet (cold-rolled steel) manufactured using conventional methods as the metallic material, and PLA filament as the polymer material. Experimental and numerical results revealed that the stability of both systems was achieved at the free end region. The damping ratios in the specified region were experimentally determined as 0.227 for the steel beam and 0.755 for the PLA beam. Numerical results indicated that the damping ratios for the steel beam system were [0.93; 0.93; 0.55; 0.55; 0.76; 0.76], while those for the PLA beam system were [1; 0.98; 0.98; 0.97; 0.97; 0.94; 0.94]. This study provides a reference that can contribute to engineering applications focused on optimizing material and system dynamics, controlling vibrations, and enhancing stability.

Keywords

• Smart beams
• Harmonic load
• Damping
• Piezo sensor
• PLA

Project Number

FDK-2022-8789

References

1. [1] M. P. (Michael P. Norton and D. G. (Denis G. ) Karczub, Fundamentals of noise and vibration analysis for engineers. Cambridge University Press, 2003.
2. [2] “S. Graham Kelly - Fundamentals of Mechanical Vibration-McGraw-Hill Science_Engineering_Math (2000)”.
3. [3] S. Saedi, E. Acar, H. Raji, S. E. Saghaian, and M. Mirsayar, “Energy damping in shape memory alloys: A review,” Sep. 15, 2023, Elsevier Ltd. doi: 10.1016/j.jallcom.2023.170286.
4. [4] M. N. Bajad, “Analytical approach for damping model,” Jan. 01, 2023, Institute for Ionics. doi: 10.1007/s42107-022-00491-3.
5. [5] M. Al Rifaie, H. Abdulhadi, and A. Mian, “Advances in mechanical metamaterials for vibration isolation: A review,” Mar. 01, 2022, SAGE Publications Inc. doi: 10.1177/16878132221082872.
6. [6] A. Raza, R. Rimašauskienė, V. Jūrėnas, and S. Mahato, “Experimental investigation of vibration amplitude control in additive manufactured PLA and PLA composite structures with MFC actuator,” Eng Struct, vol. 294, Nov. 2023, doi: 10.1016/j.engstruct.2023.116802.
7. [7] G. Song, P. Z. Qiao, and W. K. Binienda, “Active vibration damping of a composite beam using smart sensors and actuators,” in 19th AIAA Applied Aerodynamics Conference, American Institute of Aeronautics and Astronautics Inc., 2001. doi: 10.2514/6.2001-1637.
8. [8] P. A. Jadhav and K. M. Bajoria, “Free and forced vibration control of piezoelectric FGM plate subjected to electro-mechanical loading,” Smart Mater Struct, vol. 22, no. 6, Jun. 2013, doi: 10.1088/0964-1726/22/6/065021.

9. [9] U. Shukla and K. Garg, “Journey of smart material from composite to shape memory alloy (SMA), characterization and their applications-A review,” Jan. 01, 2023, KeAi Communications Co. doi: 10.1016/j.smaim.2022.10.002.
10. [10] M. Al-Ayyad, H. A. Owida, R. De Fazio, B. Al-Naami, and P. Visconti, “Electromyography Monitoring Systems in Rehabilitation: A Review of Clinical Applications, Wearable Devices and Signal Acquisition Methodologies,” Apr. 01, 2023, MDPI. doi: 10.3390/electronics12071520.
11. [11] A. H. Umar, M. A. Othman, F. K. C. Harun, and Y. Yusof, “Dielectrics for Non-Contact ECG Bioelectrodes: A Review,” Sep. 01, 2021, Institute of Electrical and Electronics Engineers Inc. doi: 10.1109/JSEN.2021.3092233.
12. [12] B. Li, T. Cheng, and Z. Guo, “A review of EEG acquisition, processing and application,” in Journal of Physics: Conference Series, IOP Publishing Ltd, May 2021. doi: 10.1088/1742-6596/1907/1/012045.
13. [13] A. S. Poudrel, V. H. Nguyen, G. Haiat, and G. Rosi, “Optimization of a smart beam for monitoring a connected inaccessible mechanical system: Application to bone-implant coupling,” Mech Syst Signal Process, vol. 192, Jun. 2023, doi: 10.1016/j.ymssp.2023.110188.
14. [14] D. Chhabra, P. Chandna, and G. Bhushan, “Design and Analysis of Smart Structures for Active Vibration Control using Piezo-Crystals,” 2011.
15. [15] M. Ghodsi, M. Mohammadzaheri, P. Soltani, and H. Ziaifar, “A new active anti-vibration system using a magnetostrictive bimetal actuator,” J Magn Magn Mater, vol. 557, Sep. 2022, doi: 10.1016/j.jmmm.2022.169463.
16. [16] S. Zhang, Y. He, L. Fan, and X. Chen, “Active vibration control of smart beam by μ-synthesis technology: modeling via finite element method based on FSDT,” Mechanics of Advanced Materials and Structures, 2022, doi: 10.1080/15376494.2022.2103217.
17. [17] N. Jain, S. Nandu Ovhal, V. Patil, and K. Nani Kartik, “Smart materials – A state-of-the-art-review,” Mater Today Proc, 2023, doi: 10.1016/j.matpr.2023.03.226.
18. [18] C. Y. Lin and H. W. Jheng, “Active vibration suppression of a motor-driven piezoelectric smart structure using adaptive fuzzy sliding mode control and repetitive control,” Applied Sciences (Switzerland), vol. 7, no. 3, 2017, doi: 10.3390/app7030240.
19. [19] G. Roy, B. Panigrahi, and G. Pohit, “Identification of crack by vibration analysis and restoration of dynamic response in beams using PZT sensor/actuator,” Nondestructive Testing and Evaluation, vol. 38, no. 2, pp. 211–232, 2023, doi: 10.1080/10589759.2022.2094378.
20. [20] B. Zhang, H. Li, S. Zhou, J. Liang, J. Gao, and D. Yurchenko, “Modeling and analysis of a three-degree-of-freedom piezoelectric vibration energy harvester for broadening bandwidth,” Mech Syst Signal Process, vol. 176, Aug. 2022, doi: 10.1016/j.ymssp.2022.109169.
21. [21] B. Singh and B. K. Nanda, “Dynamic analysis of damping in layered and welded beams,” Eng Struct, vol. 48, pp. 10–20, Mar. 2013, doi: 10.1016/j.engstruct.2012.09.037.
22. [22] H. Boudaoud, E. M. Daya, S. Belouettar, L. Duigou, and M. Potier-Ferry, “Damping analysis of beams submitted to passive and active control,” Eng Struct, vol. 31, no. 2, pp. 322–331, Feb. 2009, doi: 10.1016/j.engstruct.2008.08.009.
23. [23] “Ansys,” 2024.
24. [24] H. Karagülle, L. Malgaca, and H. F. Öktem, “Analysis of active vibration control in smart structures by ANSYS,” Smart Mater Struct, vol. 13, no. 4, pp. 661–667, Aug. 2004, doi: 10.1088/0964-1726/13/4/003.
25. [25] A. Khalatkar, V. K. Gupta, and A. Agrawal, “Analytical, FEA, and Experimental Comparisons of Piezoelectric Energy Harvesting Using Engine Vibrations,” Smart Materials Research, vol. 2014, pp. 1–8, Apr. 2014, doi: 10.1155/2014/741280.
26. [26] “Free vibration analysis of smart composite beam”.
27. [27] K. K. Vinayaga, A. Vasanthanathan, and P. Nagaraj, “Finite element modeling of smart piezoelectric beam using ANSYS®,” in Materials Today: Proceedings, Elsevier Ltd, 2018, pp. 7078–7085. doi: 10.1016/j.matpr.2017.11.372.
28. [28] F. He, H. Ning, and M. Khan, “Effect of 3D Printing Process Parameters on Damping Characteristic of Cantilever Beams Fabricated Using Material Extrusion,” Polymers (Basel), vol. 15, no. 2, Jan. 2023, doi: 10.3390/polym15020257.
29. [29] Y. S. Kushwaha, N. S. Hemanth, N. D. Badgayan, and S. K. Sahu, “Free vibration analysis of PLA based auxetic metamaterial structural composite using finite element analysis,” Mater Today Proc, vol. 56, pp. 1063–1067, Jan. 2022, doi: 10.1016/j.matpr.2021.09.482.
30. [30] E. N. Selçuk and M. Reşit, “BİYOMEKATRONİK BİR YAPI ELEMANI OLARAK KAFATASI FANTOMUNUN MÜHENDİSLİKTE KULLANIMI.”
31. [31] Y. H. Yu, T. Y. Yen, S. K. Hung, S. H. Chen, and K. Y. Wang, “A 3D-printed phantom for stereotactic body radiation therapy simulation,” Biomed Phys Eng Express, vol. 10, no. 2, Mar. 2024, doi: 10.1088/2057-1976/ad28cd.
32. [32] G. B. Tseghai, B. Malengier, K. A. Fante, and L. Van Langenhove, “A long-lasting textile-based anatomically realistic head phantom for validation of eeg electrodes,” Sensors, vol. 21, no. 14, Jul. 2021, doi: 10.3390/s21144658.
33. [33] D. Popescu, A. Zapciu, C. Amza, F. Baciu, and R. Marinescu, “FDM process parameters influence over the mechanical properties of polymer specimens: A review,” Polym Test, vol. 69, pp. 157–166, Aug. 2018, doi: 10.1016/j.polymertesting.2018.05.020.
34. [34] M. Trujillo, M. Curtin, M. Ley, B. E. Saunders, G. Throneberry, and A. Abdelkefi, “Influence of filament angle orientation on the dynamic characteristics of additively-manufactured beams,” Structures, vol. 50, pp. 418–429, Apr. 2023, doi: 10.1016/j.istruc.2023.02.047.
35. [35] S. Z. Gebrehiwot, L. Espinosa Leal, J. N. Eickhoff, and L. Rechenberg, “The influence of stiffener geometry on flexural properties of 3D printed polylactic acid (PLA) beams,” Progress in Additive Manufacturing, vol. 6, no. 1, pp. 71–81, 2021, doi: 10.1007/s40964-020-00146-2.
36. [36] M. Sethi, A. Banerjee, and B. Manna, “Vibration transmission through a cantilever beam in mass impacting metamaterial: An analytical investigation and experimentation,” Mech Syst Signal Process, vol. 220, no. March, p. 111669, 2024, doi: 10.1016/j.ymssp.2024.111669.
37. [37] S. R. Patro, A. Banerjee, and G. V. Ramana, “Vibration attenuation characteristics of finite locally resonant meta beam: Theory and experiments,” Eng Struct, vol. 278, no. December 2022, p. 115506, 2023, doi: 10.1016/j.engstruct.2022.115506.
38. [38] A. H. Orta, I. Kayabasi, and M. G. Senol, “Prediction of mechanical properties of cold rolled and continuous annealed steel grades via analytical model integrated neural networks,” Ironmaking and Steelmaking, vol. 47, no. 6, pp. 596–605, 2020, doi: 10.1080/03019233.2019.1568000.
39. [39] G. N. Eremin, V. I. Parakhin, A. N. Shibanova, and A. E. Cheglov, “Prospects of Production and Application of Cold-Rolled Electrical Steel for Magnetic Cores of Rotary Electric Machines,” Steel in Translation, vol. 51, no. 4, pp. 286–290, 2021, doi: 10.3103/S0967091221040033.
40. [40] S. M. Kusagur, G. Arunkumar, and T. C. Manjunath, “Modelling of smart intelligent materials with PZT & PVDF sensors/actuators to control the active vibrations of flexible aluminum mechanical cantilever beams using proportional integral derivative (PID) techniques,” Mater Today Proc, vol. 37, no. Part 2, pp. 2075–2082, 2020, doi: 10.1016/j.matpr.2020.07.507.
41. [41] P. Ghannadi, S. S. Kourehli, M. Noori, and W. A. Altabey, “Efficiency of grey wolf optimization algorithm for damage detection of skeletal structures via expanded mode shapes,” Advances in Structural Engineering, vol. 23, no. 13, pp. 2850–2865, 2020, doi: 10.1177/1369433220921000.
42. [42] A. Ebrahimi-Tirtashi, S. Mohajerin, M. R. Zakerzadeh, and M. A. Nojoomian, “Vibration control of a piezoelectric cantilever smart beam by ℒ 1 adaptive control system,” Systems Science and Control Engineering, vol. 9, no. 1, pp. 542–555, 2021, doi: 10.1080/21642583.2021.1946868.
43. [43] L. P. Ponci, G. Creci, and J. C. Menezes, “Simplified procedure for vibration analysis and dynamic balancing in mechanical systems with beats frequency,” Measurement (Lond), vol. 174, no. October 2020, 2021, doi: 10.1016/j.measurement.2021.109056.
44. [44] M. Al Rifaie, H. Abdulhadi, and A. Mian, “Advances in mechanical metamaterials for vibration isolation: A review,” Mar. 01, 2022, SAGE Publications Inc. doi: 10.1177/16878132221082872.
45. [45] S. Takaki, T. MasuMura, and T. TsuchiyaMa, “Young’s modulus of single crystalline iron and elastic stiffness,” Tetsu-To-Hagane/Journal of the Iron and Steel Institute of Japan, vol. 106, no. 9, pp. 679–682, Sep. 2020, doi: 10.2355/tetsutohagane.TETSU-2019-129.
46. [46] A. Bagheri, I. Buj-Corral, M. Ferrer, M. M. Pastor, and F. Roure, “Determination of the elasticity modulus of 3D printed octet-truss structures for use in porous prosthesis implants,” Materials, vol. 11, no. 12, Nov. 2018, doi: 10.3390/ma11122420.
47. [47] F. Li and G. Li, “Application of ANSYS APDL in the Design of Piezoelectric Transducer,” 2015.
48. [48] Y. Munde, A. S. Shinde, I. Siva, and P. Anearo, “Assessment of physical and vibration damping characteristics of sisal/PLA biodegradable composite,” Materials Physics and Mechanics, vol. 51, no. 7, pp. 107–116, 2023, doi: 10.18149/MPM.5172023_9.
49. [49] M. Česnik, J. Slavič, and M. Boltežar, “Accelerated vibration-fatigue characterization for 3D-printed structures: Application to fused-filament-fabricated PLA samples,” Int J Fatigue, vol. 171, 2023, doi: 10.1016/j.ijfatigue.2023.107574.
50. [50] F. Golnaraghi and B. C. Kuo, “Ninth Edition.”
51. [51] Mehmet Önder EFE, Otomatik Kontrol Sistemleri, Seçkin yayıncılık. 2024.
52. [52] A. Atangana and A. Akgül, “Can transfer function and Bode diagram be obtained from Sumudu transform,” Alexandria Engineering Journal, vol. 59, no. 4, pp. 1971–1984, Aug. 2020, doi: 10.1016/j.aej.2019.12.028.
53. [53] J. R. B. Jan Machowski, Zbigniew Lubosny, Janusz W. Bialek, Power System Dynamics. 2020. [Online]. Available: https://books.google.com.tr/books?hl=tr&lr=&id=9X_PDwAAQBAJ&oi=fnd&pg=PA19&dq=Methods+used+to+ensure+or+increase+the+stability+of+systems&ots=zP8ZJ0NTuA&sig=3wtzc2WwEK0DYEXeMS8lEuRBDnY&redir_esc=y#v=onepage&q=Methods used to ensure or increase the stabili
54. [54] G. H. Yoon, H. Choi, and H. So, “Development and optimization of a resonance-based mechanical dynamic absorber structure for multiple frequencies,” Journal of Low Frequency Noise Vibration and Active Control, vol. 40, no. 2, pp. 880–897, 2021, doi: 10.1177/1461348419855533.
55. [55] J.-S. Wu, Analytical and Numerical Methods for Vibration Analyses. 2013. [Online]. Available: https://books.google.com.tr/books?hl=tr&lr=&id=rSlwAAAAQBAJ&oi=fnd&pg=PT7&dq=system+dynamics+numerical+analysis+for+vibration,&ots=Iz1gEjuQF0&sig=sGWksuYlDijUMFmH3Bg4WcIKHVY&redir_esc=y#v=onepage&q=system dynamics numerical analysis for vibration%2C&f=fal
56. [56] G. Krivic and J. Slavič, “Simultaneous non-contact identification of the elastic modulus, damping and coefficient of thermal expansion in 3D-printed structures,” Polym Test, vol. 125, 2023, doi: 10.1016/j.polymertesting.2023.108131.
57. [57] F. Medel, J. Abad, and V. Esteban, “Stiffness and damping behavior of 3D printed specimens,” Polym Test, vol. 109, no. February, p. 107529, 2022, doi: 10.1016/j.polymertesting.2022.107529.