Realistic Finite Element Modeling Procedure of a Viscoelastic Material Characterization Test Set-Up

Öz

To determine the frequency and temperature dependent dynamic properties of viscoelastic materials, driving-point method proposed by ISO 10846-5:2008 is adopted, and accordingly a test set-up is already designed, manufactured and installed with the selected test equipment, and sample characterization tests are conducted. The efforts expended to design the test set-up are aimed at maximizing the first modal frequency of the fixture to which the test specimens are attached to be able to achieve the widest possible frequency range for accurate measurement of frequency dependent dynamic properties. When the test results are investigated, it is detected that the actual first modal frequency of the test set-up is quite low compared to the predicted frequency through finite element modeling and analysis based on the idealized conditions. Thus, in this study, finite element model of the test set-up utilized during the design process is improved by focusing on defining the connections between the components of the test set-up and the boundary conditions of the test set-up consistently with the real-life conditions. For this purpose, bolted joints between the components of the test set-up and the ground onto which the test set-up is mounted are modeled. To evaluate the finite element modal analysis results, modal tests are performed on the test set-up, and eventually the improved finite element model has yielded the first modal frequency of the test set-up as almost the same as the experimentally determined frequency with also very similar mode shapes. The main purpose of this study is to serve as a guide to similar future test set-up design studies during the finite element modeling phase.

Anahtar Kelimeler

• Viscoelastic material characterization
• Complex stiffness measurement
• Elastomer test system
• Finite element modeling
• Bolted joint modeling
• Soil-foundation-structure interaction

Bir Viskoelastik Malzeme Karakterizasyonu Test Düzeneğinin Gerçekçi Sonlu Elemanlar Modelleme Prosedürü

Öz

Viskoelastik malzemelerin frekansa ve sıcaklığa bağlı dinamik özelliklerini belirlemek için ISO 10846-5:2008 tarafından önerilen tahrik noktası metodu benimsenmiş ve buna göre bir test düzeneği önceden tasarlanmış, üretilmiş ve seçilmiş test ekipmanlarıyla birlikte kurulmuş ve örnek karakterizasyon testleri yapılmıştır. Test düzeneğinin tasarımı için harcanan çabalar, frekansa bağlı dinamik özelliklerin doğru ölçümü için mümkün olan en geniş frekans aralığını elde edebilmek için test numunelerinin bağlandığı fikstürün ilk modal frekansının maksimize edilmesini hedeflemiştir. Test sonuçları incelendiğinde test düzeneğinin gerçek ilk modal frekansının ideal koşullara dayalı sonlu elemanlar modelleme ve analizi sonucunda tahmin edilen frekansa göre oldukça düşük olduğu tespit edilmiştir. Böylece bu çalışmada, test düzeneğinin bileşenleri arasındaki bağlantıların ve test düzeneğinin sınır koşullarının gerçek yaşam koşullarıyla tutarlı olarak tanımlanmasına odaklanılarak test düzeneğinin tasarımı sürecinde kullanılan sonlu elemanlar modeli iyileştirilmiştir. Bu amaçla düzeneğin bileşenleri arasındaki cıvatalı bağlantılar ve düzeneğin üzerine monte edildiği zemin modellenmiştir. Sonlu elemanlar modal analiz sonuçlarını değerlendirmek için test düzeneğinin üzerinde modal testler yapılmıştır ve sonuç olarak iyileştirilmiş sonlu elemanlar modelinden elde edilen test düzeneğinin ilk modal frekansı deneysel olarak elde edilen frekansla neredeyse aynıdır ve bunun yanında mod şekilleri de oldukça benzerdir. Bu çalışmanın temel amacı gelecekteki benzer test düzeneği tasarımı çalışmalarına sonlu elemanlar modelleme aşamasında kılavuzluk etmektir.

Anahtar Kelimeler

• Viskoelastik malzeme karakterizasyonu
• Kompleks sertlik ölçümü
• Elastomer test sistemi
• Sonlu elemanlar modelleme
• Cıvatalı bağlantı modelleme
• Toprak-temel-yapı etkileşimi

Teşekkür

Modal testlere katkılarından ötürü Kenan Gürses’e teşekkürlerimizi sunarız.

Kaynakça

1. [1] Jones D. I. G. (2001) Handbook of Viscoelastic Vibration Damping, Chichester: John Wiley & Sons Ltd.
2. [2] Baz A. M. (2019) Active and Passive Vibration Damping, Chichester: John Wiley & Sons Ltd.
3. [3] Rivin E. I. (2003) Passive Vibration Isolation, New York, NY: ASME Press.
4. [4] Vasques C. M. A., Moreira R. A. S., Dias Rodrigues J., Viscoelastic damping technologies – Part II: Experimental identification procedure and validation, Journal of Advanced Research in Mechanical Engineering, Vol. 1 No. 2 (2010) 96-110.
5. [5] ISO 10846-2:2008, Acoustic and vibration – Laboratory measurement of vibro-acoustic transfer properties of resilient elements – Part 2: Direct method for determination of the dynamic stiffness of resilient supports for translatory motion.
6. [6] ISO 10846-3:2002, Acoustic and vibration – Laboratory measurement of vibro-acoustic transfer properties of resilient elements – Part 3: Indirect method for determination of the dynamic stiffness of resilient supports for translatory motion.
7. [7] ISO 10846-5:2008, Acoustic and vibration – Laboratory measurement of vibro-acoustic transfer properties of resilient elements – Part 5: Driving point method for determination of the low-frequency transfer stiffness of resilient supports for translatory motion.
8. [8] Cardillo R. M., Dynamic testing of elastomer mountings, Journal of Applied Polymer Science, Vol. 8 No. 1 (1964) 53-71. DOI: 10.1002/app.1964.070080104

9. [9] Oyadiji S. O., Tomlinson G. R., Determination of the complex moduli of viscoelastic structural elements by resonance and non-resonance methods, Journal of Sound and Vibration, Vol. 101 No. 3 (1985) 277-298. DOI: 10.1016/S0022-460X(85)80129-2
10. [10] Oyadiji S. O., Tomlinson G. R., Relating the complex moduli of viscoelastic materials to the complex stiffness of anti-vibration mounts, 1994 North American Conference on Smart Structures and Materials, Orlando, FL, United States (1994) 226-237. DOI: 10.1117/12.174099
11. [11] Oyadiji S. O., Tomlinson G. R., Characterization of the dynamic properties of viscoelastic elements by the direct stiffness and master curve methodologies, Part 1: Design of load frame and fixtures, Journal of Sound and Vibration, Vol. 186 No. 4 (1995) 623-647. DOI: 10.1006/jsvi.1995.0474
12. [12] Nadeau S., Champoux Y., Application of the direct complex stiffness method to engine mounts, Experimental Techniques, Vol. 24 No. 3 (2000) 21-23. DOI: 10.1111/j.1747-1567.2000.tb00906.x
13. [13] Rao M. D., Wirkner K. J., Gruenberg S., Dynamic characterization of automotive exhaust isolators, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, Vol. 218 No. 8 (2004) 891-900. DOI: 10.1243/0954407041581110
14. [14] Smith G. M., Bierman R. L., Zitek S. J., Determination of dynamic properties of elastomers over broad frequency range, Experimental Mechanics, Vol. 23 No. 2 (1983) 158-164. DOI: 10.1007/BF02320404
15. [15] Thompson D. J., Van Vliet W. J., Verheij J. W., Developments of the indirect method for measuring the high frequency dynamic stiffness of resilient elements, Journal of Sound and Vibration, Vol. 213 No. 1 (1998) 169-188. DOI: 10.1006/jsvi.1998.1492
16. [16] Ramorino G., Vetturi D., Cambiaghi D., Pegoretti A., Ricco T., Developments in dynamic testing of rubber compounds: Assessment of non-linear effects, Polymer Testing, Vol. 22 No. 6 (2003) 681-687. DOI: 10.1016/S0142-9418(02)00176-9
17. [17] Reina S., Arcos R., Clot A., Romeu J., An efficient experimental methodology for the assessment of the dynamic behaviour of resilient elements, Materials, Vol. 13 No. 13 (2020) Art. No. 2889. DOI: 10.3390/ma13132889
18. [18] Li Q., Dai B., Zhu Z., Thompson D. J., Improved indirect measurement of the dynamic stiffness of a rail fastener and its dependence on load and frequency, Construction and Building Materials, Vol. 304 (2021) Art. No. 124588. DOI: 10.1016/j.conbuildmat.2021.124588
19. [19] Allen B. R., Direct complex stiffness test system for viscoelastic material properties, 1996 Symposium on Smart Structures and Materials, San Diego, CA, United States (1996) 338-345. DOI: 10.1117/12.239101
20. [20] Moreira R. A. S., Rodrigues J. D., An efficient experimental methodology for viscoelastic complex modulus identification, II ECCOMAS Thematic Conference on Smart Structures and Materials, Lisbon, Portugal (2005) 1-12.
21. [21] Kergourlay G., Balmés E., Legal G., A characterization of frequency-temperature-prestress effects in viscoelastic films, Journal of Sound and Vibration, Vol. 297 No. 1-2 (2006) 391-407. DOI: 10.1016/j.jsv.2006.04.003
22. [22] Ozgen G. O., Design and development of a complex shear modulus measurement setup for viscoelastic materials, SAE 2005 Noise and Vibration Conference and Exhibition, Traverse City, MI, United States (2005) Art. No. 2005-01-2285. DOI: 10.4271/2005-01-2285
23. [23] Ozgen G. O., Erol F., Batihan A. C., Dynamic stiffness-based test systems for viscoelastic material characterization: Design considerations, In Allemang R., De Clerck J., Niezrecki C., Blough J. (Eds.) (2012) Proc. 30th IMAC Vol. 5: Topics in Modal Analysis I, New York, NY: Springer, 287-297. DOI: 10.1007/978-1-4614-2425-3_26
24. [24] Ungar E. E., Damping materials, In Braun S. G., Ewins D. J., Rao S. S. (Eds.) (2001) Encyclopedia of Vibration, San Diego, CA: Academic Press, 327-331.
25. [25] Jones D. I. G., Chapter 37: Applied damping treatments, In Harris C. M., Piersol A. G. (Eds.) (2002) Harris’ Shock and Vibration Handbook (Fifth edition), McGraw-Hill, 37.1-37.22.
26. [26] Budynas R. G., Nisbett J. K. (2015) Shigley’s Mechanical Engineering Design (Tenth edition), New York, NY: McGraw-Hill Education.
27. [27] Couchman G., Coelho A. M. G. (2017) Design of Joints in Steel Structures (UK edition), Brussels: European Convention for Constructional Steelwork (ECCS).
28. [28] Sarı K., Dilipak H., A software for optimum design of laterally loaded bolted joints, Gazi University Journal of Science Part C: Design and Technology, Vol. 12 No. 1 (2024) 366-377. DOI: 10.29109/gujsc.1385010
29. [29] Kulak G. L., Fisher J. W., Struik J. H. A. (2001) Guide to Design Criteria for Bolted and Riveted Joints (Second edition), Chicago, IL: American Institute of Steel Construction (AISC).
30. [30] Bickford J. H. (2008) Introduction to the Design and Behavior of Bolted Joints (Fourth edition), Boca Raton, FL: CRC Press.
31. [31] Wang J., Uy B., Li D., Song Y., Fatigue behaviour of stainless steel bolts in tension and shear under constant-amplitude loading, International Journal of Fatigue, Vol. 133 (2020) Art. No. 105401. DOI: 10.1016/j.ijfatigue.2019.105401
32. [32] Kim J., Yoon J.-C., Kang B.-S., Finite element analysis and modeling of structure with bolted joints, Applied Mathematical Modelling, Vol. 31 No. 5 (2007) 895-911. DOI: 10.1016/j.apm.2006.03.020
33. [33] Pratt J. D., Pardoen G., Numerical modeling of bolted lap joint behavior, Journal of Aerospace Engineering, Vol. 15 No. 1 (2002) 20-31. DOI: 10.1061/(ASCE)0893-1321(2002)15:1(20)
34. [34] McCarthy M. A., McCarthy C. T., Lawlor V. P., Stanley W. F., Three-dimensional finite element analysis of single-bolt, single-lap composite bolted joints: Part I – Model development and validation, Composite Structures, Vol. 71 No. 2 (2005) 140-158. DOI: 10.1016/j.compstruct.2004.09.024
35. [35] Oldfield M., Ouyang H., Mottershead J. E., Simplified models of bolted joints under harmonic loading, Computers & Structures, Vol. 84 No. 1-2 (2005) 25-33. DOI: 10.1016/j.compstruc.2005.09.007
36. [36] Mandal B., Chakrabarti A., A simple homogenization scheme for 3D finite element analysis of composite bolted joints, Composite Structures, Vol. 120 (2015) 1-9. DOI: 10.1016/j.compstruct.2014.09.061
37. [37] Vilela P. M. L., Carvalho H., Grilo L. F., Montenegro P. A., Calçada R. B., Unitary model for the analysis of bolted connections using the finite element method, Engineering Failure Analysis, Vol. 104 (2019) 308-320. DOI: 10.1016/j.engfailanal.2019.06.001
38. [38] Gray P. J., McCarthy C. T., A global bolted joint model for finite element analysis of load distributions in multi-bolt composite joints, Composites Part B: Engineering, Vol. 41 No. 4 (2010) 317-325. DOI: 10.1016/j.compositesb.2010.03.001
39. [39] Tanlak O., Sönmez F. O., Talay E., Detailed and simplified models of bolted joints under impact loading, The Journal of Strain Analysis for Engineering Design, Vol. 46 No. 3 (2011) 213-225. DOI: 10.1177/0309324710396997
40. [40] Guzas E., Behan K., Davis J., 3D finite element modeling of single bolt connections under static and dynamic tension loading, Shock and Vibration, Vol. 2015 (2015) Art. No. 205018. DOI: 10.1155/2015/205018
41. [41] Lampeas G., Perogamvros N., Analysis of composite bolted joints by a macro-modelling approach, International Journal of Structural Integrity, Vol. 7 No. 3 (2016) 412-428. DOI: 10.1108/IJSI-07-2015-0023
42. [42] Ramteke A. L., Nadgouda P. B., Improving analysis accuracy by modeling rivets/bolts as solids in sheet metal structure, 7th European LS-DYNA Conference, Salzburg, Austria (2009).
43. [43] Sakamoto Y., Kawamura S., Sunayama Y., Study of bolt model to improve accuracy of engine vibration analysis, SAE 2010 Small Engine Technology Conference and Exposition, Linz, Austria (2010) Art. No. 2010-32-0026. DOI: 10.4271/2010-32-0026
44. [44] Grzejda R., Modelling bolted joints using a simplified bolt model, Journal of Mechanical and Transport Engineering, Vol. 69 No. 1 (2017) 29-37. DOI: 10.21008/j.2449-920X.2017.69.1.03
45. [45] Grzejda R., Impact of nonlinearity on bolt forces in multi-bolted joints: A case of the assembly stage, Scientia Iranica Transactions B: Mechanical Engineering, Vol. 26 No. 3 (2019) 1299-1306. DOI: 10.24200/sci.2018.20320
46. [46] Montgomery J., Methods for modeling bolts in the bolted joint, ANSYS User’s Conference (2002).
47. [47] Omar R., Abdul Rani M. N., Yunus M. A., Wan Iskandar Mirza W. I. I., Mohd Zin M. S., Efficient finite element modelling for the investigation of the dynamic behaviour of a structure with bolted joints, International Conference on Electrical, Electronics, Materials and Applied Science, Secunderabad, India (2018) Art. No. 020082. DOI: 10.1063/1.5032044
48. [48] Kerr A. D., Elastic and viscoelastic foundation models, Journal of Applied Mechanics, Vol. 31 No. 3 (1964) 491-498. DOI: 10.1115/1.3629667
49. [49] Dutta S. C., Roy R., A critical review on idealization and modeling for interaction among soil-foundation-structure system, Computers & Structures, Vol. 80 No. 20-21 (2002) 1579-1594. DOI: 10.1016/S0045-7949(02)00115-3
50. [50] Wang Y. H., Tham L. G., Cheung Y. K., Beams and plates on elastic foundations: A review, Progress in Structural Engineering and Materials, Vol. 7 No. 4 (2005) 174-182. DOI: 10.1002/pse.202