First Steps Towards Structural Utilisation of the Lattice-Structured Cantilever Beam: System Identification, Modal and Static Structural Analysis

Abstract

Materials with lattice structure have been used in many engineering fields. However, studies including dynamic and static analysis of lattice structured beams are not common in literature. In this study, three types of cantilever beams with lattice structure were designed as 3 Dimensionally in nTopology software and analyzed in Ansys software. Square rotated, hexagonal and triangular type lattice structures were used in design of the beams. 10 Kilonewton force were applied to each beam and the displacements that were occurred at the free end side of the beams were recorded. Discrete time transfer function models, discrete time state space models and nonlinear Autoregressive with Extra Input models were obtained using input and output data set belongs to vibration of the beams. System Identification Toolbox of MATLAB was used to obtain the models. In addition, modal analysis and static analysis of the beams were realized. The results belong to system identification, modal analysis and static analysis were illustrated in figures, presented in tabular form and were discussed. After the non-lattice beam, the lowest specific deformation occurred in the triangular lattice beam. Therefore, the triangular lattice structure gave promising results for structural elements in pure bending state.

Keywords

• Cantilever beam
• System Identification
• Modal analysis
• Static Structural Analysis
• Vibration Model
• Lattice structures

Kafes Yapılı Konsol Kirişin Yapısal Kullanımına Yönelik İlk Adımlar: System Identification, Modal ve Yapısal Analiz

Öz

Kafes yapılı malzemeler birçok mühendislik alanında kullanılmaktadır. Ancak kafes yapılı kirişlerin dinamik ve statik analizini içeren çalışmalar literatürde yaygın değildir. Bu çalışmada kafes yapısına sahip üç tip konsol kiriş nTopology programında 3 boyutlu olarak tasarlanıp Ansys yazılımında analizleri yapılmıştır. Kirişlerin tasarımında kare döndürülmüş, altıgen ve üçgen tipi kafes yapıları kullanılmıştır. Her bir kirişe 10 Kilonewton kuvvet uygulanarak kirişlerin serbest uç kısmında meydana gelen yer değiştirmeler kaydedilmiştir. Kirişlerin titreşimine ait giriş ve çıkış veri seti kullanılarak ayrık zaman transfer fonksiyonu modelleri, ayrık zaman durum uzayı modelleri ve doğrusal olmayan Ekstra Girişli Otoregresif modeller elde edildi. Modellerin elde edilmesi için MATLAB'ın Sistem Tanımlama Araç Kutusu kullanıldı. Ayrıca kirişlerin modal analizi ve statik analizi gerçekleştirilmiştir. Sistem tanımlama, modal analiz ve statik analize ait sonuçlar şekiller halinde gösterilmiş, tablolar halinde sunulmuş ve tartışılmıştır. Kafes olmayan kirişten sonra en düşük spesifik deformasyon üçgen kafes kirişte meydana geldi. Bu nedenle üçgen kafes yapısı, saf eğilme durumundaki yapı elemanları için umut verici sonuçlar verdi.

Anahtar Kelimeler

• Ankastre Kiriş
• Sistem Tanımlama
• Modal Analiz
• Statik Yapısal Analiz
• Titreşim Modeli
• Kafes Yapılar

References

1. N. S. Trahair, “Beam-columns,” in Flexural-Torsional Buckling of Structures, CRC Press, 2017, pp. 205–218. doi: 10.1201/9780203755938-11.
2. S. Orhan, “Analysis of free and forced vibration of a cracked cantilever beam,” NDT & E International, vol. 40, no. 6, pp. 443–450, Sep. 2007, doi: 10.1016/J.NDTEINT.2007.01.010.
3. A. Gök, C. Gologlu, and H. I. Demirci,"Determination of form defects depending on tool deflection in ball end milling of convex and concavesurfaces", Journal of the Faculty of Engineering and Architecture of Gazi University, Vol. 29, Issue 2, pp. 365-374, 2014.
4. Z. A. Jassim, N. N. Ali, F. Mustapha, and N. A. Abdul Jalil, “A review on the vibration analysis for a damage occurrence of a cantilever beam,” Eng Fail Anal, vol. 31, pp. 442–461, 2013, doi: https://doi.org/10.1016/j.engfailanal.2013.02.016.
5. A. Ayyad, M. Chehadeh, M. I. Awad, and Y. Zweiri, “Real-Time System Identification Using Deep Learning for Linear Processes with Application to Unmanned Aerial Vehicles,” IEEE Access, vol. 8, pp. 122539–122553, 2020, doi: 10.1109/ACCESS.2020.3006277.
6. S. Çaşka and M. E. Dokuz, “Ankastre Bir Kirişin Ayrık Zamanlı Titreşim Modelinin Meta- sezgisel Optimizasyon Yöntemler i Kullanılarak Elde Edilmesi Obtaining a Discrete Time Vibration Model of a Cantilever Beam by Using Meta-heuristic Optimization Methods,” Bilecik Seyh Edebali University Journal of Science, vol. 9, no. 1, pp. 32–41, 2022.
7. A. A. Ali, R. A. R. Lateef, and M. W. Saeed, “Intelligent tuning of vibration mitigation process for single link manipulator using fuzzy logic,” Engineering Science and Technology, an International Journal, vol. 20, no. 4, pp. 1233–1241, 2017, doi: 10.1016/j.jestch.2017.08.001.
8. R. De Keyser, C. Copot, A. Hernandez, and C. Ionescu, “Discrete-time internal model control with disturbance and vibration rejection,” Journal of Vibration and Control, vol. 23, no. 1, pp. 3–15, Aug. 2015, doi: 10.1177/1077546315601935.

9. W. Liu, “Appendix A: System Identification: State and Parameter Estimation Techniques,” in Introduction to Hybrid Vehicle System Modeling and Control, John Wiley & Sons, Ltd, 2013, pp. 325–363. doi: 10.1002/9781118407400.APP1.
10. S. M. Khot and N. P. Yelve, “Modeling and response analysis of dynamic systems by using ANSYS© and MATLAB©,” Journal of Vibration and Control, vol. 17, no. 6, pp. 953–958, Oct. 2010, doi: 10.1177/1077546310377913.
11. S. Alegre, J. V Míguez, and J. Carpio, “Modelling of electric and parallel-hybrid electric vehicle using Matlab/Simulink environment and planning of charging stations through a geographic information system and genetic algorithms,” Renewable and Sustainable Energy Reviews, vol. 74, pp. 1020–1027, 2017, doi: https://doi.org/10.1016/j.rser.2017.03.041.
12. R. Sharma, V. Vashisht, and U. Singh, “Modelling and simulation frameworks for wireless sensor networks: a comparative study,” IET Wireless Sensor Systems, vol. 10, no. 5, pp. 181–197, 2020, doi: https://doi.org/10.1049/iet-wss.2020.0046.
13. M. Imran, S. Badshah, and R. Khan, “Vibration Analysis of Cracked Composite Laminated Plate: A Review,” Mehran University Research Journal of Engineering and Technology; Vol 38 No 3 (2019): July IssueDO - 10.22581/muet1982.1903.14 , Jul. 2019, [Online]. Available: https://publications.muet.edu.pk/index.php/muetrj/article/view/1140
14. E. J. Sapountzakis and I. N. Tsiptsis, “Generalized vibration analysis of beams including warping effects by isogeometric methods,” Journal of Vibration and Control, vol. 24, no. 6, pp. 1032–1050, Jan. 2017, doi: 10.1177/1077546316685679.
15. A. Gök, H. Demirci, K. Gök, “Determination of experimental, analytical, and numerical values of tool deflection at ball end milling of inclined surfaces”, Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, vol. 230, Issue 2, pp. 111-119, Jun. 2016, doi:10.1177/0954408914540633.
16. S. Korucu, K. Gök, M. Tümsek, G. Soy, ve A. Gök, “Farklı Profillere Sahip Kirişlerde Meydana Gelen Eğilme Gerilmesi ve Sehim Miktarının Teorik ve Nümerik Yöntemler ile Analizi”, DEUFMD, vol. 21, Issue 62, pp. 469–482, 2019, doi: 10.21205/deufmd.2019216213.
17. K. Gok, S. Inal, L. Urtekin, and A. Gok, “Biomechanical performance using finite element analysis of different screw materials in the parallel screw fixation of Salter–Harris Type 4 fractures,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 41, no. 3, p. 143, 2019, doi: 10.1007/s40430-019-1640-z.
18. K. Gök, A. B. Selçuk, and A. Gök, “Computer-Aided Simulation Using Finite Element Analysis of Protect Against to Coronavirus (COVID-19) of Custom-Made New Mask Design,” Transactions of the Indian Institute of Metals, vol. 74, no. 5, pp. 1029–1033, 2021, doi: 10.1007/s12666-021-02227-4.
19. Y. Pirhan, K. Gök, and A. Gök, “Comparison of two different bowel anastomosis types using finite volume method,” Comput Methods Biomech Biomed Engin, vol. 23, no. 8, pp. 323–331, Jun. 2020, doi: 10.1080/10255842.2020.1722809.
20. M. E. Dokuz, M. Aydın, and M. Uyaner, “Production of Bioactive Various Lattices as an Artificial Bone Tissue by Digital Light Processing 3D Printing,” J Mater Eng Perform, 2021, doi: 10.1007/s11665-021-06067-7.
21. B. K. Nagesha, V. Dhinakaran, M. Varsha Shree, K. P. Manoj Kumar, D. Chalawadi, and T. Sathish, “Review on characterization and impacts of the lattice structure in additive manufacturing,” Mater Today Proc, vol. 21, pp. 916–919, Jan. 2020, doi: 10.1016/J.MATPR.2019.08.158.
22. H. Deniz Ada, M. Erdem, and K. Gok, “Computational fluid dynamics simulation of erosion-corrosion in abrasive water jet machining,” Surface Review and Letters, vol. 28, no. 05, p. 2150031, Jan. 2021, doi: 10.1142/S0218625X21500311.
23. S. Çaşka, K. Gök., M. Aydın and İ. Özdemir, “Finite element method based structural analysis of quadcopter UAV chassis produced with 3D printer.” Journal Of Science And Technology Of Dumlupınar University, Issue 44, pp. 24-32, June 2020