Düz ve Bükümlü Plakaların Büküm Açısına Bağlı Modal Analizi

Abstract

İzotropik ince plakaların dinamik özelliklerinden biri olan doğal frekans üzerinde bükümlü açı ve sınır koşulu farklılıklarının etkisi araştırılmıştır. Düz ve bükümlü yapıların modal analizleri tek ve çift tarafı sabit sınır koşulları altında ANSYS ile yapılmıştır. Yapıların serbest titreşim sonuçlarının validasyonu Solidworks ile yapılmıştır. Her yapının ilk beş doğal frekansı elde edilmiş ve boyutsuz doğal frekans parametreleri cinsinden değerler tablo ve grafiklerle yorumlanmıştır. Tek tarafı sabit sınır koşulu için ilk beş doğal frekansta büküm açısındaki artışa bağlı olarak hem bir artış hem de bir azalma gözlemlenebilirken, çift taraflı sabit durumda büküm açısındaki artışın doğal frekanslar üzerindeki etkisi yüksek katlanmış açı değerlerinde çok daha azdır. Büküm açısı - boyutsuz doğal frekans grafiklerindeki ani değişimlerin sebebinin mode şekli değişimi olduğu görülmektedir.

Keywords

• Büküm açısı
• Serbest titreşim analizi
• Sonlu elemanlar yöntemi
• İnce plaka
• Modal analiz

FOLDED ANGLE DEPENDENT MODAL ANALYSIS OF THE FLAT AND FOLDED PLATES

Abstract

The effect of folded angle and boundary condition differences on the natural frequency, which is one of the dynamic characteristics of isotropic thin plates, is investigated. Modal analyzes of flat and folded structures are performed with ANSYS under cantilever and two-side-fixed boundary conditions. The validation of the free vibration results of the structures is performed with Solidworks. The first five natural frequencies of each structure are obtained, and the values in terms of non-dimensional natural frequency parameters are interpreted with the tables and graphics. While both an increase and a decrease can be observed depending on the increase in the folded angle in the first five natural frequencies for the cantilever boundary condition, the effect of the increase in the folded angle on the natural frequencies in the two-sided-fixed structures is much less in the higher folded angle values. It is seen that the reason for the sudden changes in the folded angle - non-dimensional natural frequency graphs is the mode shape change.

Keywords

• Folded angle
• Free vibration analysis
• Finite element method
• Thin plate
• Modal analysis

References

1. 1. Bahrami, S., Shirmohammadi, F. and Saadatpour, M.M. (2017) Vibration analysis of thin shallow shells using spectral element method. Applied Mathematical Modelling, 44, 470– 480. doi: 10.1016/j.apm.2017.02.001
2. 2. Eisenberger, M. and Deutsch, A. (2019) Solution of thin rectangular plate vibrations for all combinations of boundary conditions. Journal of Sound and Vibration, 452, 1–12. doi:10.1016/j.jsv.2019.03.024
3. 3. Gonenli, C. and Das, O. (2021) Effect of crack location on buckling and dynamic stability in plate frame structures, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 43(6), 311. doi:10.1007/s40430-021-03032-2
4. 4. Gonenli, C., Ozturk, H. and Das, O. (2021) Effect of crack on free vibration of a pre-stressed curved plate. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 095440622199486. doi:10.1177/0954406221994869
5. 5. Guha Niyogi, A., Laha, M.K. and Sinha, P.K. (1999) Finite element vibration analysis of laminated composite folded plate structures. Shock and Vibration, 6(5-6), 273-283. doi: 10.1155/1999/354234
6. 6. Guo, X., Zhang, Y., Zhang, W. and Sun, L. (2019) Theoretical and experimental investigation on the nonlinear vibration behavior of Z-shaped folded plates with inner resonance. Engineering Structures, 182, 123-140. doi:10.1016/j.engstruct.2018.12.066
7. 7. Huang, C.S., Lee, M.C. and Chang, M.J. (2018) Vibration and Buckling Analysis of Internally Cracked Square Plates by the MLS-Ritz Approach. International Journal of Structural Stability and Dynamics, 18(09), 1850105. doi:10.1142/S0219455418501055
8. 8. Kumar, A., Singha, M.K. and Tiwari, V. (2017) Nonlinear bending and vibration analyses of quadrilateral composite plates. Thin-Walled Structures, 113, 170–180. doi:10.1016/j.tws.2017.01.011

9. 9. Kumari, E. and Saxena, D. (2021) Buckling analysis of folded structures. Materials Today: Proceedings, 43, 1421-1430. doi:10.1016/j.matpr.2020.09.179
10. 10. Lee, S.Y., Wooh, S.C. and Yhim, S.S. (2004) Dynamic behavior of folded composite plates analyzed by the third order plate theory. International Journal of Solids and Structures, 41(7), 1879-1892. doi:10.1016/j.ijsolstr.2003.11.026
11. 11. Li, R., Wang, B., Li, G. and Tian, B. (2016) Hamiltonian system-based analytic modeling of the free rectangular thin plates’ free vibration. Applied Mathematical Modelling, 40(2), 984– 992. doi:10.1016/j.apm.2015.06.019
12. 12. Li, R., Wang, P., Yang, Z., Yang, J. and Tong, L. (2018) On new analytic free vibration solutions of rectangular thin cantilever plates in the symplectic space. Applied Mathematical Modelling, 53, 310–318. doi:10.1016/j.apm.2017.09.011
13. 13. Liu, W.H. and Huang, C.C. (1992). Vibration analysis of folded plates. Journal of Sound and Vibration, 157(1), 123-137. doi:10.1016/0022-460X(92)90570-N
14. 14. Meyer, C. and Scordelis, A.C. (1971). Analysis of curved folded plate structures. Journal of the Structural Division, 97(10). doi:10.1061/JSDEAG.0003020
15. 15. Mohammadi, H. and Setoodeh, A.R. (2019) FSDT-Based isogeometric analysis for free vibration behavior of functionally graded skew folded plates. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 44, 841-863. doi:10.1007/s40997- 019-00320-0
16. 16. Ozturk, H. (2011) In-plane free vibration of a pre-stressed curved beam obtained from a large deflected cantilever beam. Finite Elements in Analysis and Design, 47(3), 229–236. doi:10.1016/j.finel.2010.10.003
17. 17. Petyt, M. (2015) Introduction to finite element vibration analysis, Cambridge University Press, UK.
18. 18. Pramanik, S., Das, S. and Niyogi, A.G. (2021) Free vibration and buckling analysis of stiffened sandwich plates with repeated fold. J. Inst. Eng. India Ser. C, 102(1), 87-98. doi:10.1007/s40032-020-00627-x
19. 19. Robeller, C., Gamerro, J. and Weinand, Y. (2017) A double-layered timber folded plate structure. Journal of the Association for Shell and Spatial Structures, 58(4), 295-314. doi:10.20898/j.iass.2017.194.864
20. 20. Roche, S., Mattoni, G. and Weinand, Y. (2015) Rotational stiffness at ridges of timber foldedplate structures. International Journal of Space Structures, 30(2), 153-167. doi:10.1260/0266-3511.30.2.153
21. 21. Shell181 Element Description (2021). 4-node Structural Shell. Url: https://www.mm.bme.hu/~gyebro/files/ans_help_v182/ans_elem/Hlp_E_SHELL181.html (Access Date: 10.10.2021)
22. 22. Soleimani, H., Goudarzi, T. and Aghdam, M.M. (2021) Advanced structural modeling of a fold in Origami/Kirigami inspired structures. Thin-Walled Structures, 161, 107406. doi:10.1016/j.tws.2020.107406
23. 23. Vescovini, R. and Dozio, L.A. (2016) Variable-kinematic model for variable stiffness plates: vibration and buckling analysis, Composite Structures, 142. doi:15–26. 10.1016/j.compstruct.2016.01.068