Genelleştirilmiş Laminasyon Teorisi Kullanılarak Delaminasyon Etkileri Göz Önüne Alınan Lamine Kompozit Kirişlerin Serbest Titreşim Analizi

Year 2025, Volume: 9 Issue: 1, 117 - 124, 30.06.2025

Sebahat Şimşek

https://doi.org/10.46460/ijiea.1693283

Abstract

Lamine kompozitler oldukça karmaşık hasar mekanizmaları sergiler. Bu yapılarda karşılaşılan en kritik hasar türlerinden biri, bitişik katmanlar arasındaki ayrılmayı ifade eden ve yapısal rijitlikte önemli azalmalarla sonuçlanabilen delaminasyondur. Delaminasyonun en büyük zorluklarından biri, malzeme yüzeyinden görünmemesi nedeniyle görsel olarak tespit edilememesidir. Titreşime dayalı hasar tespit yöntemleri delaminasyonun belirlenmesinde umut vadeden bir çözüm sunsa da, bu yaklaşımların etkinliği, delaminasyonlu yapıların davranışını doğru şekilde temsil edebilecek sayısal bir modelin varlığına bağlıdır. Bu çalışma, lamine kompozit kirişlerdeki delaminasyon hasarlarının modellenmesine ve bunların serbest titreşim davranışlarının genelleştirilmiş laminasyon teorisi ve sonlu elemanlar yöntemi aracılığıyla incelenmesine odaklanmaktadır. Her bir lamina içerisindeki yer değiştirme alanının doğrusal Lagrange polinomlarına göre değiştiği varsayılmış; delaminasyon kaynaklı katmanlar arası kayma ve ayrılmaları ifade eden terimler modele açık biçimde dâhil edilmiştir. Hareket denklemleri Hamilton prensibi kullanılarak türetilmiş, ilgili kütle ve rijitlik matrisleri ise Galerkin yöntemiyle elde edilmiştir. Delaminasyonun konumu ve uzunluğunun doğal frekanslar ve mod şekilleri üzerindeki etkileri, farklı sınır koşulları ve katman dizilimleri altında incelenmiştir. Önerilen modelin doğruluğunu değerlendirmek amacıyla elde edilen sonuçlar literatürdeki mevcut çalışmalarla karşılaştırılmıştır. Ayrıca, ANSYS® yazılımı kullanılarak üç boyutlu sonlu eleman modelleri oluşturulmuş ve karşılaştırmalı analizler gerçekleştirilmiştir. Delaminasyonlu ara yüzeylerin modellenmesi için iki farklı strateji ele alınmıştır: ilkinde, delaminasyonlu yüzeylerdeki düğüm noktalarının birbirinden bağımsız hareket etmesine izin verilmiş; ikincisinde ise, katmanlar arası göreli hareketi sınırlamak amacıyla temas elemanları kullanılmıştır. Bu iki modelleme yaklaşımının simülasyon sonuçlarına etkileri detaylı şekilde değerlendirilmiştir.

Keywords

Delaminasyon, Katmanlı kompozit kiriş, Sonlu elemanlar yöntemi, Serbest titreşim, Genelleştirilmiş laminasyon teorisi

Free Vibration Analysis of Laminated Composite Beams Considering Delamination Effects Using Generalized Lamination Theory

Abstract

Laminated composites exhibit highly complex damage mechanisms. One of the most critical failure modes is delamination, which refers to the separation between adjacent layers and can lead to significant reductions in structural stiffness. A major challenge associated with delamination is its invisibility on the material surface, making visual detection difficult. Although vibration-based damage detection methods offer a promising solution for identifying delamination, the effectiveness of such approaches relies on the availability of an accurate numerical model that can capture the behavior of delaminated structures. This study focuses on the modeling of delamination damage in laminated composite beams and the investigation of their free vibration behavior through the generalized lamination theory and finite element analysis. The displacement field within each lamina is assumed to vary linearly based on Lagrange polynomials, while terms accounting for interlayer sliding and separation caused by delamination are explicitly included. The governing equations of motion are derived using Hamilton’s principle, and the corresponding mass and stiffness matrices are formulated using the Galerkin method. The influence of delamination length and position on the natural frequencies and mode shapes is examined under various boundary conditions and laminate stacking sequences. The results are compared with existing studies in the literature to validate the accuracy of the proposed model. Additionally, three-dimensional finite element models are developed using ANSYS® software to perform a comparative analysis. Two different modeling strategies for the delaminated interfaces are considered: in the first, nodes on the delaminated surfaces are allowed to move independently; in the second, contact elements are used to constrain the relative motion between layers. The impact of these two modeling approaches on the simulation results is evaluated in detail.

Keywords

Delamination, Layered composite beam, Finite element method, Free vibration, Generalized lamination theory.

References

• Ghobadi, A. (2017). Common type of damages in composites and their inspections. World Journal of Mechanics, 7(2), 24–33.
• Li, D. (2021). Layerwise theories of laminated composite structures and their applications: A review. Archives of Computational Methods in Engineering, 28, 577–600.
• Torabi, K., Shariati-Nia, M., & Heidari-Rarani, M. (2016). Experimental and theoretical investigation on transverse vibration of delaminated cross-ply composite beams. International Journal of Mechanical Sciences, 115–116, 1–11.
• Della, C. N., & Shu, D. (2007). Vibration of delaminated composite laminates: A review. Applied Mechanics Reviews, 60(1), 1.
• Goyal, V. K., & Kapania, R. K. (2007). A shear-deformable beam element for the analysis of laminated composites. Finite Elements in Analysis and Design, 43(6–7), 463–477.
• Aguiar, R. M., Moleiro, F., & Mota Soares, C. M. M. (2012). Assessment of mixed and displacement-based models for static analysis of composite beams of different cross-sections. Composite Structures, 94(2), 601–616.
• Sayyad, A. S., & Ghugal, Y. M. (2017). Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature. Composite Structures, 171, 486–504.
• Hajianmaleki, M., & Qatu, M. S. (2013). Vibrations of straight and curved composite beams: A review. Composite Structures, 100, 218–232.
• Li, D. (2020). Layerwise theories of laminated composite structures and their applications: A review. Archives of Computational Methods in Engineering, 1(0123456789), 3.
• Lansing, E., & Lansing, E. (1999). C0 zig-zag finite element for analysis of laminated composite beams. Journal of Engineering Mechanics, 125(3), 323–330.
• Zhen, W., & Wanji, C. (2008). An assessment of several displacement-based theories for the vibration and stability analysis of laminated composite and sandwich beams. Composite Structures, 84(4), 337–349.
• Khan, A. A., Alam, M. N., & Wajid, M. (2016). Finite element modelling for static and free vibration response of functionally graded beam. Latin American Journal of Solids and Structures, 13(4), 690–714.
• Filippi, M., & Carrera, E. (2016). Bending and vibrations analyses of laminated beams by using a zig-zag-layer-wise theory. Composites Part B: Engineering, 98, 269–280.
• Chen, W. Q., Lv, C. F., & Bian, Z. G. (2003). Elasticity solution for free vibration of laminated beams. Composite Structures, 62(1), 75–82.
• Kant, T., Gupta, A. B., Pendhari, S. S., & Desai, Y. M. (2008). Elasticity solution for cross-ply composite and sandwich laminates. Composite Structures, 83(1), 13–24.
• Liew, K. M., Pan, Z. Z., & Zhang, L. W. (2019). An overview of layerwise theories for composite laminates and structures: Development, numerical implementation and application. Composite Structures, 216, 240–259.
• Ji, M., Sekiguchi, Y., Naito, M., & Sato, C. (2025). A modified spectral collocation method for vibration of sandwich beams based on a higher-order layer-wise beam theory. Thin-Walled Structures, 209, Article 112949.
• Filippi, M., Giusa, D., Pagani, A., Zappino, E., & Carrera, E. (2020). Assessment of classical, advanced, and layer-wise theories for the vibration of rotating composite anisotropic blades. Composite Structures, 245, Article 112315.
• Augello, R., Carrera, E., & Saputo, S. (2025). Component-Wise measure of elastic energy contributions in laminated composite beams. Composite Structures, 355, Article 118842.
• Reddy, J. N. (2003). Mechanics of laminated composite plates and shells: Theory and analysis (2nd ed.). CRC Press/Balkema.
• Na, W. J. (2008). Damage analysis of laminated composite beams under bending loads using the layer-wise theory [Doctoral dissertation, Texas A&M University].
• Dinh-Cong, D., Vo-Duy, T., Nguyen-Minh, N., Ho-Huu, V., & Nguyen-Thoi, T. (2017). A two-stage assessment method using damage locating vector method and differential evolution algorithm for damage identification of cross-ply laminated composite beams. Advances in Structural Engineering, 20(12), 1807–1827.
• Wang, J. T. S., Liu, Y. Y., & Gibby, J. A. (1982). Vibrations of split beams. Journal of Sound and Vibration, 84(4), 491–502.
• Zhang, Z., Shankar, K., Morozov, E. V., & Tahtali, M. (2016). Vibration-based delamination detection in composite beams through frequency changes. Journal of Vibration and Control, 22(2), 496–512.