Kalın ve katmanlı kompozit plakaların temel doğal frekansının mekanik özelliklerin küçük değişimlerine duyarlılığı

Year 2021, , 547 - 553, 15.04.2021

Murat Kara

https://doi.org/10.17714/gumusfenbil.773473

Abstract

Kompozit plakaların istenilen özelliklere göre tasarımı genellikle deneme yanılma ile yapılmaktadır. Bu durum elde edilen nihai tasarım sürecini uzatmaktadır. Dolayısıyla tasarım sırasında istenilen tasarım amaç fonksiyonu üzerinde etkili tasarım parametrelerin belirlenmesi oldukça önemlidir. Bu bağlamda duyarlılık analizi sıklıkla kullanılan yöntemlerden birisidir. Bu çalışmada farklı kalınlıklardaki kalın katmanlı kompozit plakaların temel (birinci) doğal frekansının duyarlılık analizi gerçekleştirilmiştir. Fiber ve fibere dik yöndeki elastisite modülü ve üç yöndeki kayma modülleri tasarım parametreleri olarak seçilmiştir. Ardından sonlu elemanlar tabanlı Monte Carlo simülasyonu ile tasarım parametrelerinin kombinasyonuna karşılık gelen doğal frekanslar hesaplanmıştır. Daha sonra duyarlılık analizi gerçekleştirmek amacıyla matematiksel bir model oluşturulmuştur. Sonuçta kalınlığa bağlı olarak temel doğal frekansın duyarlılığı elde edilmiştir.

Keywords

Doğal frekans, Duyarlılık analizi, Kalın kompozit plaka, Serbest titreşim

Sensitivity of fundamental natural frequency of thick and laminated composite plates in small changes of mechanical properties

Abstract

The design of composite plates according to the desired properties is usually performed by trial and error. This prolongs the final design process. Therefore, it is very important to determine the effective design parameters on the desired design objective function in design processes. In this regard, sensitivity analysis is one of the frequently used methods. In this study, the sensitivity analysis of the fundamental (first) natural frequency of thick layered composite plates with different thicknesses was performed. The elasticity modulus perpendicular to the fibre and among the fibre and the shear modules in the three directions are selected as design parameters. Then, natural frequencies corresponding to the combination of design parameters were calculated with finite element based Monte Carlo simulation. Next, a mathematical model was constructed to perform. As a result, the sensitivity of the fundamental natural frequency was obtained depending on the thickness.

Keywords

Natural frequency, Sensitivity analysis, Thick composite plate, Free vibration

References

• Adelman, H. M. and Haftka, R. T. (1986). Sensitivity analysis of discrete structural systems. AIAA Journal, 24(5), 823–832. https://doi.org/10.2514/3.48671.
• Arora, J. S. and Haugt, E. J. (1979). Methods of design sensitivity analysis in structural optimization. AIAA Journal, 17(9), 970–974. https://doi.org/10.2514/3.61260.
• Dey, S., Mukhopadhyay, T. and Adhikari, S. (2015). Stochastic free vibration analysis of angle-ply composite plates - A RS-HDMR approach. Composite Structures, 122, 526–536. https://doi.org/10.1016/j.compstruct.2014.09.057.
• Fox, R. L. and Kapoor, M. P. (1968). Rates of change of eigenvalues and eigenvectors. AIAA Journal, 6(12), 2426–2429. https://doi.org/10.2514/3.5008.
• Grenestedt, J. L. (1989). Layup optimization and sensitivity analysis of the fundamental eigenfrequency of composite plates. Composite Structures, 12(3), 193–209. https://doi.org/10.1016/0263-8223(89)90022-6.
• Hyer, M. W. and Lee, H. H. (1991). The use of curvilinear fiber format to improve buckling resistance of composite plates with central circular holes. Composite Structures, 18(3), 239–261. https://doi.org/10.1016/0263-8223(91)90035-W.
• Juhász, Z., Turcsán, T., Tóth, T. B. and Szekrényes, A. (2018). Sensitivity analysis for frequency based prediction of crack size in composite plates with through-the-width delamination. International Journal of Damage Mechanics, 27(6), 859–876. https://doi.org/10.1177/1056789517709893.
• Kengtung, C. (1986). Sensitivity analysis and a mixed approach to the optimization of symmetric layered composite plates. Engineering Optimization, 9(4), 233–247. https://doi.org/10.1080/03052158608902516.
• Khdeir, A. A. and Librescu, L. (1988). Analysis of symmetric cross-ply laminated elastic plates using a higher-order theory: Part II-Buckling and free vibration. Composite Structures, 9(4), 259–277. https://doi.org/10.1016/0263-8223(88)90048-7.
• Kompella, M. S. and Bernhard, R. J. (1993). Measurement of the statistical variation of structural-acoustic characteristics of automotive vehicles. SAE Technical Paper 931272. https://doi.org/10.4271/931272.
• Li, D. H., Liu, Y. and Zhang, X. (2013). Linear statics and free vibration sensitivity analysis of the composite sandwich plates based on a layerwise/solid-element method. Composite Structures, 106, 175–200. https://doi.org/10.1016/j.compstruct.2013.05.056.
• Lima, A. M. G. d., Faria, A. W. and Rade, D. A. (2010). Sensitivity analysis of frequency response functions of composite sandwich plates containing viscoelastic layers. Composite Structures, 92(2), 364–376. https://doi.org/10.1016/j.compstruct.2009.08.017.
• Mateus, H. C., Soares, C. M. M. and Soares, C. A. M. (1991). Sensitivity analysis and optimal design of thin laminated composite structures. Computers and Structures, 41(3), 501–508. https://doi.org/10.1016/0045-7949(91)90144-B.
• Pouresmaeeli, S., Fazelzadeh, S. A., Ghavanloo, E. and Marzocca, P. (2018). Uncertainty propagation in vibrational characteristics of functionally graded carbon nanotube-reinforced composite shell panels. International Journal of Mechanical Sciences, 149, 549–558. https://doi.org/10.1016/j.ijmecsci.2017.05.049.
• Pouresmaeeli, S. and Fazelzadeh, S. A. (2017). Uncertain buckling and sensitivity analysis of functionally graded carbon nanotube-reinforced composite beam. International Journal of Applied Mechanics, 9(5). https://doi.org/10.1142/S1758825117500715.
• Soares, C. M. M., Correia, V. F., Mateus, H. and Herskovits, J. (1995). A discrete model for the optimal design of thin composite plate-shell type structures using a two-level approach. Composite Structures, 30(2), 147–157. https://doi.org/10.1016/0263-8223(94)00042-5.
• Whitney, J. M. (1987). Structural analysis of laminated anisotropic plates. Pennsylvania: Technomic Publishing.
• Zak, A. J., Cartmell, M. P. and Ostachowicz, W. M. (2003). A sensitivity analysis of the dynamic performance of a composite plate with shape memory alloy wires. Composite Structures, 60(2), 145–157. https://doi.org/10.1016/S0263-8223(02)00316-1.
• Zhang, Z., Zhan, C., Shankar, K., Morozov, E. V., Singh, H. K. and Ray, T. (2017). Sensitivity analysis of inverse algorithms for damage detection in composites. Composite Structures, 176, 844–859. https://doi.org/10.1016/j.compstruct.2017.06.019.