Sentaktik Köpük Eğri Kirişlerin Diferansiyel Quadrature Metodu ile Serbest Titreşim Analizi

Yıl 2024, Cilt: 14 Sayı: 2, 835 - 847, 01.06.2024

Sinan Maraş

https://doi.org/10.21597/jist.1368876

Öz

Bu çalışmada, iki ucu basit mesnetli sınır şartına sahip sentaktik köpük eğri kirişlerin serbest titreşim analizleri Diferansiyel Qaudrature metodu (DQM) ile nümerik olarak incelenmiştir. Yer değiştirme alanı, klasik kiriş teorisine göre ifade edilmiş; Newton’un hareket yasaları kullanılarak hareket denklemleri elde edilmiştir. Bu amaçla, MATLAB kullanılarak bir DQM kodu geliştirilmiş ve epoksi/cam mikro balon (MB) bazlı sentaktik köpük eğri kirişlerin MB hacim oranları, MB yoğunlukları gibi malzeme parametrelerinin ve eğrilik açısı ve eğrilik yarıçapı gibi geometrik parametrelerinin serbest titreşim analizi üzerindeki etkilerini incelemek için yapıların doğal frekansları elde edilmiştir. Araştırmadan elde edilen sonuçlar, MB hacim oranlarının, yoğunluklarının ve eğri kirişin geometrik özelliklerinin sentaktik köpük eğri kirişlerin titreşim davranışlarını önemli ölçüde etkilediğini ortaya koymaktadır.

Anahtar Kelimeler

Sentetik köpük, Titreşim analizi, Nümerik analiz, Diferansiyel quadrature metodu

Free Vibration Analysis of Syntactic Foam Curved Beams by Differential Quadrature Method

Öz

In this study, the free vibration analysis of syntactic foam curved beams with two simply supported ends was numerically investigated by the Differential Quadrature Method (DQM). The displacement field was expressed according to classical beam theory, and motion equations were derived by Newton's laws of motion. For this purpose, a DQM code was developed using MATLAB, and the natural frequencies of structures were obtained to examine the effects of material parameters such as microballoon (MB) volume fractions, MB densities, as well as geometric parameters like curvature angle and curvature radius on the free vibration analysis of epoxy/glass microballoon-based syntactic foam curved beams. The results obtained from the research indicate that MB volume fractions, densities, and the geometric characteristics of curved beams significantly influence the vibration behavior of syntactic foam curved beams.

Anahtar Kelimeler

Syntactic foam, Vibration analysis, Numerical analysis, Differential quadrature method

Kaynakça

• Anirudh, S., Jayalakshmi, C., Anand, A., Kandasubramanian, B., ve Ismail, S. O. (2022). Epoxy/hollow glass microsphere syntactic foams for structural and functional application-A review. European Polymer Journal, 171, 111163.
• Bardella, L., ve Genna, F. (2001). On the elastic behavior of syntactic foams. International Journal of Solids and Structures, 38(40-41), 7235-7260.
• Bellman, R., ve Casti, J. (1971). Differential quadrature and long-term integration. Journal of mathematical analysis and Applications, 34(2), 235-238.
• Culver, C. G. (1967). Natural frequencies of horizontally curved beams. Journal of the Structural Division, 93(2), 189-204.
• Gupta, N., Gupta, S. K., ve Mueller, B. J. (2008). Analysis of a functionally graded particulate composite under flexural loading conditions. Materials Science and Engineering: A, 485(1-2), 439-447.
• Gupta, N., Ye, R., ve Porfiri, M. (2010). Comparison of tensile and compressive characteristics of vinyl ester/glass microballoon syntactic foams. Composites Part B: Engineering, 41(3), 236-245.
• Hajianmaleki, M., ve Qatu, M. S. (2012). Static and vibration analyses of thick, generally laminated deep curved beams with different boundary conditions. Composites Part B: Engineering, 43(4), 1767-1775.
• Kadioglu, F., ve Iyidogan, C. (2009). Free vibration of laminated composite curved beams using mixed finite element formulation. Science and Engineering of Composite Materials, 16(4), 247-258.
• Kang, K., Bert, C. W., ve Striz, A. G. (1996). Vibration analysis of horizontally curved beams with warping using DQM. Journal of Structural Engineering, 122(6), 657-662.
• Karamanli, A., Wattanasakulpong, N., Lezgy-Nazargah, M., ve Vo, T. P. (2023). Bending, buckling and free vibration behaviours of 2D functionally graded curved beams. Structures, 55, 778-798.
• Liang, M., Lu, F., ve Li, X. (2017). Dynamic responses and failure of short glass-fiber reinforced syntactic foams. International Journal of Applied Mechanics, 9(01), 1750002.
• Maraş, S., Yaman, M., ve Şansveren, M. F. (2019). Dynamic Analysis of Laminated Syntactic Foam Beams. 3rd International Conference on Advanced Engineering Technologies.
• Moghaddasi, M., ve Kiani, Y. (2022). Free and forced vibrations of graphene platelets reinforced composite laminated arches subjected to moving load. Meccanica, 57(5), 1105-1124.
• Osman, M. Y., ve Suleiman, O. M. E. (2017). Free vibration analysis of laminated composite beams using finite element method'. International Journal of Engineering Research and Advanced Technology (IJERAT), 3(2), 5-22.
• Porfiri, M., ve Gupta, N. (2009). Effect of volume fraction and wall thickness on the elastic properties of hollow particle filled composites. Composites Part B: Engineering, 40(2), 166-173.
• Poveda, R. L., Achar, S., ve Gupta, N. (2014). Viscoelastic properties of carbon nanofiber reinforced multiscale syntactic foam. Composites Part B: Engineering, 58, 208-216.
• Qatu, M. (1992). In-plane vibration of slightly curved laminated composite beams. Journal of Sound and Vibration, 159(2), 327-338.
• Sayyad, A. S., ve Avhad, P. V. (2022). A new higher order shear and normal deformation theory for the free vibration analysis of sandwich curved beams. Composite Structures, 280, 114948.
• Shore, S., ve Chaudhuri, S. (1972). Free vibration of horizontally curved beams. Journal of the Structural Division, 98(3), 793-796.
• Siddiqi, Z. A. (1995). Analysis of interacting subdomains in structural mechanics problems by the differential quadrature method: The University of Oklahoma.
• Skoptsov, K. A., Sheshenin, S. V., Galatenko, V. V., Malakho, A. P., Shornikova, O. N., Avdeev, V. V., ve Sadovnichy, V. A. (2016). Particle simulation for predicting effective properties of short fiber reinforced composites. International Journal of Applied Mechanics, 8(02), 1650016.
• Srinivasa, C. V., Suresh, Y. J., ve Kumar, W. P. (2014). Experimental and finite element studies on free vibration of skew plates. International Journal of Advanced Structural Engineering (IJASE), 6(1), 48.
• Şansveren, M. F., ve Yaman, M. (2019). The effect of carbon nanofiber on the dynamic and mechanical properties of epoxy/glass microballoon syntactic foam. Advanced Composite Materials, 28(6), 561-575.
• Tan, C. P., ve Shore, S. (1968). Dynamic response of a horizontally curved bridge. Journal of the Structural Division, 94(3), 761-781.
• Yoo, C. H., ve Fehrenbach, J. P. (1981). Natural frequencies of curved girders. Journal of the Engineering Mechanics Division, 107(2), 339-354.
• Yoon, K.-Y., Park, N.-H., Choi, Y.-J., ve Kang, Y.-J. (2006). Natural frequencies of thin-walled curved beams. Finite elements in analysis and design, 42(13), 1176-1186.