Semi Analytical and Numerical Investigation of Vibration of Beams Partially Supported by Elastic Foundation

Year 2020, , 2679 - 2691, 15.12.2020

Hakan Erdoğan , Safa Bozkurt Coşkun

https://doi.org/10.21597/jist.722522

Abstract

In this study vibration of a beam partially supported by an elastic foundation is investigated. Euler beam model and Winkler foundation as the most widely used foundation model are selected. There are numerous studies in the literature about the vibration of beams on elastic foundations. However, limited studies exist in the literature about the vibration of beams on partially supported by foundation while no analytical solution is available. To this aim a semi-analytical solution is obtained using variational iteration method and then finite element solutions are computed via SAP 2000 software. Free vibration frequencies of a beam on partially supported by foundation are calculated according to different combinations of boundary conditions and first four free vibration frequencies with the varying foundation region are computed.

Keywords

Partial elastic foundation, Beam, Vibration, Variational iteration method, Finite element method

Kısmen Elastik Zemin Üzerindeki Kiriş Titreşiminin Yarı Analitik ve Nümerik Yöntemler ile İncelenmesi

Abstract

Bu çalışmada kısmen elastik zemin üzerindeki bir kirişin serbest titreşim problemi incelenmiştir. Kiriş modeli olarak Euler kirişi modeli, zemin modeli olarak da en yaygın kullanılan zemin modeli olan Winkler modeli kullanılmıştır. Elastik zemin üzerindeki kirişlerin titreşim problemi ile ilgili çeşitli araştırmalar literatürde mevcut olmakla birlikte, kısmen elastik zemin problemi için analitik çözümler mevcut olmayıp ve diğer yöntemlerle yapılan çalışmalarda oldukça sınırlıdır. Bu amaçla problemin varyasyonel iterasyon metodu ile önce yarı analitik çözümü yapılmış daha sonra da SAP 2000 yazılımı ile sonlu eleman analizleri gerçekleştirilmiştir. Farklı sınır koşulları altında kısmen elastik zemin üzerindeki kirişlerin analizi gerçekleştirilmiş, elastik zeminle desteklenen bölgenin değişimine bağlı olarak ilk dört serbest titreşim frekansı elde edilmiştir.

Keywords

Kısmen elastik zemin, Kiriş, Titreşim, Varyasyonel iterasyon metodu, Sonlu eleman yöntemi

References

• Cazzani A, 2013. On the dynamics of a beam partially supported by an elastic foundation: an exact solution set. International Journal of Structural Stability and Dynamics, 13: 1350045,1-30.
• Coşkun SB, Atay MT, Öztürk B, 2011. Transverse vibration analysis of Euler-Bernoulli beams using analytical approximate techniques. Advances in Vibration Analysis Research, F. Ebrahimi, IntechOpen Press, pp.1-22.
• Coşkun SB, Öztürk B, Mutman, U, 2014. Adomian decomposition method for vibration of nonuniform Euler beams on elastic foundation. Proceedings of the 9th International Conference on Structural Dynamics (EURODYN 2014), Porto, June 30-July 2, 2014, pp:1935-1940.
• CSI, SAP2000, Static and Dynamic Finite Element Analysis of Structures, Version 21.02, Computers and Structures, Inc., Berkeley, USA.
• Çinçin C, 2018. Kısmen elastik zemin üzerindeki kiriş titreşiminin Adomian ayrıştırma yöntemi ile analizi, Kocaeli Üniversitesi Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi (Basılmış).
• Çinçin C, Coşkun SB, 2019. Analysis of beam vibrations on partial elastic foundation using Adomian decomposition method. Kocaeli Journal of Science and Engineering, 2: 28-33.
• Doyle PF, Pavlovic MN, 1982. Vibration of beams on partial elastic foundations. Earthquake Engineering and Structural Dynamics, 10: 663-674.
• Eisenberger M, Yankelevsky DZ, Adin MA, 1985. Vibrations of beams fully or partially supported on elastic foundations. Earthquake Engineering and Structural Dynamics, 13: 652-660.
• He JH, 1999. Variational iteration method – a kind of nonlinear analytical technique. International Journal of Nonlinear Mechanics, 34: 699-708.
• He JH, 2007. The variational iteration method: Reliable, efficient and promising. Computers and Mathematics with Applications, 54: 879-880.
• Kukla S, 1991. Free vibration of a beam supported on a stepped elastic foundation. Journal of Sound and Vibration, 149: 259-265.
• Laura PAA, Cortinez VH, 1987. Vibrating beam partially embedded in Winkler-type foundation. Journal of Engineering Mechanics, 113: 143-147.
• Motaghian, SE, Mofida M, Alanjari P, 2011. Exact solution to free vibration of beams partially supported by an elastic foundation. Scientia Iranica, 18: 861-866.
• Öztürk B, 2009. Free vibration analysis of beam on elastic foundation by the variational iteration method, International Journal of Nonlinear Sciences and Numerical Simulation, 10: 1255-1262.
• Öztürk B, Coşkun SB, 2013. Analytical solution for free vibration analysis of beam on elastic foundation with different support conditions, Mathematical Problems in Engineering, ID 470927, 7 pages
• Thambiratnam D, Zhuge Y, 1996. Free vibration analysis of beams on elastic foundation, Computers and Structures, 60: 971-980.