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

Öz

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.

Anahtar Kelimeler

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

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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

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