Forced Vibration Analysis of A Heterogeneous Rod by Complementary Functions Method

Öz

The axial vibration problem formulation and solution of a heterogeneous rod modelled as a continuous system were analyzed. By applying Laplace transformation to the differential equations that model to this problem, time independent boundary value problems were obtained in the axial coordinates, then this problem is solved by the complementary functions method. The equations solved numerically is converted into time space with the help of Durbin’s numerical inverse transformation. The numerical results that obtained for each load type and inhomogeneity parameter were compared with analytical and ANSYS results in the literature. This unified method is well-structured, simple and efficient.

Anahtar Kelimeler

• Heterogeneous rod,Forced vibration,Laplace,Complementary functions method

Tamamlayıcı Fonksiyonlar Yöntemi ile Heterojen Bir Çubuğun Zorlanmış Titreşim Analizi

Öz

Sürekli sistem olarak modellenen eksenel yüklenmiş heterojen bir çubuğun elastik davranış problemi analiz edilmiştir. Bu problemi modelleyen diferansiyel denklemlere Laplace dönüşümü uygulanarak zamandan bağımsız sınır değer problemi eksenel koordinatlarda elde edilmiş daha sonra bu problem tamamlayıcı fonksiyonlar metodu (TFM) tarafından çözülmüştür. Sayısal olarak çözülen denklemler Durbin’in sayısal ters dönüşümünü yardımıyla zaman uzayına dönüştürülmüştür. Her bir yükleme tipi ve inhomojenlik parametresi için elde edilen sayısal sonuçlar, analitik sonuçlar ve ANSYS sonuçları ile karşılaştırılmıştır. Bu birleşik yöntem, iyi yapılandırılmış, basit ve etkili bir yöntemdir.

Anahtar Kelimeler

• Heterojen çubuk,Zorlanmış titreşim,Laplace,Tamamlayıcı fonksiyonlar yöntemi

Kaynakça

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