Damped and Undamped Forced Vibration Analysis of Beams Made of Functionally Graded Materials

Öz

In this study, a research has been conducted on the forced vibration behavior of beams with functionally graded (FG) material along the height of the cross-section under various dynamic loads. The effects of different boundary conditions, length-height (L/h) ratios and material variation coefficients on damped and undamped forced vibrations of Euler-Bernoulli and Timoshenko beams are also examined parametrically. The equations of motion which govern the behavior of the beams with FG material have been obtained with the help of the minimum total energy principle. The canonical differential equations obtained are solved numerically in the Laplace space with the aid of Complementary Functions Method (CFM). Kelvin type damping model is used in case of viscoelastic material. In this model, elastic constants are replaced by their complex counterparts in the Laplace space by means of the elastic- viscoelastic analogy. The accuracy of the results of the proposed method has been confirmed by comparing it with the results of the ANSYS finite element package program.

Anahtar Kelimeler

• Functionally graded materials
• Complementary functions method
• Inverse Laplace transform
• Kelvin damping model

Fonksiyonel Derecelenmiş Malzemeli Kirişlerin Sönümlü ve Sönümsüz Zorlanmış Titreşim Analizi

Öz

Bu çalışmada, kesit yüksekliği boyunca fonksiyonel olarak derecelendirilmiş (FD) malzemeli kirişlerin çeşitli dinamik yükler altında zorlanmış titreşim davranışı üzerine bir araştırma yapılmıştır. Farklı sınır koşulları, uzunluk-yükseklik (L/h) oranları ve malzeme değişim katsayılarının Euler-Bernoulli ve Timoshenko kirişlerinin sönümlü ve sönümsüz zorlanmış titreşimleri üzerindeki etkileri de parametrik olarak incelenmiştir. FD malzemeli çubukların davranışını idare eden hareket denklemleri, minimum toplam enerji prensibi yardımıyla elde edilmiştir. Elde edilen kanonik diferansiyel denklemler, Tamamlayıcı Fonksiyonlar Yöntemi (TFY) yardımıyla Laplace uzayında sayısal olarak çözülmüştür. Viskoelastik malzeme durumunda Kelvin tipi sönüm modeli kullanmıştır. Bu modelde elastik sabitler, elastik-viskoelastik analoji ile Laplace uzayındaki kompleks karşıtları ile değiştirilir. Önerilen yöntemin sonuçlarının doğruluğu, ANSYS sonlu elemanlar paket programının sonuçları ile karşılaştırılarak kanıtlanmıştır.

Anahtar Kelimeler

• Fonksiyonel derecelenmiş malzeme
• Tamamlayıcı fonksiyonlar yöntemi
• Ters Laplace dönüşümü
• Kelvin sönüm modeli

Kaynakça

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