Yerel olmayan elastisite teorisine göre akışkan taşıyan nanokirişin serbest titreşimlerinin analizi

Yıl 2017, Cilt: 23 Sayı: 1, 6 - 11, 01.03.2017

Süleyman Murat Bağdatlı , Necla Toğun

Öz

Bu
çalışmada, basit-basit ve ankastre-ankastre sınır şartları altında akışkan
taşıyan nanokirişin doğrusal titreşimleri incelenmiştir. Eringen’in yerel
olmayan elastisite teorisi Euler-Bernoulli kiriş modeline uygulanmıştır. Yerel
olmayan elastisite teorisi MEMS ve NEMS yapıların mekaniksel analizinde gelişen
popüler bir tekniktir. Hareket denklemlerini ve sınır şartlarını elde etmek
için Hamilton prensibi kullanılmıştır. Denklemler boyutsuz formda elde
edilmiştir. Elde edilen hareket denklemi ve sınır şartları malzeme ve geometrik
yapıdan bağımsız hale getirilmiştir. Akışkan hızının, ortalama sabit bir hız
etrafında harmonik olarak değiştiği kabul edilmiştir. Perturbasyon
metotlarından biri olan çok zaman ölçekli metot kullanılarak yaklaşık çözümler
elde edilmiştir. Perturbasyon serisindeki ilk terim doğrusal problemi
oluşturmaktadır. Doğrusal problemin çözümü ile tabii frekanslar ve mod yapıları
farklı sınır şartları için hesaplanmıştır. Her iki mesnet durumu için yerel
olmayan parametre



















 ve akışkan hızı

 artığında tabii frekanslar azalmaktadır.
Sonuçlar grafiklerle sunulmuş ve yorumlanmıştır.

Anahtar Kelimeler

Titreşim, Akışkan taşıyan nano ölçekli kiriş, Perturbasyon metodu, Yerel olmayan elastisite teorisi

Free vibrations analysis of fluid conveying nanobeam based on nonlocal elasticity theory

Öz

In
this study, linear vibration analysis of a nanobeam conveying fluid is
investigated under simple-simple and clamped-clamped boundary conditions.
Eringen’s nonlocal elasticity theory is applied to Euler-Bernoulli beam model.
Nonlocal elasticity theory is a popular growing technique for the mechanical
analyses of MEMS and NEMS structures. The Hamilton’s principle is employed to
derive the governing equations and boundary conditions. Non-dimensional form of
equations is obtained. The obtained equations of motion and boundary conditions
are independent from material and geometric structure. It is assumed that fluid
velocity is harmonically changed about a constant average speed. Approximate
solutions were obtained using the Method of Multiple Scales, a perturbation
method. The first term in perturbation series composes linear problem. Natural
frequencies and mode shapes are calculated by solving the linear problem for
different boundary conditions. For both boundary conditions, the natural
frequencies are decreased by increasing the nonlocal parameter



















 and the fluid velocity

. The
results are presented and interpreted by graphics.

Anahtar Kelimeler

Vibration, Nanobeam conveying fluid, Perturbation method, Nonlocal elasticity theorem

Kaynakça

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