Yerel olmayan elastisite teorisine göre akışkan taşıyan nanokirişin serbest titreşimlerinin analizi

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

Abstract

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.

Keywords

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

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