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

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 (γ) and the fluid velocity (v0). The results are presented and interpreted by graphics.

Yerel olmayan elastisite teorisine göre akýþkan taþýyan nanokiriþin serbest titreþimlerinin analizi

Bu çalýþmada, basit-basit ve ankastre-ankastre sýnýr þartlarý altýnda akýþkan taþýyan nanokiriþin doðrusal titreþimleri incelenmiþtir. Eringen’in yerel olmayan elastisite teorisi Euler-Bernoulli kiriþ modeline uygulanmýþtýr. Yerel olmayan elastisite teorisi MEMS ve NEMS yapýlarýn mekaniksel analizinde geliþen popüler bir tekniktir. Hareket denklemlerini ve sýnýr þartlarýný elde etmek için Hamilton prensibi kullanýlmýþtýr. Denklemler boyutsuz formda elde edilmiþtir. Elde edilen hareket denklemi ve sýnýr þartlarý malzeme ve geometrik yapýdan baðýmsýz hale getirilmiþtir. Akýþkan hýzýnýn, ortalama sabit bir hýz etrafýnda harmonik olarak deðiþtiði kabul edilmiþtir. Perturbasyon metotlarýndan biri olan çok zaman ölçekli metot kullanýlarak yaklaþýk çözümler elde edilmiþtir. Perturbasyon serisindeki ilk terim doðrusal problemi oluþturmaktadýr. Doðrusal problemin çözümü ile tabii frekanslar ve mod yapýlarý farklý sýnýr þartlarý için hesaplanmýþtýr. Her iki mesnet durumu için yerel olmayan parametre (γ) ve akýþkan hýzý (v0) artýðýnda tabii frekanslar azalmaktadýr. Sonuçlar grafiklerle sunulmuþ ve yorumlanmýþtýr.