Yerel olmayan elastisite teorisi kullanılarak nano ölçekli çubuklarda nonlineer dalga yayılımı

Year 2019, Volume: 21 Issue: 1, 190 - 204, 15.03.2019

Güler Gaygusuzoğlu

https://doi.org/10.25092/baunfbed.543422

Abstract

Bu çalışmada, yerel olmayan elastisite teorisi kullanılarak nano ölçekli çıbuklarda zayıf nonlineer dalga yayılımı incelenmiştir. Mühendislik, fizik ve doğal bilimlerde birçok sistem nonlineerdir ve nonlineer denklemlerle modellenir. Lineer olmayan bilimin bir dalı olan dalga yayılımı son yıllarda yaygın olarak çalışılan konulardan biridir.  Yerel olmayan elastisite teorisi microelektromekanik ve nanoelektromekanik gibi sistemlerin analizinde gelişen popüler bir tekniktir. Formülasyonlarda Eringen’in yerel olmayan elastisite teorisine dayanan bünye denklemleri kullanılmıştır. Hareket denklemleri malzeme koordinatları cinsinden yazılmış ve nano ölçekli çubuğun doğrusal olmayan hareket denklemleri yerel olmayan elastisite teorisine göre elde edilmiştir. İndirgeyici pertürbasyon metodu kullanılarak zayıf nonlineer dalgaların hareketini yöneten evolüsyon denklemi olarak Korteweg de Vries (KdV) denklemi elde edilmiştir.  KdV denkleminde yerel olmayan etkiyi nümerik olarak gözlemleyebilmek için, karbon nanotüplerin fiziksel ve geometrik özellikleri göz önünde bulundurulmuştur.

Keywords

Nano ölçekli çubuk, Yerel olayan elastisite teorisi, nonlineer dalgalar, indirgeyici pertürbasyon metodu

Propagation of weakly nonlinear waves in nanorods using nonlocal elasticity theory

Abstract

The present research examines the propagation of weakly solitary waves in nanorods by employing nonlocal elasticity theory. Many systems in physics, engineering, and natural sciences are nonlinear and modeled with nonlinear equations. Wave propagation, as a branch of nonlinear science, is one of the most widely studied subjects in recent years. Nonlocal elasticity theory represents a technique with increasing popularity for the purpose of conducting the mechanical analysis of microelectromechanical and nanoelectromechanical systems. The nonlinear equation of motion of nanorods is derived by utilizing nonlocal elasticity theory. The reductive perturbation technique is employed for the purpose of examining the propagation of weakly nonlinear waves in the longwave approximation, and the Korteweg-de Vries equation is acquired as the governing equation. The steady-state solitary-wave solution is known to be admitted by the KdV equation. To observe the nonlocal effects on the KdV equation numerically, the existence of solitary wave solution has been investigated using the physical and geometric properties of carbon nanotubes. 

Keywords

Nanorod, nonlocal elasticity theory, Nonlinear waves, reductive perturbation technique

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