Investigation of axial vibration of nanorod in elastic media using nonlocal elasticity theory

Yıl 2022, , 11 - 25, 30.09.2022

Güler Gaygusuzoğlu

https://doi.org/10.17714/gumusfenbil.1013450

Öz

In this study, axial vibration of a nano rod in an elastic media is discussed using the non-local elasticity theory. Equations of motion of the problem are obtained by means of equilibrium conditions and solved analytically. The expressions giving the free vibration frequencies of the fixed-fixed nanorod and fixed-free nanorod were found depending on the non-local parameter and the elastic medium parameters. For fixed-fixed and fixed-free boundary conditions, the relationships between vibration frequencies and elastic medium parameter and nonlocal parameter are examined and the results are shown on graphs. Physical and material properties of the carbon nanotube were used for numerical results. With the results, it was seen that free vibration frequencies are remarkably be subject to size and the size effect is more effective in high modes. The frequency values which obtained using the classical elasticity theory are very distinct than obtained using the non-local elasticity theory.

Anahtar Kelimeler

Axial vibration, Nanorod, Nonlocal elasticity theory

Yerel olmayan elastisite teorisi kullanılarak elastik ortam içerisindeki nano çubuğun eksenel titreşiminin incelenmesi

Öz

Bu çalışmada, yerel olmayan elastisite teorisi kullanılarak elastik ortamda bir nano çubuğun eksenel titreşimi ele alınmıştır. Probleme ait hareket denklemleri denge şartları vasıtasıyla elde edilmiş ve analitik olarak çözülmüştür. İki ucu ankastre ve bir ucu ankastre bir ucu serbest nano çubuğun serbest titreşim frekanslarını veren ifadeler yerel olmayan parametre ve elastik ortam parametrelerine bağlı olarak bulunmuştur. Ankastre-ankastre ve ankastre-serbest sınır koşulları için, titreşim frekansları ile elastik ortam parametresi ve yerel olmayan parametrenin ilişkileri incelenerek sonuçlar grafikler üzerinde gösterilmiştir. Sayısal sonuçlar için karbon nano çubuğa ait fiziksel ve malzeme özellikleri kullanılmıştır. Elde edilen sonuçlarla serbest titreşim frekanslarının boyuta önemli ölçüde bağlı olduğu ve boyut etkisinin yüksek modlarda daha etkili olduğu görülmüştür. Yerel teori ile elde edilen frekans değerleri, yerel olmayan elastisite teorisi kullanılarak elde edilenlerden çok farklıdır.

Anahtar Kelimeler

Eksenel titreşim, Nano çubuk, Yerel olmayan elastisite teorisi

Kaynakça

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