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Journals / Gümüşhane Üniversitesi Fen Bilimleri Dergisi / 2022 / IOCENS'21 Konferansı Ek Sayısı

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

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

Güler GAYGUSUZOĞLU
Pages
11–25
Publication Date
2022-09-30
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The frequency values which obtained using the classical elasticity theory are very distinct than obtained using the non-local elasticity theory.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, axial vibration of a nano rod in an elastic media is discussed using the non-local elasticity theory.
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Key Findings & Data:Equations of motion of the problem are obtained by means of equilibrium conditions and solved analytically.
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Conclusion & Impact:The frequency values which obtained using the classical elasticity theory are very distinct than obtained using the non-local elasticity theory.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Eksenel titreşim · Nano çubuk · Yerel olmayan elastisite teorisi

Abstract

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.

Özet

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.

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Cite This Article

GAYGUSUZOĞLU, G. (2022). Investigation of axial vibration of nanorod in elastic media using nonlocal elasticity theory. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, IOCENS'21 Konferansı Ek Sayısı, 11–25. https://ajindex.com/articles/668285

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