Axial Vibration Analysis of a Nanorod Embedded in Elastic Medium Using Nonlocal Strain Gradient Theory

Elastik zemine gömülü bir nano çubuğun boyut etkisine bağlı eksenel titreşimi yerel olmayan şekil değiştirme gradyanı teorisi çerçevesinde ilk olarak bu çalışmada incelenmiştir. Probleme ait yönetici hareket denklemi denge şartı kullanılarak çıkarılmış, iki ucu ankastre nano çubuğun serbest titreşim frekansına ait kesin ifadeyi elde etmek için yönetici denklem analitik olarak çözülmüştür. Yerel olmayan parametre, malzeme uzunluk ölçek parametresi ve elastik zemin parametresinin serbest titreşim frekansları üzerindeki etkisi detaylı olarak incelenmiştir. Elde edilen sayısal sonuçlar göstermiştir ki; serbest titreşim frekansları boyut etkisine önemli derecede bağlıdır ve boyut etkisi yüksek modlarda daha çok önem kazanmaktadır. Bu nedenlerden dolayı, klasik sürekli ortamlar mekaniği nano ölçekteki yapıların analizi için uygun değildir.

Yerel Olmayan ŞekilDeğiştirme Gradyanı Teorisi Kullanılarak Elastik Zemine Gömülü Nano Çubuğun Eksenel Titreşim Analizi

Size-dependent axial vibration of a nanorod embedded in elastic medium is studied for the first time in this paper within the framework of the nonlocal strain gradient theory. The governing equation of motion of the problem is derived using the equilibrium condition and it is solved analytically to obtain the exact expression of vibration frequency for a fixed-fixed nanorod. The influences of the nonlocal parameter, the material length scale parameter and the elastic medium coefficient on the free vibration frequencies are investigated in detail. The results show that free vibration frequencies are significantly dependent on the size effects, and the size effects gain more importance at higher modes. Therefore, the classical continuum theory is inappropriate to investigate the mechanical behavior of nanostructures

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