Free torsional vibration of nanotubes based on nonlocal stress theory

C. W. Lim, C. Li, J. L. Yu

    Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

    86 Citations (Scopus)

    Abstract

    A new elastic nonlocal stress model and analytical solutions are developed for torsional dynamic behaviors of circular nanorods/nanotubes. Unlike the previous approaches which directly substitute the nonlocal stress into the equations of motion, this new model begins with the derivation of strain energy using the nonlocal stress and by considering the nonlinear history of straining. The variational principle is applied to derive an infinite-order differential nonlocal equation of motion and the corresponding higher-order boundary conditions which contain a nonlocal nanoscale parameter. Subsequently, free torsional vibration of nanorods/nanotubes and axially moving nanorods/nanotubes are investigated in detail. Unlike the previous conclusions of reduced vibration frequency, the solutions indicate that natural frequency for free torsional vibration increases with increasing nonlocal nanoscale. Furthermore, the critical speed for torsional vibration of axially moving nanorods/nanotubes is derived and it is concluded that this critical speed is significantly influenced by the nonlocal nanoscale. © 2012 Elsevier Ltd. All rights reserved.
    Original languageEnglish
    Pages (from-to)2798-2808
    JournalJournal of Sound and Vibration
    Volume331
    Issue number12
    DOIs
    Publication statusPublished - 4 Jun 2012

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