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DYnAMIC AnALYSIS OF A GRADIEnT ELASTIC POLYMERIC FIBER

Acta Mechanica Solida Sinica 2013年第1期26卷 9-20页

作者： K.Y.Xu K.A.Alnefaie n.h.abu-hamdeh K.h.Almitani E.C.Aifantis Department of Mechanics Shanghai University Department of Mechanical Engineering King Abdulaziz University Lab of Mechanics and Materials Polytechnic SchoolAristotle University

A dynamic analysis of an elastic gradient-dependent polymeric fiber subjected to a periodic excitation is considered. A nonlinear gradient elasticity constitutive equation with strain- dependent gradient coefficients is first derived and the dispersive wave propagation properties for its linearized counterpart are briefly discussed. For the linearized problem a variational formulation is also developed to obtain related boundary conditions of both classical （standard） and non-classical （gradient） type. Analytical solutions in the form of Fourier series for the fiber＇s displacement and strain fields are provided. The solutions depend on a dimensionless scale parameter （the diameter to length radio d = D/L） and, therefore, size effects are captured.

关键词： gradient elasticity polymeric fibers periodic excitations size effects

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FREE TRAnSVERSE VIBRATIOnS OF A DOUBLE-WALLED CARBOn nAnOTUBE:GRADIEnT AnD InTERnAL InERTIA EFFECTS

引用

Acta Mechanica Solida Sinica 2014年第4期27卷 345-352页

作者： K.Y.Xu K.A.Alnefaie n.h.abu-hamdeh K.h.Almitani E.C.Aifantis Department of Mechanics Shanghai University Department of Mechanical Engineering King Abdulaziz University Jeddah 21589 Saudi Arabia Lab of Mechanics and Materials Polytechnic School Aristotle University Thessaloniki 54124 Greece

This is a modest contribution on higher-order continuum theory for predicting size effects in small-scale objects. It relates to a preceding article of the journal by the same authors（AMSS, 2013, 26： 9-20） which considered the longitudinal dynamical analysis of a gradient elastic fiber but, in addition to an internal length, an internal time parameter is also introduced to model delay/acceleration effects associated with the underlying microstructure. In particular, the free transverse vibration of a double-walled carbon nanotube（DWnT） is studied by employing gradient elasticity with internal inertia. The inner and outer carbon nanotubes are modeled as two individual elastic beams interacting with each other through van der Waals（vdW） forces. General explicit expressions are derived for the natural frequencies and the associated inner-to-outer tube amplitude ratios for the case of simply supported DWnTs. The effects of internal length（or scale）and internal time（or inertia） on the vibration behavior are evaluated. The results indicate that the internal length and time parameters of the adopted strain gradient-internal inertia generalized elasticity model have little influence on the lower order coaxial and noncoaxial vibration modes,but a significant one on the higher order modes.

关键词： carbon nanotubes gradient elasticity internal inertia vibration behavior

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