Torsional vibration of nonprismatically nonhomogeneous nanowires with multiple defects: Surface energy-nonlocal-integro-based formulations

Abstract

Torsional vibration of nonuniformly nonhomogeneous nanowires with multiple defects is going to be comprehensively examined using advanced continuum-based mechanics. The nonlocal-differential/integral-surface energy-based equations of motion of the defected nanostructure are derived, and the non-classical conditions at the local defects and the ends are displayed. Concerning the nonlocal-differential-based model, in the particular case of uniformly homogeneous nanowire, an exact solution is presented, and the characteristic equations of the nanowire with multiple defects are explicitly presented for several end conditions. Subsequently, a semi-analytical approach is established through dividing the consisting nanosegments of the defected nanowire into adequately tiny subsegments, expressing their amplitude field functions, and enforcing the conditions at their ends. To capture the free dynamic response more systematically, novel fully/partially nonlocal-integral formulations are also developed and solved numerically. The finite-element method is applied to the newly developed nonlocal-differential/integral-based models, and the natural frequencies are successfully verified with those of the semi-analytical approach. Using the suggested nonlocal-integral model, the influences of the nonlocality, surface energy, number of defects, location of defects, non-homogeneity, cross-sectional non-uniformity on the torsional frequencies are noticed and discussed.