On vibrations of nanobeam systems

Abstract

Differential form of Eringen's nonlocal elastic theory has some inaccuracies in analyzing small-scale structures with different boundary conditions. For this reason, Eringen's two-phase local/nonlocal integral model as a reliable well-posed form of the theory attracted a great deal of attention in modeling size-dependent effects. Accordingly, in this work a comprehensive study on vibration behavior of double-layered nanobeam systems (DNBS) is presented within the framework of Eringen's two-phase local/nonlocal integral model. DNBS's vibrational behavior is formulated for three different cases by having in-phase vibration, out-phase vibration and by fixing the underneath layer and analyzing beams on a medium. Governing equations are presented for different boundary conditions especially cantilever DNBS model where the differential form of Eringen's nonlocal theory is unable to model. In order to show the influence of nonlocal terms in Eringen's two-phase model and the elastic coupling term on dynamic behavior of such structures, a comprehensive parametric study is carried out. It is shown that these parameters can have a significant effect on the natural frequency terms which could lead to more accurate and reliable dynamic models with different boundary conditions.