Download Wave Propagation in Nanostructures: Nonlocal Continuum by Srinivasan Gopalakrishnan, Saggam Narendar PDF

By Srinivasan Gopalakrishnan, Saggam Narendar

Wave Propagation in Nanostructures describes the elemental and complicated strategies of waves propagating in buildings that experience dimensions of the order of nanometers. The publication is essentially in keeping with non-local elasticity idea, which include scale results within the continuum version. The e-book predominantly addresses wave habit in carbon nanotubes and Graphene constructions, even if the tools of research supplied during this textual content are both acceptable to different nanostructures.

The e-book takes the reader from the basics of wave propagation in nanotubes to extra complicated issues reminiscent of rotating nanotubes, coupled nanotubes, and nanotubes with magnetic box and floor results. the 1st few chapters disguise the fundamentals of wave propagation, varied modeling schemes for nanostructures and introduce non-local elasticity theories, which shape the development blocks for figuring out the cloth supplied in later chapters. a few attention-grabbing examples are supplied to demonstrate the real gains of wave habit in those low dimensional constructions.

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For example, modeling technique such as ab intio atomistic modeling or molecular dynamics methods can be employed to study wave propagation in such nanostructures. However, the main limitation of these methods is the computational time that these methods will take. Some researchers have used finite element method coupled with molecular mechanics model to solve such problems. However, if the frequency content of the problem is of the terahertz level, then for FE modeling, one needs a FE mesh compatible with its wavelength, which is extremal small at the terahertz frequency.

33] from the REBO potential. They also presented results of molecular dynamics on vibration characteristics of nanotubes. The MD simulation technique (using NanoHive-1 software [38]) is used to simulate torsional wave propagation on (6,6) and (10,10) armchair nanotubes by Khademolhosseini et al. [39]. The simulations are based on the Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential [40] which is widely used for simulating CNTs. They estimated the wave group and phase speeds in (6,6) and (10,10) CNTs using MD simulation and the results are compared with the nonlocal continuum shell (nonlocal elasticity models are explained in Sect.

6) =r 2 ∂x ∂x ∂t where p, q, and r are known constants depending on the material properties and geometry of the waveguide. u(x, t) is the field variable to be solved for with x being the spatial dimension and t the temporal dimension. 7) n=1 where ωn is the discrete circular frequency in rad/sec and N is the total number of frequency points used in the transformation. 8) ωn = nΔω = N N Δt T where Δt is the time sampling rate and ω f is the highest frequency captured by Δt. The frequency content of the load decides N and consideration of the wrap around and aliasing problem decides Δω.

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