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Gaygusuzoglu, Guler; Aydogdu, Metin; Gul, Ufuk

Nonlinear wave modulation in nanorods using nonlocal elasticity theory. (English) Zbl 1435.74046

Int. J. Nonlinear Sci. Numer. Simul. 19, No. 7-8, 709-719 (2018).
The classical elasticity theory is based on the interactions of neighboring particles whereas the nonlocal elasticity theory takes into account the long range forces. In the present work, the authors first derived the equations of rods by considering that the material obeys the rule of nonlocal elasticity theory which accounts the geometrical nonlinearity, but linear constitutive equations. Then, by using the reductive perturbation method, the authors studied the amplitude modulation of the field equations of nonlocal rods and obtained nonlinear Schrödinger (NLS) equation as the evolution equation. For the purpose of numerical investigation of nonlocal effects on the NLS equation, the existence of envelope solitary wave solution is discussed. Amplitude dependent wave frequencies, phase and group velocities have been obtained for linear local, linear nonlocal and nonlinear nonlocal theories and they are compared with each other.
The work is well written and may be useful for readers working in the area of nano-materials.
Reviewer: Hilmi Demiray (Istanbul)

Cited in 1 Document

MSC:

74J30 Nonlinear waves in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)

Keywords:

nanorods; nonlocal elasticity; wave modulation; reductive perturbation technique
PDFBibTeX XMLCite
\textit{G. Gaygusuzoglu} et al., Int. J. Nonlinear Sci. Numer. Simul. 19, No. 7--8, 709--719 (2018; Zbl 1435.74046)
Full Text: DOI

References:

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