scholarly journals Nonlinear Wave Modulation in Nanorods Based on Nonlocal Elasticity Theory by Using Multiple-Scale Formalism

2018 ◽  
Vol 10 (3) ◽  
pp. 140-158
Author(s):  
Güler Gaygusuzoğlu
Keyword(s):  
Elasticity Theory ◽  
Nonlinear Wave ◽  
Nonlocal Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Multiple Scale ◽  
Wave Modulation

Nonlinear Wave Modulation in Nanorods Using Nonlocal Elasticity Theory

2018 ◽  
Vol 19 (7-8) ◽  
pp. 709-719 ◽  
Author(s):  
Guler Gaygusuzoglu ◽  
Metin Aydogdu ◽  
Ufuk Gul
Keyword(s):  
Elasticity Theory ◽  
Nonlinear Equations ◽  
Nonlinear Wave ◽  
Nonlocal Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Reductive Perturbation Method ◽  
Nls Equation ◽  
Dispersive Waves ◽  
Weakly Nonlinear ◽  
Wave Modulation

AbstractIn this study, nonlinear wave modulation in nanorods is examined on the basis of nonlocal elasticity theory. Eringen's nonlocal elasticity theory is employed to derive nonlinear equations for the motion of nanorods. The analysis of the modulation of axial waves in nonlocal elastic media is performed, and the reductive perturbation method is used for the solution of the nonlinear equations. The propagation of weakly nonlinear and strongly dispersive waves is investigated, and the nonlinear Schrödinger (NLS) equation is acquired as an evolution equation. For the purpose of a numerical investigation of the nonlocal impacts on the NLS equation, it has been investigated whether envelope solitary wave solutions exist by utilizing the physical and geometric features of the carbon nanotubes. Amplitude dependent wave frequencies, phase and group velocities have been obtained and they have compared for the linear local, the linear nonlocal, the nonlinear local and the nonlinear nonlocal cases.

scholarly journals Double mode model of size-dependent chaotic vibrations of nanoplates based on the nonlocal elasticity theory

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
Olga Mazur
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Scale Effects ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Phase Portraits ◽  
Small Scale ◽  
Governing System ◽  
Account Due

AbstractIn this paper vibrations of the isotropic micro/nanoplates subjected to transverse and in-plane excitation are investigated. The governing equations of the problem are based on the von Kármán plate theory and Kirchhoff–Love hypothesis. The small-size effect is taken into account due to the nonlocal elasticity theory. The formulation of the problem is mixed and employs the Airy stress function. The two-mode approximation of the deflection and application of the Bubnov–Galerkin method reduces the governing system of equations to the system of ordinary differential equations. Varying the load parameters and the nonlocal parameter, the bifurcation analysis is performed. The bifurcations diagrams, the maximum Lyapunov exponents, phase portraits as well as Poincare maps are constructed based on the numerical simulations. It is shown that for some excitation conditions the chaotic motion may occur in the system. Also, the small-scale effects on the character of vibrating regimes are illustrated and discussed.

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