Weakly nonlinear wave propagation in nanorods embedded in an elastic medium using nonlocal elasticity theory

2020 ◽  
Vol 42 (11) ◽  
Author(s):  
Guler Gaygusuzoglu ◽  
Sezer Akdal
Keyword(s):  
Wave Propagation ◽  
Elastic Medium ◽  
Elasticity Theory ◽  
Nonlinear Wave ◽  
Nonlocal Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Nonlinear Wave Propagation ◽  
Weakly Nonlinear

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.

TORSIONAL WAVE PROPAGATION AND VIBRATION OF CIRCULAR NANOSTRUCTURES BASED ON NONLOCAL ELASTICITY THEORY

2014 ◽  
Vol 06 (02) ◽  
pp. 1450011 ◽  
Author(s):  
Z. M. ISLAM ◽  
P. JIA ◽  
C. W. LIM
Keyword(s):  
Wave Propagation ◽  
Elasticity Theory ◽  
Constitutive Relation ◽  
Nonlocal Elasticity ◽  
Numerical Solutions ◽  
Nonlocal Elasticity Theory ◽  
Torsional Wave ◽  
Nonlocal Model ◽  
Boundary Characteristics ◽  
Propagation Properties

The presence of size effects represented by a small nanoscale on torsional wave propagation properties of circular nanostructure, such as nanoshafts, nanorods and nanotubes, is investigated. Based on the nonlocal elasticity theory, the dynamic equation of motion for the structure is formulated. By using the derived equation, simple analytical solutions for the relation between wavenumber and frequency via the differential nonlocal constitutive relation and the numerical solutions for a discrete nonlocal model via the integral nonlocal constitutive relation have been obtained. This results not only show that the dispersion characteristics of circular nanostructures are greatly affected by the small nanoscale and the classical theory overestimates the stiffness of nanostructures, but also highlights the significance of the integral nonlocal model which is able to capture some boundary characteristics that do not appear in the differential nonlocal model.

Cylindrical Bending Vibration of Multiple Graphene Sheet Systems Embedded in an Elastic Medium

2019 ◽  
Vol 19 (04) ◽  
pp. 1950035
Author(s):  
Chih-Ping Wu ◽  
Yen-Jung Chen
Keyword(s):  
Elastic Medium ◽  
Elasticity Theory ◽  
Plane Strain ◽  
Graphene Sheet ◽  
Nonlocal Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Mode Shapes ◽  
Cylindrical Bending ◽  
Bending Vibration ◽  
Motion Equations

Based on the Eringen nonlocal elasticity theory and multiple time scale method, an asymptotic nonlocal elasticity theory is developed for cylindrical bending vibration analysis of simply-supported, [Formula: see text]-layered, and uniformly or nonuniformly-spaced, graphene sheet (GS) systems embedded in an elastic medium. Both the interactions between the top and bottom GSs and their surrounding medium and the interactions between each pair of adjacent GSs are modeled as one-parameter Winkler models with different stiffness coefficients. In the formulation, the small length scale effect is introduced to the nonlocal constitutive equations by using a nonlocal parameter. The nondimensionalization, asymptotic expansion, and successive integration mathematical processes are performed for a typical GS. After assembling the motion equations for each individual GS to form those of the multiple GS system, recurrent sets of motion equations can be obtained for various order problems. Nonlocal multiple classical plate theory (CPT) is derived as a first-order approximation of the current nonlocal plane strain problem, and the motion equations for higher-order problems retain the same differential operators as those of nonlocal multiple CPT, although with different nonhomogeneous terms. Some nonlocal plane strain solutions for the natural frequency parameters of the multiple GS system with and without being embedded in the elastic medium and their corresponding mode shapes are presented to demonstrate the performance of the asymptotic nonlocal elasticity theory.

Modeling and Analysis of Nonlinear Wave Propagation in One-Dimensional Phononic Structures

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
M. Liu ◽  
W. D. Zhu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Propagation ◽  
Band Structure ◽  
Band Gap ◽  
Nonlinear Wave ◽  
Elastic Waves ◽  
Propagation Characteristics ◽  
Nonlinear Wave Propagation ◽  
Weakly Nonlinear

Different from elastic waves in linear periodic structures, those in phononic crystals (PCs) with nonlinear properties can exhibit more interesting phenomena. Linear dispersion relations cannot accurately predict band-gap variations under finite-amplitude wave motions; creating nonlinear PCs remains challenging and few examples have been studied. Recent studies in the literature mainly focus on discrete chain-like systems; most studies only consider weakly nonlinear regimes and cannot accurately obtain some relations between wave propagation characteristics and general nonlinearities. This paper presents propagation characteristics of longitudinal elastic waves in a thin rod and coupled longitudinal and transverse waves in an Euler–Bernoulli beam using their exact Green–Lagrange strain relations. We derive band structure relations for a periodic rod and beam and predict their nonlinear wave propagation characteristics using the B-spline wavelet on the interval (BSWI) finite element method. Influences of nonlinearities on wave propagation characteristics are discussed. Numerical examples show that the proposed method is more effective for nonlinear static and band structure problems than the traditional finite element method and illustrate that nonlinearities can cause band-gap width and location changes, which is similar to results reported in the literature for discrete systems. The proposed methodology is not restricted to weakly nonlinear systems and can be used to accurately predict wave propagation characteristics of nonlinear structures. This study can provide good support for engineering applications, such as sound and vibration control using tunable band gaps of nonlinear PCs.

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