Wave Propagation in Periodically Supported Nanoribbons: A Nonlocal Elasticity Approach

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Giuliano Allegri ◽  
Fabrizio Scarpa ◽  
Rajib Chowdhury ◽  
Sondipon Adhikari
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Nonlocal Elasticity ◽  
Graphene Nanoribbons ◽  
Stop Band ◽  
Flexural Waves ◽  
Finite Element Approach ◽  
Analytical Formulation ◽  
Simply Supported ◽  
Element Approach

We develop an analytical formulation describing propagating flexural waves in periodically simply supported nanoribbons by means of Eringen's nonlocal elasticity. The nonlocal length scale is identified via atomistic finite element (FE) models of graphene nanoribbons with Floquet's boundary conditions. The analytical model is calibrated through the atomistic finite element approach. This is done by matching the nondimensional frequencies predicted by the analytical nonlocal model and those obtained by the atomistic FE simulations. We show that a nanoribbon with periodically supported boundary conditions does exhibit artificial pass-stop band characteristics. Moreover, the nonlocal elasticity solution proposed in this paper captures the dispersive behavior of nanoribbons when an increasing number of flexural modes are considered.

scholarly journals A Nitsche Finite Element Approach for Elliptic Problems with Discontinuous Dirichlet Boundary Conditions

2018 ◽  
Vol 18 (3) ◽  
pp. 373-381 ◽  
Author(s):  
Ramona Baumann ◽  
Thomas P. Wihler
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mesh Size ◽  
Singular Part ◽  
Dirichlet Boundary Conditions ◽  
Diffusion Reaction ◽  
Discrete Solution ◽  
Finite Element Approach ◽  
Element Approach

AbstractWe present a numerical approximation method for linear elliptic diffusion-reaction problems with possibly discontinuous Dirichlet boundary conditions. The solution of such problems can be represented as a linear combination of explicitly known singular functions as well as of an {H^{2}}-regular part. The latter part is expressed in terms of an elliptic problem with regularized Dirichlet boundary conditions, and can be approximated by means of a Nitsche finite element approach. The discrete solution of the original problem is then defined by adding back the singular part of the exact solution to the Nitsche approximation. In this way, the discrete solution can be shown to converge of second order in the {L^{2}}-norm with respect to the mesh size.

A Finite Element Approach for Nonhomogeneous Nonlocal Elastic Problems

2008 ◽  
Author(s):  
Aurora Pisano ◽  
Alba Sofi ◽  
Paolo Fuschi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Nonlocal Elasticity ◽  
Elastic Moduli ◽  
Strain Difference ◽  
Relevant Literature ◽  
Stiffness Tensor ◽  
Finite Element Approach ◽  
Numerical Examples ◽  
Element Approach

The paper deals with the implementation of a method, known in the relevant literature as Nonlocal Finite Element Method, for solving 2D boundary value problems in the context of nonhomogeneous nonlocal elasticity. The method, founded on a consistent thermodynamic formulation, is here improved making use of a phenomenological strain-difference-based nonhomogeneous nonlocal elasticity model. The latter assumes a two components local/nonlocal constitutive relation in which the stress is conceived as the sum of two contributions governed by the standard elastic moduli tensor and by a nonlocal stiffness tensor, respectively. Two numerical examples are presented and the obtained results are discussed both to verify the reliability of the method and to show its potential and limits for the analysis of nonhomogeneous nonlocal elastic problems.

A Finite Element Approach to the Transient Dynamics of Rolling Tires with Emphasis on Rolling Noise Simulation4

2007 ◽  
Vol 35 (3) ◽  
pp. 165-182 ◽  
Author(s):  
Maik Brinkmeier ◽  
Udo Nackenhorst ◽  
Heiner Volk
Keyword(s):  
Finite Element ◽  
Traffic Noise ◽  
Complex Eigenvalue ◽  
Arbitrary Lagrangian Eulerian ◽  
Finite Element Approach ◽  
Road Systems ◽  
Element Approach ◽  
Road Surface Roughness ◽  
Complex Eigenvalue Analysis ◽  
Rolling Noise

Abstract The sound radiating from rolling tires is the most important source of traffic noise in urban regions. In this contribution a detailed finite element approach for the dynamics of tire/road systems is presented with emphasis on rolling noise prediction. The analysis is split into sequential steps, namely, the nonlinear analysis of the stationary rolling problem within an arbitrary Lagrangian Eulerian framework, and a subsequent analysis of the transient dynamic response due to the excitation caused by road surface roughness. Here, a modal superposition approach is employed using complex eigenvalue analysis. Finally, the sound radiation analysis of the rolling tire/road system is performed.

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