scholarly journals A dispersive nonlocal model for wave propagation in periodic composites

2009 ◽  
Vol 4 (5) ◽  
pp. 951-976 ◽  
Author(s):  
Juan Miguel Vivar-Pérez ◽  
Ulrich Gabbert ◽  
Harald Berger ◽  
Reinaldo Rodríguez-Ramos ◽  
Julián Bravo-Castillero ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Nonlocal Model ◽  
Periodic Composites

A dispersive nonlocal model for shear wave propagation in laminated composites with periodic structures

2015 ◽  
Vol 49 ◽  
pp. 35-48 ◽  
Author(s):  
H. Brito-Santana ◽  
Yue-Sheng Wang ◽  
R. Rodríguez-Ramos ◽  
J. Bravo-Castillero ◽  
R. Guinovart-Díaz ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Shear Wave ◽  
Periodic Structures ◽  
Laminated Composites ◽  
Nonlocal Model

Effective Dynamic Properties of Microstructured Heterogeneous Materials

2012 ◽  
Author(s):  
Ankit Srivastava ◽  
Sia Nemat-Nasser
Keyword(s):  
Wave Propagation ◽  
Explicit Form ◽  
Constitutive Equations ◽  
Effective Properties ◽  
Dynamic Properties ◽  
Effective Property ◽  
Bloch Wave ◽  
Periodic Composites ◽  
Effective Dynamic ◽  
Dynamic Effective Properties

Central to the idea of metamaterials is the concept of dynamic homogenization which seeks to define frequency dependent effective properties for Bloch wave propagation. While the theory of static effective property calculations goes back about 60 years, progress in the actual calculation of dynamic effective properties for periodic composites has been made only very recently. Here we discuss the explicit form of the effective dynamic constitutive equations. We elaborate upon the existence and emergence of coupling in the dynamic constitutive relation and further symmetries of the effective tensors.

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.

Theory of scalar wave propagation in periodic composites: A k·p approach

1994 ◽  
Vol 91 (1) ◽  
pp. 65-69 ◽  
Author(s):  
P.M. Hui ◽  
W.M. Lee ◽  
N.F. Johnson
Keyword(s):  
Wave Propagation ◽  
Scalar Wave ◽  
Periodic Composites

Wave Propagation in Two Dimensional Periodic Composites

2011 ◽  
Author(s):  
Hossein Sadeghi ◽  
Ankit Srivastava ◽  
Ryan Griswold ◽  
Sia Nemat-Nasser
Keyword(s):  
Wave Propagation ◽  
Theoretical Calculations ◽  
Experimental Results ◽  
Two Dimensional ◽  
Shape Information ◽  
Periodic Composites ◽  
Numerical Predictions ◽  
Periodic Composite ◽  
Longitudinal And Shear Waves ◽  
Phase And Group Velocities

In this paper we present theoretical calculations and experimental results concerning acoustic wave propagation in a 2-D periodic composite. It is known that the microstructure below the length scale of the wavelength affects the macroscale wave and makes the composite dispersive [1,2]. This dispersion manifests as frequency dependent phase and group velocities. We present a mixed variational formulation originally proposed by Nemat-Nasser for the evaluation of the dispersive characteristics of periodic composites. We employ the formulation to calculate the dispersion relation for a two-dimensional composite consisting of brass rods embedded in epoxy. The method allows for the calculation of the band structure of the composite and the identification of the relevant modes through mode shape information. We finally present experimental results on a fabricated sample for the 2-D composite. The experiments include longitudinal and shear wave propagation through the sample. The transmitted energy of the longitudinal and shear waves are used to evaluate the location of the pass-bands and stop-bands and to compare the results with the numerical predictions.

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