scholarly journals The Korteweg–de Vries, Burgers and Whitham limits for a spatially periodic Boussinesq model

2018 ◽  
Vol 149 (1) ◽  
pp. 191-217 ◽  
Author(s):  
Roman Bauer ◽  
Wolf-Patrick Düll ◽  
Guido Schneider
Keyword(s):  
Original System ◽  
Bloch Wave ◽  
Energy Estimates ◽  
Periodic Medium ◽  
Wave Analysis ◽  
Amplitude Equations ◽  
Boussinesq Model ◽  
De Vries ◽  
Spatially Periodic ◽  
Bloch Wave Analysis

We are interested in the Korteweg–de Vries (KdV), Burgers and Whitham limits for a spatially periodic Boussinesq model with non-small contrast. We prove estimates of the relations between the KdV, Burgers and Whitham approximations and the true solutions of the original system that guarantee these amplitude equations make correct predictions about the dynamics of the spatially periodic Boussinesq model over their natural timescales. The proof is based on Bloch wave analysis and energy estimates and is the first justification result of the KdV, Burgers and Whitham approximations for a dispersive partial differential equation posed in a spatially periodic medium of non-small contrast.

scholarly journals Coupled Bloch-Wave Analysis of Active PhC Waveguides and Cavities

2018 ◽  
Author(s):  
Marco Saldutti ◽  
Jesper Mork ◽  
Paolo Bardella ◽  
Ivo Montrosset ◽  
Mariangela Gioannini
Keyword(s):  
Bloch Wave ◽  
Wave Analysis ◽  
Bloch Wave Analysis

Bloch Wave Analysis of Long Leaky Coaxial Cables

2008 ◽  
Vol 56 (6) ◽  
pp. 1548-1554 ◽  
Author(s):  
Giuseppe Addamo ◽  
Renato Orta ◽  
Riccardo Tascone
Keyword(s):  
Bloch Wave ◽  
Wave Analysis ◽  
Bloch Wave Analysis

Design of Miura-Ori Patterns With Acoustic Bandgaps

2017 ◽  
Author(s):  
Phanisri P. Pratapa ◽  
Phanish Suryanarayana ◽  
Glaucio H. Paulino
Keyword(s):  
Wave Propagation ◽  
Material Properties ◽  
Bloch Wave ◽  
Acoustic Metamaterials ◽  
Analysis Framework ◽  
Wave Analysis ◽  
Material Inhomogeneity ◽  
Propagation Behavior ◽  
Unit Cells ◽  
Bloch Wave Analysis

We study the wave propagation behavior in Miura-ori patterns by using the Bloch-wave analysis framework. Our investigation focuses on acoustic bandgaps that act as stopping bands for wave propagation at certain frequencies in periodic solids or structures. We show that bandgaps can be created in two-dimensional periodic Miura-ori patterns by introducing material inhomogeneity. First, we perform Bloch-wave analysis of homogeneous Miura-ori patterns with finite panel rigidity and find that no bandgaps are present. We then introduce bandgaps by making the pattern non-uniform — by changing the mass and axial rigidity of origami panels of alternating unit cells. We discuss the dependence of the magnitude of the bandgap on the contrast between material properties. We find that higher magnitudes of bandgaps are possible by using higher contrast ratios (mass and stiffness). These observations indicate the potential of origami-based patterns to be useful as acoustic metamaterials for vibration control.

Wave Directionality in Three-Dimensional Periodic Lattices

2017 ◽  
Vol 85 (1) ◽  
Author(s):  
Alireza Bayat ◽  
Stavros Gaitanaros
Keyword(s):  
Three Dimensional ◽  
Finite Size ◽  
Bloch Wave ◽  
Wave Analysis ◽  
Low Frequencies ◽  
Cubic Lattice ◽  
Wave Directionality ◽  
Bloch Wave Analysis ◽  
Complete Bandgap ◽  
Kelvin Foam

This work focuses on elastic wave propagation in three-dimensional (3D) low-density lattices and explores their wave directionality and energy flow characteristics. In particular, we examine the dynamic response of Kelvin foam, a simple-and framed-cubic lattice, as well as the octet lattice, spanning this way a range of average nodal connectivities and both stretching-and bending-dominated behavior. Bloch wave analysis on unit periodic cells is employed and frequency diagrams are constructed. Our results show that in the low relative-density regime analyzed here, only the framed-cubic lattice displays a complete bandgap in its frequency diagram. New representations of iso-frequency contours and group-velocity plots are introduced to further analyze dispersive behavior, wave directionality, and the presence of partial bandgaps in each lattice. Significant wave beaming is observed for the simple-cubic and octet lattices in the low frequency regime, while Kelvin foam exhibits a nearly isotropic behavior in low frequencies for the first propagating mode. Results of Bloch wave analysis are verified by explicit numerical simulations on finite size domains under a harmonic perturbation.

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