Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 1.1 A Polyethylene-based metamaterial for acoustic control 1.1 A Polyethylene-based metamaterial for acoustic control 2 Relaxed micromorphic modelling of finite-size metamaterials 2 Relaxed micromorphic modelling of finite-size metamaterials 2.1 Tetragonal Symmetry / Shape of elastic tensors (in Voigt notation) 2.1 Tetragonal Symmetry / Shape of elastic tensors (in Voigt notation) 3 Dispersion curves 3 Dispersion curves 4 New considerations on the relaxed micromorphic parameters 4 New considerations on the relaxed micromorphic parameters 4.1 Consistency of the relaxed micromorphic model with respect to a change in the unit cell’s bulk material properties 4.1 Consistency of the relaxed micromorphic model with respect to a change in the unit cell’s bulk material properties 4.2 Consistency of the relaxed micromorphic model with respect to a change in the unit cell’s size 4.2 Consistency of the relaxed micromorphic model with respect to a change in the unit cell’s size 4.3 Relaxed micromorphic cut-offs 4.3 Relaxed micromorphic cut-offs 5 Fitting of the relaxed micromorphic parameters: the particular case of vanishing curvature (without Curl P and Curl P˙) 5 Fitting of the relaxed micromorphic parameters: the particular case of vanishing curvature (without Curl P and Curl P˙) 5.1 Asymptotes 5.1 Asymptotes 5.2 Fitting 5.2 Fitting 5.3 Discussion 5.3 Discussion 6 Fitting of the relaxed micromorphic parameters with curvature (with Curl P) 6 Fitting of the relaxed micromorphic parameters with curvature (with Curl P) 6.1 Asymptotes and 6.2 Fitting 6.1 Asymptotes and 6.2 Fitting 6.3 Discussion 6.3 Discussion 7 Fitting of the relaxed micromorphic parameters with enhanced kinetic energy (with Curl P˙) and 7.1 Asymptotes 7 Fitting of the relaxed micromorphic parameters with enhanced kinetic energy (with Curl P˙) and 7.1 Asymptotes 7.2 Fitting 7.2 Fitting 7.3 Discussion 7.3 Discussion 8 Summary of the obtained results 8 Summary of the obtained results 9 Conclusion and perspectives, Acknowledgements, and References 9 Conclusion and perspectives, Acknowledgements, and References A Most general 4th order tensor belonging to the tetragonal symmetry class A Most general 4th order tensor belonging to the tetragonal symmetry class B Coefficients for the dispersion curves without Curl P B Coefficients for the dispersion curves without Curl P C Coefficients for the dispersion curves with P C Coefficients for the dispersion curves with P D Coefficients for the dispersion curves with P◦ D Coefficients for the dispersion curves with P◦ A Most general 4th order tensor belonging to the tetragonal symmetry class Considering the following quadratic form where L is a 4th order tensor and D is a 2nd order one, the most general form of L if it belongs to the tetragonal symmetry class written in Voigt notation is where the order of the element of the vector associated with the quadratic form A.1 is If we now split the tensor D in its symmetric and skew-symmetric part, the corresponding vector in Voigt notation are Because of the class of symmetry considered, it is necessary to take into account a mixed constitutive matrix that couples the symmetric and skew-symmetric part of D in order to build back the quadratic form Y B Coefficients for the dispersion curves without Curl P C Coefficients for the dispersion curves with Curl P This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv Authors:
(1) Jendrik Voss, Institute for Structural Mechanics and Dynamics, Technical University Dortmund and a Corresponding Author (jendrik.voss@tu-dortmund.de);
(2) Gianluca Rizzi, Institute for Structural Mechanics and Dynamics, Technical University Dortmund;
(3) Patrizio Neff, Chair for Nonlinear Analysis and Modeling, Faculty of Mathematics, University of Duisburg-Essen;
(4) Angela Madeo, Institute for Structural Mechanics and Dynamics, Technical University Dortmund. Authors: Authors: (1) Jendrik Voss, Institute for Structural Mechanics and Dynamics, Technical University Dortmund and a Corresponding Author (jendrik.voss@tu-dortmund.de); (2) Gianluca Rizzi, Institute for Structural Mechanics and Dynamics, Technical University Dortmund; (3) Patrizio Neff, Chair for Nonlinear Analysis and Modeling, Faculty of Mathematics, University of Duisburg-Essen; (4) Angela Madeo, Institute for Structural Mechanics and Dynamics, Technical University Dortmund.

Part of HackerNoon's growing list of open-source research papers, promoting free access to academic material.

The Role of Curl Terms in Micromorphic Models

Semi-Analytical Algorithm for Metamaterial Parameter Fitting

Can You Reach the End of the Labyrinthine? 

Too Long; Didn't Read

Boost your HackerNoon story @ $159.99! 🚀

How Symmetric and Skew-Symmetric Tensors Interact

About Author

Comments

TOPICS

THIS ARTICLE WAS FEATURED IN

Related Stories

A New Method for Predicting How Waves Move Through Materials

How 3D-Printed Sound Panels Can Absorb Noise More Efficiently

Shhh! The Future of Noise Control Is Twisting Through 3D-Printed Labyrinths

Can 3D Printing Improve Soundproofing? This Study Says Yes

The Science of Soundproofing: A Look at 3D-Printed Acoustic Panels

How This Acoustic Panel Performed in a Real-World Sound Test

A New Method for Predicting How Waves Move Through Materials

How 3D-Printed Sound Panels Can Absorb Noise More Efficiently

Shhh! The Future of Noise Control Is Twisting Through 3D-Printed Labyrinths

Can 3D Printing Improve Soundproofing? This Study Says Yes

The Science of Soundproofing: A Look at 3D-Printed Acoustic Panels

How This Acoustic Panel Performed in a Real-World Sound Test

Light-Mode

Classic

Newspaper

Dark-Mode

Neon Noir

Minty

HN StartUps