Hierarchical Design of Phononic Materials and Structures

2005 ◽  
Author(s):  
Mahmoud I. Hussein ◽  
Gregory M. Hulbert ◽  
Richard A. Scott
Keyword(s):  
Wave Scattering ◽  
Design Methodology ◽  
Periodic Structures ◽  
Building Blocks ◽  
Hierarchical Design ◽  
Material Interfaces ◽  
Dynamical Characteristics ◽  
Constituent Material ◽  
Unit Cells ◽  
Damping Materials

Within periodically heterogeneous materials and structures, wave scattering and dispersion occur across constituent material interfaces leading to a banded frequency response. A novel multiscale dispersive design methodology is presented by which periodic unit cells are designed for desired frequency band structures, and are used as building blocks for forming fully or partially periodic structures, typically at larger length scales. Structures resulting from this hierarchical design approach are tailored to desired dynamical characteristics without the necessity for altering the overall geometric shape of the structure nor employing dissipative damping materials. Case studies are presented for shock isolation and frequency sensing.

Band-Gap Engineering of Elastic Waveguides Using Periodic Materials

2003 ◽  
Author(s):  
Mahmoud I. Hussein ◽  
Gregory M. Hulbert ◽  
Richard A. Scott
Keyword(s):  
Wave Attenuation ◽  
Material Interfaces ◽  
Band Gap Engineering ◽  
Attenuation Effect ◽  
Constituent Material ◽  
Unit Cells ◽  
Guide Wall ◽  
Forced Vibration Analysis ◽  
Periodic Materials ◽  
Elastic Waveguides

Within periodically heterogeneous materials, wave scattering takes place across constituent material interfaces in such a way that an overall wave attenuation effect arises at certain frequency ranges known as band gaps. This phenomenon can be utilized in developing structures with tailored dynamic characteristics. In this work, periodic materials are used to synthesize elastic waveguides within bounded structures. The underlying local-global design process is described, and the effect of the number of periodic cells used to form the guide “wall” is studied. Using forced vibration analysis, it is shown that with only three or four periodic unit cells, the desired wave attenuation capacity required to form a guide is attained.

MODIFICATION OF CASIMIR FORCES DUE TO BAND GAPS IN PERIODIC STRUCTURES

2002 ◽  
Vol 17 (06n07) ◽  
pp. 798-803 ◽  
Author(s):  
C. VILLARREAL ◽  
R. ESQUIVEL-SIRVENT ◽  
G. H. COCOLETZI
Keyword(s):  
Density Of States ◽  
Casimir Force ◽  
Periodic Structures ◽  
Local Density ◽  
Band Gaps ◽  
Basic Unit ◽  
Local Density Of States ◽  
Casimir Forces ◽  
Unit Cells ◽  
The Difference

The Casimir force between inhomogeneous slabs that exhibit a band-like structure is calculated. The slabs are made of basic unit cells each made of two layers of different materials. As the number of unit cells increases the Casimir force between the slabs changes, since the reflectivity develops a band-like structure characterized by frequency regions of high reflectivity. This is also evident in the difference of the local density of states between free and boundary distorted vacuum, that becomes maximum at frequencies corresponding to the band gaps. The calculations are restricted to vacuum modes with wave vectors perpendicular to the slabs.

Design of Three-Dimensional, Triply Periodic Unit Cell Scaffold Structures for Additive Manufacturing

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Mazher Iqbal Mohammed ◽  
Ian Gibson
Keyword(s):  
Additive Manufacturing ◽  
Periodic Structures ◽  
Three Dimensional ◽  
Unit Cell ◽  
Final Size ◽  
Fused Filament Fabrication ◽  
Cell Structures ◽  
Triply Periodic ◽  
Unit Cells ◽  
Scaffold Structure

Highly organized, porous architectures leverage the true potential of additive manufacturing (AM) as they can simply not be manufactured by any other means. However, their mainstream usage is being hindered by the traditional methodologies of design which are heavily mathematically orientated and do not allow ease of controlling geometrical attributes. In this study, we aim to address these limitations through a more design-driven approach and demonstrate how complex mathematical surfaces, such as triply periodic structures, can be used to generate unit cells and be applied to design scaffold structures in both regular and irregular volumes in addition to hybrid formats. We examine the conversion of several triply periodic mathematical surfaces into unit cell structures and use these to design scaffolds, which are subsequently manufactured using fused filament fabrication (FFF) additive manufacturing. We present techniques to convert these functions from a two-dimensional surface to three-dimensional (3D) unit cell, fine tune the porosity and surface area, and examine the nuances behind conversion into a scaffold structure suitable for 3D printing. It was found that there are constraints in the final size of unit cell that can be suitably translated through a wider structure while still allowing for repeatable printing, which ultimately restricts the attainable porosities and smallest printed feature size. We found this limit to be approximately three times the stated precision of the 3D printer used this study. Ultimately, this work provides guidance to designers/engineers creating porous structures, and findings could be useful in applications such as tissue engineering and product light-weighting.

Modeling Wave Scattering by GC-liked Periodic Structures

2021 ◽  
Author(s):  
V.D. Dushkin ◽  
O.V. Kostenko ◽  
S.V. Zhuchenko
Keyword(s):  
Wave Scattering ◽  
Periodic Structures

An Executable Notation, With Illustrations From Elementary Crystallography

1994 ◽  
Author(s):  
Donald B. Mclntyre
Keyword(s):  
Plate Tectonics ◽  
Periodic Structures ◽  
Dimensional Space ◽  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Cubic Symmetry ◽  
Multiple Data ◽  
Special Cases ◽  
Unit Cells ◽  
Crystallographic Axes

Elementary crystallography is an ideal context for introducing students to mathematical geology. Students meet crystallography early because rocks are made of crystalline minerals. Moreover, morphological crystallography is largely the study of lines and planes in real three-dimensional space, and visualizing the relationships is excellent training for other aspects of geology; many algorithms learned in crystallography (e.g., rotation of arrays) apply also to structural geology and plate tectonics. Sets of lines and planes should be treated as entities, and crystallography is an ideal environment for introducing what Sylvester (1884) called "Universal Algebra or the Algebra of multiple quantity." In modern terminology, we need SIMD (Single Instruction, Multiple Data) or even MIMD. This approach, initiated by W.H. Bond in 1946, dispels the mysticism unnecessarily associated with Miller indices and the reciprocal lattice; edges and face-normals are vectors in the same space. The growth of mathematical notation has been haphazard, new symbols often being introduced before the full significance of the functions they represent had been understood (Cajori, 1951; Mclntyre, 1991b). Iverson introduced a consistent notation in 1960 (e.g., Iverson 1960, 1962, 1980). His language, greatly extended in the executable form called J (Iverson, 1993), is used here. For information on its availability as shareware, see the Appendix. Publications suitable as tutorials in , J are available (e.g., Iverson. 1991; Mclntyre, 1991 a, b; 1992a,b,c; 1993). Crystals are periodic structures consisting of unit cells (parallelepipeds) repeated by translation along axes parallel to the cell edges. These edges define the crystallographic axes. In a crystal of cubic symmetry they are orthogonal and equal in length (Cartesian). Those of a triclinic crystal, on the other hand, are unequal in length and not at right angles. The triclinic system is the general case; others are special cases. The formal description of a crystal gives prominent place to the lengths of the axes (a, b, and c) and the interaxial angles ( α, β, and γ). A canonical form groups these values into a 2 x 3 table (matrix), the first row being the lengths and the second the angles.

Hierarchical Design Method for Multi-Agent Systems

2015 ◽  
Vol 7 (2) ◽  
pp. 105-134
Author(s):  
Bouneb Messaouda ◽  
Saïdouni Djamel Eddine
Keyword(s):  
Design Methodology ◽  
Design Method ◽  
Transition System ◽  
Hierarchical Design ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Labeled Transition System ◽  
System Assessment ◽  
Definition Of

This paper proposes a new hierarchical design method for the specification and the verification of multi agent systems (MAS). For this purpose, the authors propose the model of Refinable Recursive Petri Nets (RRPN) under a maximality semantics. In this model, a notion of undefined transitions is considered. The underlying semantics model is the Abstract Maximality-based Labeled Transition System (AMLTS). Hence, the model supports a definition of a hierarchical design methodology. The example of goods transportation is used for illustrating the approach. For the system assessment, the properties are expressed in CTL logic and verified using the verification environment FOCOVE (Formal Concurrency Verification Environment).

Atomic Dynamics in Complex Metallic Alloys

2013 ◽  
Vol 1517 ◽  
Author(s):  
Holger Euchner ◽  
Stephane Pailhès ◽  
Tsunetomo Yamada ◽  
Ryuji Tamura ◽  
Tsutomu Ishimasa ◽  
...  
Keyword(s):  
Lattice Dynamics ◽  
Structural Complexity ◽  
Building Blocks ◽  
Metallic Alloys ◽  
Strong Reduction ◽  
Large Numbers ◽  
Unit Cells ◽  
Dynamics Simulations ◽  
The Impact ◽  
Complex Metallic Alloys

ABSTRACTComplex Metallic Alloys (CMAs) are metallic solids of high structural complexity, consisting of large numbers of atoms in their unit cells. Consequences of this structural complexity are manifold and give rise to a variety of exciting physical properties. The impact that such structural complexity may have on the lattice dynamics will be discussed. The surprising dynamical flexibility of Tsai-type clusters with the symmetry breaking central tetrahedron will be addressed for Zn6Sc, while in the Ba-Ge-Ni clathrate system the dynamics of encaged Ba guest atoms in the surrounding Ge-Ni host framework is analysed with respect to the experimentally evidenced strong reduction of lattice thermal conductivity. For both systems experimental results from neutron scattering are analyzed and interpreted on atomistic scale by means of ab initio and molecular dynamics simulations, resulting in a picture with the respective structural building blocks as the origin of the peculiarities in the dynamics.

Topology Optimization of Periodic Structures With Substructuring

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Junjian Fu ◽  
Liang Xia ◽  
Liang Gao ◽  
Mi Xiao ◽  
Hao Li
Keyword(s):  
Topology Optimization ◽  
Linear System ◽  
Periodic Structures ◽  
Computational Cost ◽  
Optimization Method ◽  
Displacement Fields ◽  
Element Analysis ◽  
Level Set Function ◽  
Static Condensation ◽  
Unit Cells

Topology optimization of macroperiodic structures is traditionally realized by imposing periodic constraints on the global structure, which needs to solve a fully linear system. Therefore, it usually requires a huge computational cost and massive storage requirements with the mesh refinement. This paper presents an efficient topology optimization method for periodic structures with substructuring such that a condensed linear system is to be solved. The macrostructure is identically partitioned into a number of scale-related substructures represented by the zero contour of a level set function (LSF). Only a representative substructure is optimized for the global periodic structures. To accelerate the finite element analysis (FEA) procedure of the periodic structures, static condensation is adopted for repeated common substructures. The macrostructure with reduced number of degree of freedoms (DOFs) is obtained by assembling all the condensed substructures together. Solving a fully linear system is divided into solving a condensed linear system and parallel recovery of substructural displacement fields. The design efficiency is therefore significantly improved. With this proposed method, people can design scale-related periodic structures with a sufficiently large number of unit cells. The structural performance at a specified scale can also be calculated without any approximations. What’s more, perfect connectivity between different optimized unit cells is guaranteed. Topology optimization of periodic, layerwise periodic, and graded layerwise periodic structures are investigated to verify the efficiency and effectiveness of the presented method.

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