scholarly journals Linking Time-Domain Vibration Behaviors to Spatial-Domain Propagating Waves in a Leaf-like Gradient-Index Phononic Crystal Lens

Crystals ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 1490
Author(s):  
Kuo-Chih Chuang ◽  
Dan-Feng Wang ◽  
Jun-Jie Liu ◽  
Chan-Yi Liao
Keyword(s):  
Time Domain ◽  
Periodic Structures ◽  
Phononic Crystal ◽  
Plane Waves ◽  
Spatial Domain ◽  
Gradient Index ◽  
Transient Wave ◽  
Element Analysis ◽  
Propagating Waves ◽  
Unit Cells

It is known that a propagating wave at a certain spatial point can be decomposed into plane waves propagating at different angles. In this work, by designing a gradient index phononic crystal lens (GRIN PCL) with transverse-continuous leaf-like unit cells, we theoretically and experimentally show that the spatial-domain propagating waves in finite periodic structures can be linked to their time-domain vibration behaviors. The full-field instantaneous focusing behaviors of Lamb waves in the proposed leaf-like GRIN PCL give an example of the wave-vibration linkage in finite periodic structures while allowing a certain complexity. The conclusion in this paper can help one skip iterative time-consuming finite element analysis (e.g., time-stepping solutions) to avoid possible numerical instabilities occurred in calculating transient wave field on practical finite metamaterials or phononic crystals having unit cells with complicated configurations.

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.

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 and Analysis of Viscoelastic Seismic Dampers

2002 ◽  
Author(s):  
N. Shimizu ◽  
H. Nasuno ◽  
T. Yazaki ◽  
K. Sunakoda
Keyword(s):  
Finite Element ◽  
Constitutive Relation ◽  
Time Domain ◽  
Dynamic Properties ◽  
Design Procedure ◽  
Fe Analysis ◽  
Damping Capacity ◽  
Element Formulation ◽  
Element Analysis ◽  
Equivalent Viscous Damping

This paper describes a methodology of design and analysis of viscoelastic seismic dampers by means of the time domain finite element analysis. The viscoelastic constitutive relation of material incorporating with the fractional calculus has been derived and the finite element formulation based on the constitutive relation has been developed to analyze the dynamic property of seismic damper. A time domain computer program was developed by using the formulation. Dynamic properties of hysteresis loop, damping capacity, equivalent viscous damping coefficient, and equivalent spring constant are calculated and compared with the experimental results. Remarkable correlation between the FE analysis and the experiment is gained, and consequently the design procedure with the help of the FE analysis has been established.

scholarly journals Organizing Cells Within Non-Periodic Microarchitectured Materials That Achieve Graded Thermal Expansions

2015 ◽  
Author(s):  
Jonathan B. Hopkins ◽  
Lucas A. Shaw ◽  
Todd H. Weisgraber ◽  
George R. Farquar ◽  
Christopher D. Harvey ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Thermal Expansion ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Element Analysis ◽  
Thermal Expansion Coefficients ◽  
Large Lattice ◽  
Unit Cells ◽  
Expansion Coefficients ◽  
Bulk Behavior

The aim of this paper is to introduce an approach for optimally organizing a variety of different unit cell designs within a large lattice such that the bulk behavior of the lattice exhibits a desired Young’s modulus with a graded change in thermal expansion over its geometry. This lattice, called a graded microarchitectured material, can be sandwiched between two other materials with different thermal expansion coefficients to accommodate their different expansions or contractions caused by changing temperature while achieving a desired uniform stiffness. First, this paper provides the theory necessary to calculate the thermal expansion and Young’s modulus of large multi-material lattices that consist of periodic (i.e., repeating) unit cells of the same design. Then it introduces the theory for calculating the graded thermal expansions of a large multimaterial lattice that consists of non-periodic unit cells of different designs. An approach is then provided for optimally designing and organizing different unit cells within a lattice such that both of its ends achieve the same thermal expansion as the two materials between which the lattice is sandwiched. A MATLAB tool is used to generate images of the undeformed and deformed lattices to verify their behavior and various examples are provided as case studies. The theory provided is also verified and validated using finite element analysis and experimentation.

scholarly journals One-dimensional broadband phononic crystal filter with unit cells made of two non-uniform impedance-mirrored elements

AIP Advances ◽  
2013 ◽  
Vol 3 (2) ◽  
pp. 022105 ◽  
Author(s):  
Il Kyu Lee ◽  
Yoon Jae Kim ◽  
Joo Hwan Oh ◽  
Yoon Young Kim
Keyword(s):  
Phononic Crystal ◽  
One Dimensional ◽  
Unit Cells
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