Wave transmission characteristics in periodic media of finite length: multilayers and fiber arrays

Kobayashi, Futoshi; Biwa, Shiro; Ohno, Nobutada

doi:10.1016/j.ijsolstr.2004.06.017

Cited by 60 publications

(30 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Among various ways to compute dispersion relations in PCs such as the finite element method (Hussein 2009;Langlet et al 1995), the plane wave expansion method (Kushwaha et al 1994), the finite difference time domain method (Cao et al 2004), and the transfer matrix method (Kobayashi et al 2004), we will use the finite element method that appears to be most suitable for the topology optimization formulation to design selfcollimating PCs. In infinitely-periodic structures, responses such as displacement field possess some periodic characteristics because of their periodic nature.…”

Section: Finite Element Formulation For Pcsmentioning

confidence: 99%

Design of phononic crystals for self-collimation of elastic waves using topology optimization method

Park

Sik

Kim

2014

Struct Multidisc Optim

View full text Add to dashboard Cite

Self-collimating phononic crystals (PCs) are periodic structures that enable self-collimation of waves. While various design parameters such as material property, period, lattice symmetry, and material distribution in a unit cell affect wave scattering inside a PC, this work aims to find an optimal material distribution in a unit cell that exhibits the desired selfcollimation properties. While earlier studies were mainly focused on the arrangement of self-collimating PCs or shape changes of inclusions in a unit cell having a specific topological layout, we present a topology optimization formulation to find a desired material distribution. Specifically, a finite element based formulation is set up to find the matrix and inclusion material distribution that can make elastic shear-horizontal bulk waves propagate along a desired target direction. The proposed topology optimization formulation newly employs the geometric properties of equi-frequency contours (EFCs) in the wave vector space as essential elements in forming objective and constraint functions. The sensitivities of these functions with respect to design variables are explicitly derived to utilize a gradient-based optimizer. To show the effectiveness of the formulation, several case studies are considered.

show abstract

Section: Finite Element Formulation For Pcsmentioning

confidence: 99%

Design of phononic crystals for self-collimation of elastic waves using topology optimization method

Park

Sik

Kim

2014

Struct Multidisc Optim

View full text Add to dashboard Cite

show abstract

“…Due to the periodicity of the layered three-component phononic crystals, based on the Bloch theory, the displacement and shear stress at the boundaries between two neighboring unit cells satisfy the following relation [29,30]:…”

Section: Transfer Matrix and Dispersion Relationmentioning

confidence: 99%

Wave localization in randomly disordered layered three-component phononic crystals with thermal effects

Wang

Kishimoto

et al. 2009

Arch Appl Mech

View full text Add to dashboard Cite

In this paper, the propagation and localization of elastic waves in randomly disordered layered threecomponent phononic crystals with thermal effects are studied. The transfer matrix is obtained by applying the continuity conditions between three consecutive sub-cells. Based on the transfer matrix method and Bloch theory, the expressions of the localization factor and dispersion relation are presented. The relation between the localization factors and dispersion curves is discussed. Numerical simulations are performed to investigate the influences of the incident angle on band structures of ordered phononic crystals. For the randomly disordered ones, disorders of structural thickness ratios and Lamé constants are considered. The incident angles, disorder degrees, thickness ratios, Lamé constants and temperature changes have prominent effects on wave localization phenomena in three-component systems. Furthermore, it can be observed that stopbands locate in very low-frequency regions. The localization factor is an effective way to investigate randomly disordered phononic crystals in which the band structure cannot be described.

show abstract

“…To increase the TL of a sandwich panel, multilayer absorbers were inserted between the double panels (Chen et al 2000;Chen 2001, 2003;Mu et al 2011). The shape effects of the periodically repeated cell on the acoustic attenuation performance have been investigated by many researchers (Kobayashi et al 2004;Lee et al 2010;Legault and Atalla 2010). In addition, the effects of holes in a perforated panel and the internal cavity on transmission characteristics were investigated (Chen 1996;Sakagami et al 2010;Toyoda et al 2011).…”

Section: Introductionmentioning

confidence: 99%

Optimum core design to improve noise attenuation performance and stiffness of sandwich panels used for high-speed railway vehicles

Yoon

Lee

2016

Struct Multidisc Optim

View full text Add to dashboard Cite

In this study, we optimally design the core of a metal sandwich panel used in high-speed railway vehicles to minimize the amount of metal solid in the core and subsequently reduce its weight. The optimum core must satisfy constraints regarding sound transmission class (STC) and compliance. Because the solid-void layout in the core strongly affects the acoustic and static characteristics of sandwich panels, the core layout should be carefully designed when reducing the amount of metal solid. To this end, three topology-optimization problems and one size-optimization problem are formulated and sequentially solved. A single unit cell is periodically repeated in the core. Thus, structural and acoustic topology-optimization problems are first formulated and solved for the unit cell. Based on the optimal topologies obtained for the unit cell, a moderate initial solid-void layout in the unit cell is determined for the size-optimization problem to optimally design core. The effectiveness of the current design approach for the core of the sandwich panel is validated by comparing the STC and compliance values of the optimal core design and a reference design. Nomenclature A N n¼1 finite element assembly operator Bmatrix relating the element strain vector to its nodal displacement vector C m e a nc o m p l i a n c e C ini initial mean compliance c speed of sound in air D constitutive matrix d 1 thickness of thin flat plates at both ends in a sandwich panel d 2 thickness of the bar inside a sandwich panel dis (r,m) distance between the centers of the r th and m th elements E r (χ r ) Young's modulus of the r th element

show abstract

Wave transmission characteristics in periodic media of finite length: multilayers and fiber arrays

Cited by 60 publications

References 23 publications

Design of phononic crystals for self-collimation of elastic waves using topology optimization method

Design of phononic crystals for self-collimation of elastic waves using topology optimization method

Wave localization in randomly disordered layered three-component phononic crystals with thermal effects

Optimum core design to improve noise attenuation performance and stiffness of sandwich panels used for high-speed railway vehicles

Contact Info

Product

Resources

About