Ribbed elastic structures under a mean flow

2005 ◽  
Vol 461 (2056) ◽  
pp. 913-931
Author(s):  
Paul D Metcalfe
Keyword(s):  
Band Structure ◽  
Transfer Matrix ◽  
Anderson Localization ◽  
Stop Band ◽  
Matrix Inversion ◽  
Mean Flow ◽  
Elastic Structures ◽  
Band Matrix ◽  
Disordered Structures ◽  
Static Fluid

The problem of a ribbed membrane or plate submerged in a fluid with mean flow is studied. We first derive a method which can be used to reduce this, and similar problems to a band matrix inversion. We then find the pass and stop band structure found in the case of static fluid persists when a mean flow is introduced, and we give an explanation in terms of the eigenvalues of the transfer matrix of the system. We then study disordered structures and observe the phenomenon of Anderson localization. In some parameter régimes the addition of disorder causes significant delocalization.

Disorder and localization in ribbed structures with fluid loading

1994 ◽  
Vol 444 (1920) ◽  
pp. 73-89 ◽  
Keyword(s):  
Steady State ◽  
Band Structure ◽  
Transfer Matrix ◽  
Stop Band ◽  
Localization Length ◽  
Fluid Loading ◽  
Transfer Matrices ◽  
Matrix Solution ◽  
Harmonic Response ◽  
Irregular Case

The paper considers the steady-state harmonic response of an elastic fluid-loaded membrane supported by irregularly spaced ribs. Under the assumption of subsonic wave coupling, the solution is given exactly for any configuration as a product of 2 x 2 transfer matrices. It is well known that the response of a periodically ribbed membrane exhibits a pass/stop band structure. Although this structure is destroyed in the irregular case, we find that two distinct régimes remain: smooth and fluctuating exponential decay. The transfer matrix solution is used to explain these regions. The average transfer matrix is obtained exactly; where the decay is smooth its eigenvalues approximately determine the localization length.

scholarly journals 110x110 optical mode transfer matrix inversion

2013 ◽  
Vol 22 (1) ◽  
pp. 96 ◽  
Author(s):  
Joel Carpenter ◽  
Benjamin J. Eggleton ◽  
Jochen Schröder
Keyword(s):  
Transfer Matrix ◽  
Matrix Inversion ◽  
Optical Mode

Elastic Wave Propagation in a Bio-Inspired Phononic Crystal

2020 ◽  
Vol 1012 ◽  
pp. 9-13
Author(s):  
H.V. Cantanhêde ◽  
E.J.P. Miranda Jr. ◽  
J.M.C. dos Santos
Keyword(s):  
Wave Propagation ◽  
Band Structure ◽  
Vibrational Energy ◽  
Periodic Structures ◽  
Chemical Elements ◽  
Phononic Crystal ◽  
Stop Band ◽  
Elastic Vibration ◽  
Band Gaps ◽  
Sound Waves

The wave propagation in a two-dimensional bio-inspired phononic crystal (PC) is analysed. When composite materials and structures consist of two or more different materials periodically, there will be stop band characteristic, in which there are no mechanical propagating waves. These periodic structures are known as PCs. PCs have shown an excellent potential in many disciplines of science and technology in the last decade. They have generated lots of interests due to their ability to manipulate mechanical waves like sound waves and thermal properties which are not available in nature. The physical properties of PCs are not essentially determined by chemical elements and bonds in the materials, but rather on the internal specific structures. Structures of this type have the ability to inhibit the propagation of vibrational energy over certain ranges of frequencies forming band gaps. The main purpose of this study is to investigate the band structure and especially the location and width of band gaps. For this analysis, it is used the finite element method (FEM) and plane wave expansion (PWE). The results are shown in the form of band structure and wave modes. Band structures calculated by FEM and PWE present good agreement. We suggest that the bio-inspired PC considered should be feasible for elastic vibration control.

Electronic properties of superlattices

1990 ◽  
Vol 68 (3) ◽  
pp. 268-272 ◽  
Author(s):  
D. Aitelhabti ◽  
P. Vasilopoulos ◽  
J. F. Currie
Keyword(s):  
Wave Function ◽  
Dispersion Relation ◽  
Band Structure ◽  
Electronic Properties ◽  
Transfer Matrix ◽  
Current Density ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Tight Binding ◽  
Effective Masses

Using the transfer-matrix method, we evaluate the exact normalized wave function analytically, the band structure, and the current density associated with an electron in a superlattice, with different or equal effective masses between wells and barriers. Also, we evaluate numerically the dispersion relation, the bandwidth, and the current density (in the tight-binding limit) for both equal and different effective masses between wells and barriers.

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