The discontinuous enrichment method for multiscale and higher‐frequency wave propagation problems.

2009 ◽  
Vol 125 (4) ◽  
pp. 2565-2565
Author(s):  
Charbel Farhat ◽  
Radek Tezaur
Keyword(s):  
Wave Propagation ◽  
Enrichment Method ◽  
Frequency Wave ◽  
Discontinuous Enrichment

A Spectral Finite Element Model for Wave Propagation Analysis in Laminated Composite Plate

2006 ◽  
Vol 128 (4) ◽  
pp. 477-488 ◽  
Author(s):  
A. Chakraborty ◽  
S. Gopalakrishnan
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Shear Deformation ◽  
Mechanical Response ◽  
Laminated Composite ◽  
Wave Number ◽  
Single Element ◽  
Element Formulation ◽  
Frequency Wave ◽  
Spectral Finite Element

A new spectral plate element (SPE) is developed to analyze wave propagation in anisotropic laminated composite media. The element is based on the first-order laminated plate theory, which takes shear deformation into consideration. The element is formulated using the recently developed methodology of spectral finite element formulation based on the solution of a polynomial eigenvalue problem. By virtue of its frequency-wave number domain formulation, single element is sufficient to model large structures, where conventional finite element method will incur heavy cost of computation. The variation of the wave numbers with frequency is shown, which illustrates the inhomogeneous nature of the wave. The element is used to demonstrate the nature of the wave propagating in laminated composite due to mechanical impact and the effect of shear deformation on the mechanical response is demonstrated. The element is also upgraded to an active spectral plate clement for modeling open and closed loop vibration control of plate structures. Further, delamination is introduced in the SPE and scattered wave is captured for both broadband and modulated pulse loading.

scholarly journals Thin-layer solutions of the Helmholtz equation

2020 ◽  
pp. 1-15
Author(s):  
J. R. OCKENDON ◽  
R. H. TEW
Keyword(s):  
Wave Propagation ◽  
Thin Layer ◽  
Helmholtz Equation ◽  
Open Problem ◽  
High Frequency ◽  
Mathematical Structure ◽  
Mathematical Physics ◽  
Thin Layers ◽  
Frequency Wave ◽  
High Frequency Wave

This paper gives a brief overview of some configurations in which high-frequency wave propagation modelled by Helmholtz equation gives rise to solutions that vary rapidly across thin layers. The configurations are grouped according to their mathematical structure and tractability and one of them concerns a famous open problem of mathematical physics.

Harmonic Wave Propagation in a Periodically Layered, Infinite Elastic Body: Plane Strain, Analytical Results

1979 ◽  
Vol 46 (1) ◽  
pp. 113-119 ◽  
Author(s):  
T. J. Delph ◽  
G. Herrmann ◽  
R. K. Kaul
Keyword(s):  
Wave Propagation ◽  
Asymptotic Behavior ◽  
Plane Strain ◽  
Elastic Body ◽  
Harmonic Wave ◽  
Wave Number ◽  
Periodic Medium ◽  
Frequency Wave ◽  
Wave Numbers ◽  
Band Characteristic

The problem of harmonic wave propagation in an unbounded, periodically layered elastic body in a state of plane strain is examined. The dispersion spectrum is shown to be governed by the roots of an 8 × 8 determinant, and represents a surface in frequency-wave number space. The spectrum exhibits the typical stopping band characteristic of wave propagation in a periodic medium. The dispersion equation is shown to uncouple along the ends of the Brillouin zones, and also in the case of wave propagation normal to the layering. The significance of this uncoupling is examined. Also, the asymptotic behavior of the spectrum for large values of the wave numbers is investigated.

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