Convergence of variational eigenvalues and eigenfunctions to the Dirichlet problem for the p-Laplacian in domains with fine-grained boundary

2010 ◽  
Vol 140 (3) ◽  
pp. 573-596
Author(s):  
Pavel Drábek ◽  
Yuliya Namlyeyeva ◽  
Šárka Nečasová
Keyword(s):  
Eigenvalue Problems ◽  
Additional Term ◽  
Expansion Method ◽  
Critical Levels ◽  
Eigenvalues And Eigenfunctions ◽  
Dirichlet Eigenvalue ◽  
Perforated Domains ◽  
Fine Grained ◽  
New Equation ◽  
Asymptotic Expansion Method

We study the problem of the homogenization of Dirichlet eigenvalue problems for the p-Laplace operator in a sequence of perforated domains with fine-grained boundary. Using the asymptotic expansion method, we derive the homogenized problem for the new equation with an additional term of capacity type. Moreover, we show that a sequence of eigenvalues for the problem in perforated domains converges to the corresponding critical levels of the homogenized problem.

Vibration Analysis of Composite Beams With End Effects via the Formal Asymptotic Method

2009 ◽  
Author(s):  
Jun-Sik Kim ◽  
K. W. Wang
Keyword(s):  
Finite Element ◽  
Asymptotic Expansion ◽  
Cross Section ◽  
Asymptotic Method ◽  
Vibration Analysis ◽  
Eigenvalue Problems ◽  
Free Vibration Analysis ◽  
Expansion Method ◽  
Composite Beams ◽  
Asymptotic Expansion Method

Free vibration analysis of composite beams is carried out by using a finite element-based formal asymptotic expansion method. The formulation begins with three-dimensional equilibrium equations in which cross-sectional coordinates are scaled by the characteristic length of the beam. Microscopic 2D and macroscopic 1D equations obtained via the asymptotic expansion method are discretized by applying a conventional finite element method. Boundary conditions associated with macroscopic 1D equations are also considered in order to investigate the end effect. We then describe how to form and solve the eigenvalue problems derived from the asymptotic method beyond the classical approximation. The results obtained are compared to those of 3D FEM and those available in literature for composite beams with solid cross-section and thin-walled cross-section.

The Higher Order Crack Tip Fields of Exponential Gradient FGMs Plates with Reissner’s Effect

2013 ◽  
Vol 278-280 ◽  
pp. 491-494
Author(s):  
Yao Dai ◽  
Xiao Chong
Keyword(s):  
Asymptotic Expansion ◽  
Crack Tip ◽  
Expansion Method ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Shear Deformation ◽  
Plate Bending ◽  
Graded Materials ◽  
Fundamental Significance ◽  
Asymptotic Expansion Method

The Reissner’s plate bending theory with consideration of transverse shear deformation effects is adopted to study the fundamental fracture problem in functionally graded materials (FGMs) plates for a crack perpendicular to material gradient. The crack-tip higher order asymptotic fields of FGMs plates are obtained by the asymptotic expansion method. This study has fundamental significance as Williams’ solution.

scholarly journals Bragg Resonance around the Coast of Hardwall

2016 ◽  
Vol 7 (4) ◽  
pp. 275
Author(s):  
Viska Noviantri ◽  
Ro’fah Nur Rachmawati
Keyword(s):  
Wave Length ◽  
Expansion Method ◽  
Wave Transmission ◽  
Bragg Resonance ◽  
Incoming Wave ◽  
Approximation Solution ◽  
Multi Scale ◽  
The Right ◽  
Asymptotic Expansion Method ◽  
Transmission And Reflection

Basically, when waves pass an uneven basis, then this wave will be split into transmission and reflection waves. First of all, it will be shown that a sinusoidal seabed can lead to the phenomenon of Bragg resonance. Bragg resonance occurs when the wave-length comes at twice the wave-length of a sinusoidal basis. The method used to obtain approximation solution is a multi-scale asymptotic expansion method. A research on the effect of Bragg resonance on sinusoidal basis had been studied. Sinusoidal basis can reduce the amplitude of the incoming wave so that the amplitude of the wave transmission is quite small. In these researcher, the coast is assumed ideal and can absorb all the energy of the wave transmission. If the beach can reflect waves, this indicates that the existence of sinusoidal basis is more harmful to the coast. This mechanism relies on the distance between the base sinusoidal and beaches. The present research will examined the influence of the base, when there was a beach of hard-wall on the right, which was perfectly capable of reflecting waves. Having regard to the phase difference, from super positioned waves when they hit the beach, so it can determine the safert and the most dangerous distance.

scholarly journals EIGENVALUE ESTIMATES FOR HIGHER ORDER ELLIPTIC EQUATIONS

1994 ◽  
Vol 25 (3) ◽  
pp. 267-278
Author(s):  
HSU-TUNG KU ◽  
MEI-CHIN KU ◽  
XIN-MIN ZHANG
Keyword(s):  
Lower Bound ◽  
Elliptic Equations ◽  
Eigenvalue Problems ◽  
Higher Order ◽  
Bounded Domains ◽  
Dirichlet Eigenvalue ◽  
Eigenvalue Estimates

In this paper, we obtain good lower bound estimates of eigenvalues for various Dirichlet eigenvalue problems of higher order elliptic equations on bounded domains in $\mathbb{R}^n$.

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