On the bending of plates with transverse shear deformation and mixed periodic boundary conditions

Constanda, Christian; Лобо, М.; Pérez, Eugenia

doi:10.1002/mma.1670180502

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2002

2024

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Cited by 4 publications

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“…where v i; denotes @v i =@x , e ÿ (v)= 1 2 (v ; ÿ + v ÿ; ), and a ÿ are the elastic coe cients, a ÿ = ÿ + ( ÿ + ÿ ) with + ¿0 and ¿0 (see References [25,18,26], for example). We denote by V the space (H 1 0 ( )) 3 with the scalar product deÿned by E(·; ·).…”

Section: Statement Of the Problemmentioning

confidence: 99%

On the vibrations of a plate with a concentrated mass and very small thickness

Gómez

Лобо

Pérez

2002

Math Methods in App Sciences

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SUMMARYWe consider the vibrations of an elastic plate that contains a small region whose size depends on a small parameter . The density is of order O( −m ) in the small region, the concentrated mass, and it is of order O(1) outside; m is a positive parameter. The thickness plate h being ÿxed, we describe the asymptotic behaviour, as → 0, of the eigenvalues and eigenfunctions of the corresponding spectral problem, depending on the value of m: Low-and high-frequency vibrations are studied for m¿2. We also consider the case where the thickness plate h depends on ; then, di erent values of m are singled out.

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Section: Statement Of the Problemmentioning

confidence: 99%