VIBRATIONS OF A MEMBRANE WITH MANY CONCENTRATED MASSES NEAR THE BOUNDARY

DOI10.1142/S0218202595000334zbMath0845.73040OpenAlexW2034463001MaRDI QIDQ4854686

Miguel Sousa Lobo, M. Eugenia Pérez

Publication date: 15 September 1996

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202595000334

zbMATH Keywords

energy methodsmall parametermatched asymptotic expansionsFourier transform methodasymptotic behavior of eigenvaluesglobal vibrationslocal vibrations

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Plates (74K20) Inhomogeneity in solid mechanics (74E05) Asymptotic distributions of eigenvalues in context of PDEs (35P20)

Related Items (17)

Membranes with thin and heavy inclusions: Asymptotics of spectra ⋮ VIBRATIONS OF A THICK PERIODIC JUNCTION WITH CONCENTRATED MASSES ⋮ On the vibrations of a plate with a concentrated mass and very small thickness ⋮ Unnamed Item ⋮ Asymptotics of eigenelements to spectral problem in thick cascade junction with concentrated masses ⋮ ON VIBRATING MEMBRANES WITH VERY HEAVY THIN INCLUSIONS ⋮ On Vibrating Thin Membranes with Mass Concentrated Near the Boundary: An Asymptotic Analysis ⋮ The best Sobolev trace constant in domains with holes for critical or subcritical exponents ⋮ On multi-scale asymptotic structure of eigenfunctions in a boundary value problem with concentrated masses near the boundary ⋮ Asymptotic analysis of boundary-value problems for the Laplace operator with frequently alternating type of boundary conditions ⋮ Long time approximations for solutions of wave equations via standing waves from quasimodes ⋮ Spectral stiff problems in domains surrounded by thin bands: asymptotic and uniform estimates for eigenvalues ⋮ ON THE WHISPERING GALLERY MODES ON INTERFACES OF MEMBRANES COMPOSED OF TWO MATERIALS WITH VERY DIFFERENT DENSITIES ⋮ Asymptotic expansion of eigenelements of the Laplace operator in a domain with a large number of ‘light’ concentrated masses sparsely situated on the boundary. Two-dimensional case ⋮ Hausdorff convergence and asymptotic estimates of the spectrum of a perturbed operator ⋮ Vibrations of elastic systems with a large number of tiny heavy inclusions ⋮ On vibrations of bodies with concentrated masses near boundaries

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