Asymptotics of the frequencies of natural oscillations of elastic beams joined in the form of the letter \(\Pi\).
type: Item
instance of: scholarly article
title: Asymptotics of the frequencies of natural oscillations of elastic beams joined in the form of the letter \(\Pi\).
zbMATH Open document ID: 1090.74601
author: D. Massart
published in: Doklady Mathematics
publication date: 2004-06-15T00:00:00Z
review text: The asymptotics of the frequencies of natural oscillations of elastic beams joined in the form of the letter \(\Pi\) is investigated with regard for so-called moving elements of a beam which can perform rigid longitudinal displacements comparable with deflections of the other beams. The presence of such an element in junctions changes the essence of the one-dimensional model. The model becomes non-differential because of the introduction of algebraic unknowns; junction conditions are non-local and a part of the differential equations is projected on a subset of functions with zero mean. In order to detect the moving elements, a global weighted and anisotropic Korn inequality is required. For the sake of brevity, the simplest junction with moving beam whose one-dimensional model has all the above mentioned peculiarities is considered.
reviewed by: G. Jaiani
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74H10
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74K30
zbMATH DE Number: 2074896
zbMATH Keywords: anisotropic Korn inequality
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2074896