Spectrum of a network of Euler-Bernoulli beams

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:337

Article

Mercier, D.¹  Regnier, V.¹ 

[1] Univ Valenciennes & Hainaut Cambresis, Inst Sci & Tech Valenciennes, Lab Math & Applicat Valenciennes, F-59313 Valenciennes 9, France

关键词: network;    flexible beams;    point masses;    spectrum;    characteristic equation;    asymptotics;   

DOI  :  10.1016/j.jmaa.2007.03.080

来源: Elsevier

【 摘 要 】

A network of N flexible beams connected by n vibrating point masses is considered. The spectrum of the spatial operator involved in this evolution problem is studied. If lambda(2) is any real number outside a discrete set of values S and if lambda is an eigenvalue, then it satisfies a characteristic equation which is given. The associated eigenvectors are also characterized. If lambda(2) lies in S and if the N beams are identical (same mechanical properties), another characteristic equation is available. It is not the case for different beams: no general result can be stated. Some numerical examples and counterexamples are given to illustrate the impossibility of such a generalization. At last the asymptotic behaviour of the eigenvalues is investigated by proving the so-called Weyl's formula. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free