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Dekoninck, Bertrand; Nicaise, Serge

The eigenvalue problem for networks of beams. (English) Zbl 0979.74026

Linear Algebra Appl. 314, No. 1-3, 165-189 (2000).
Summary: We perform spectral analysis of different models of networks of Euler-Bernoulli beams. First, we derive the characteristic equation for the spectrum. Secondly, in some particular situations, we show that the spectrum depends only on the structure of the graph. Thirdly, we investigate the asymptotic behaviour of eigenvalues by proving the so-called Weyl’s formula.

Cited in 38 Documents

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics

Keywords:

networks of Euler-Bernoulli beams; characteristic equation; spectrum; graph; asymptotic behaviour of eigenvalues; Weyl’s formula
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References:

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