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Modeling the vibrations of a multi-rod structure. (English) Zbl 0895.73037

Summary: We show that the eigenvalues and eigenfunctions of three-dimensional linearized elasticity in a body consisting of two rods of thickness \(\varepsilon\), converge towards the eigenvalues and eigenfunctions of a limit 1d-1d rod model, as the thickness of the rods goes to zero.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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References:

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