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On the stability of a nonlinear nonhomogeneous multiply hinged beam. (English) Zbl 1473.74068

Summary: The paper deals with a nonlinear evolution equation describing the dynamics of a nonhomogeneous multiply hinged beam, subject to a nonlocal restoring force of displacement type. First, a spectral analysis for the associated weighted stationary problem is performed, providing a complete system of eigenfunctions. Then, a linear stability analysis for bimodal solutions of the evolution problem is carried out, with the final goal of suggesting optimal choices of the density and of the position of the internal hinged points in order to improve the stability of the beam. The analysis exploits both analytical and numerical methods; the main conclusion of the investigation is that nonhomogeneous density functions improve the stability of the structure.

MSC:

74H55 Stability of dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74E05 Inhomogeneity in solid mechanics
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