軸方向弾性拘束を受ける変断面偏平アーチのカオス振動

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  • Chaotic Vibrations of Shallow Arches with Variable-cross-section constrained by an Axial Elastic Support.
  • ジク ホウコウ ダンセイ コウソク オ ウケル ヘンダンメン ヘンペイ アーチ

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Analytical results are presented on chaotic vibrations of arches with axial elastic constraints. The arch with variable-cross-section is subjected to a periodic lateral force. The mode shape function proposed by the senior author-satisfies four sets of boundary conditions combined with a simply supported end and a clamped end. Basic equation is reduced to an ordinary differential equation of multiple-degrees-of-freedom system by the Galerkin procedure. Steady-state responses of the arches are calculated by the harmonic balance method. When the arch is contained simply supported condition, chaotic responses are excited easily in a specific frequency region. The chaotic responses are examined by the Runge-kutta-gill method. Following conclusion was obtained. In the chaos of the arch with the rigid axial constraint, many natural modes of vibration of both symmetric and asymmetric modes are excited simultaneously. The Lyapunov dimension increases as the rigid axial constraint of the arch becomes more tight. Furthermore, the chaotic attractors in the Poincare section show fractal geometries.

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