3810 周期横励振を受ける懸垂状偏平はりのカオス振動挙動の解析

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Analytical result is presented on nonlinear vibrations of suspended beams in a shape of catenary. The beam having a small deflection is simply supported at both ends and subjected to a periodic lateral force. Basic equations are reduced to the ordinary differential equation of multiple-degrees-of-freedom systems by the Galerkin procedure. To find out the effect of sag-to-span ratio on chaotic motions, first, steady-state responses are calculated by the harmonic balance method. The chaotic responses are examined by numerical integration. The following results are obtained : chaotic vibrations appears mainly in the subharmonic resonance of 1/3 order and ultra-subharmonic resonance of 3/2 order corresponding to the lowest symmetric mode of vibration. Decreasing the exciting frequency from high frequency range to low one, the chaotic vibration is generated with the two bifurcation types. Those are the periodic doubling bifurcation and the bifurcation originated for the internal resonance. As the sag-to-span ratio increases, chaotic motion appears in a wide range of frequency. Furthermore, chaotic responses are bifurcated from the subharmonic resonances both 1/2 and 1/3orders in the same frequency region.
2000-07-31