Abstract
Analytical result is presented on chaotic vibrations of a suspended beam in a shape of catenary. The flexural beam due to gravitational force is simply supported at both ends and subjected to a periodic lateral force. Introducing modal expansion, basic equations are reduced to ordinary differential equation of multiple-degrees-of-freedom systems by the Galerkin procedure. Changing a sag-to-span ratio of the beam, first, steady-state responses are calculated by the harmonic balance method. The chaotic responses are examined by numerical integration. Chaotic vibrations are generated predominantly in the frequency region of subharmonic resonance of 1/3 order and ultra-subharmonic resonance of 3/2 order corresponding to the lowest symmetric mode of vibration. Other chaotic vibrations appears at the regions of subharmonic resonance of 1/2 order and surperharmonic resonances of both second and third orders. As the sag-to-span ratio increases, chaotic motion appears in a wide range of exciting frequency. Furthermore, chaotic responses are bifurcated from the subharmonic resonances both 1/2 and 1/3 orders in the same frequency region.
