懸垂形状を有する偏平アーチのカオス振動

フォーマット:

論文

責任表示:

丸山, 真一 ; 永井, 健一 ; 服部, 伯慕 ; 山口, 誉夫

言語:

日本語

出版情報:

日本機械学会, 2004-11-25

著者名:

• 丸山, 真一
• 永井, 健一
• 服部, 伯慕
• 山口, 誉夫

掲載情報:

日本機械学會論文集. C編

ISSN:

0387-5024    

巻:

70

通号:

699

開始ページ:

2993

終了ページ:

3000

バージョン:

VoR

概要:

application/pdf<br />Journal Article<br />Analytical results are presented on chaotic vibrations of a shallow arch with initial configuration of catenary. The shallow arch is simply supported at both ends and is subjected to periodic lateral force. Equations of motion are reduced to ordinary differential equations of multiple-degree-of-freedom system by the Galerkin procedure. To clarify effects of sag-to-span ratio on chaotic motions, first, steady-state … responses are calculated by the harmonic balance method. The chaotic responses are obtained by numerical integration and are examined by Poincare projection, the maximum Lyapunov exponent and bifurcation diagrams. For the arch with comparatively small sag-to-span ratio, chaotic vibrations are generated mainly in the regions of subharmonic resonance of 1/3 order and of ultra-subharmonic resonance of 3/2 order, accompanied by the lowest-symmetric-mode of vibration. As the sag-to-span ratio increases, chaotic responses are generated from the subharmonic resonances both of 1/2 and 1/3 orders. Furthermore, chaotic motion appears within a wider range of exciting frequency and the number of modes that contribute to the chaos increases. Period doubling bifurcation was mainly observed in the bifurcation from periodic responses to chaotic ones. Hopf bifurcation was also found for the arch that satisfies the condition of internal resonance. 続きを見る