同济大学学报（自然科学版）2011，Vol.39Issue(5)：666-674,9.DOI:10.3969/j.issn.0253-374x.2011.05.008
梁索耦合结构的非线性振动
Nonlinear Vibration of Coupled Structure of Cable-stayed Beam
摘要
Abstract
Based on a series of partial differential equations describing the effect of curvature of the main cables and deformation of the stay cables on the structure,the non-linear ordinary differential equations of the first order approximation on time-domain are obtained by Galerkin method and studied by multi-scale method.An analysis is made of the principal resonance and 1 : 2 internal resonance.The analytical solutions of the first order approximation and the vibration amplitude response curves for the amplitude of excitation as a parameter are derived.The results indicate the first order approximate analytical solutions have a higher accuracy.In the internal resonance condition,there are jump phenomena of the vibration amplitudes of the main cables and the beam.But the low-order resonance bifurcation values of the jump phenomena are less than the high-order resonance bifurcation values,which indicates that the low-frequency resonance vibration is easier to generate substantial vibrations than the lowfrequency.The study results are significant for engineering applications关键词
梁索耦合结构/非线性振动/Galerkin法/多尺度法/1:2内共振Key words
coupling of cable-stayed beam/ non-linear vibration/ Galerkin method/ multi-scale methed/ 1 : 2 internal resonance分类
数理科学引用本文复制引用
黄坤,冯奇..梁索耦合结构的非线性振动[J].同济大学学报（自然科学版）,2011,39(5):666-674,9.基金项目
国家自然科学基金(A10672121) （A10672121）
上海市重点学科建设(B302) （B302）
