One-to-one internal resonance of a cable-beam structure subjected to a concentrated load
One-to-one internal resonance of a cable-beam structure subjected to a concentrated load
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DOI：
10.1016/j.jsv.2022.116915
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发表时间：
2022-03
影响因子：
4.7
通讯作者：
Yunyue Cong;Houjun Kang;Tieding Guo;Xiaoyang Su
中科院分区：
文献类型：
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作者：
Yunyue Cong;Houjun Kang;Tieding Guo;Xiaoyang Su
索梁组合结构，如悬臂施工的斜拉桥和塔式起重机吊装荷载，将承受动力激励。为了研究这一阶段的动力学行为，建立了索支承悬臂梁模型，在梁的悬臂端受到集中简谐激励。考虑了轴压荷载对梁的二阶效应和索的动态伸长引起的梁与索之间的动力相互作用。通过Galerkin离散化得到一个简化的二自由度系统。采用多时间尺度法求解常微分方程组。基于导出的调制方程和常微分方程，给出了系统的频率响应、幅值响应、相平面和时程曲线，以探讨系统的动力学行为。考虑三种不同长度的斜拉悬臂梁体系，研究其动力特性的变化。为了验证在每种情况下的有效性，采用龙格-库塔法直接求解原常微分方程，两个结果具有令人满意的一致性。分析结果表明，梁和拉索的频率响应均表现出硬化弹簧特性;拉索的动力特性比梁更丰富、更复杂，如拉索具有更显著的跳跃现象。
Cable-beam composite structure, such as a cable-stayed bridge in cantilever construction and a tower crane hoisting load, will sustain dynamic excitation. In order to investigate the dynamic behaviors at this stage, a cable-supported cantilever beam model subjected to a concentrated harmonic excitation at the cantilever end of the beam is established. The interactions including the second-order effect of the axial compressive load on the beam and the dynamic interaction between the beam and the cable due to cable's dynamic elongation are considered. A reduced two-degree-of-freedom system is obtained by using Galerkin discretization. Multiple time scales method is applied to solve the ordinary differential equations. Based on the derived modulation equations and the ordinary differential equations, frequency response, amplitude response, phase plane and time history curves are provided to explore the dynamic behaviors of the system. Three different lengths of the cable-stayed cantilever beam system are considered to study the changes in dynamic behaviors. In order to verify the validity in each case, Runge-Kutta method is used to directly solve the original ordinary differential equations and two results have a satisfying consistence. The analysis results show that frequency responses of both the beam and the cable exhibit hardening spring properties; the cable has more rich and complicated dynamic behaviors than the beam, for example the cable has more significant jump phenomenon.