Comparison of instantaneous phase-frequency characteristics of suspended cables under external and end excitation
SUN Ceshi1, LI Cong1, DENG Zhengke2, TAN Chao1
1.College of Civil Engineering, Chongqing Jiaotong University, Chongqing 400074, China;
2.Hunan City University Design and Research Institute Co., Ltd., Changsha 410005, China
Abstract:It is generally believed that the response phase of the cables is constant when the excitation frequency is fixed, but in fact, the nonlinear effect makes the phase change periodically with time, and its characteristics are closely related to the excitations. The similarities and differences of the instantaneous phase-frequency characteristics of suspended cables under external and end excitations are studied. Firstly, the governing equations of motion under the two kinds of excitations are discretized into ordinary differential equations by using Galerkin method, and the Multiple Scales Method (MSM) is used to solve the equations. Secondly, the responses of the cables with different Irvine parameters λ2 (and the corresponding sag-span ratio) and excitation frequency Ω under two kinds of excitations are calculated through numerical examples, respectively. Finally, the instantaneous phases of the responses and the excitations are obtained by Hilbert transform to study the variations of their phase difference and amplitude in the λ2-Ω plane. It is shown that the drift term and the doubling-frequency term in the high-order approximate solution of the system make the response phase vary periodically with time under any kind of excitation. The right term of the frequency response equations of the suspended cables under the two excitations are different, which makes the response amplitude different, and then the phase-frequency characteristics can be affected by the drift term and the doubling-frequency term in the high-order solution. The amplitudes pmax of the instantaneous phase difference between the response and excitation under both external and end excitation suddenly increases in a local range which shows an anti-symmetric distribution centered at λ2 ≈ 3.0 and Ω ≈ 1.12. However, the value of the former is a long and narrow band, while the latter is a point field. Besides, the value of the former is significantly larger than that of the latter.
Key words: Suspended cable; Instantaneous phase-frequency characteristics; External excitation; End excitation; Instantaneous phase difference
孙测世1,李聪1,邓正科2,谭超1 . 分布与端部激励下悬索瞬时相频特性对比[J]. 振动与冲击, 2022, 41(24): 249-255.
SUN Ceshi1, LI Cong1, DENG Zhengke2, TAN Chao1. Comparison of instantaneous phase-frequency characteristics of suspended cables under external and end excitation. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(24): 249-255.
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