Volume 42 Issue 11
Nov.  2021
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DENG Zhengke, SUN Ceshi, YANG Rudong. Transient Primary Resonance Phase-Frequency Characteristics of Stay Cables With Different Tensions[J]. Applied Mathematics and Mechanics, 2021, 42(11): 1126-1135. doi: 10.21656/1000-0887.420033
Citation: DENG Zhengke, SUN Ceshi, YANG Rudong. Transient Primary Resonance Phase-Frequency Characteristics of Stay Cables With Different Tensions[J]. Applied Mathematics and Mechanics, 2021, 42(11): 1126-1135. doi: 10.21656/1000-0887.420033

Transient Primary Resonance Phase-Frequency Characteristics of Stay Cables With Different Tensions

doi: 10.21656/1000-0887.420033
  • Received Date: 2021-01-28
  • Rev Recd Date: 2021-05-09
  • Available Online: 2021-12-07
  • Publish Date: 2021-11-30
  • The transient phase-frequency characteristics of stay cables with different cable forces were studied in view of the cable sag and geometric nonlinearity. The method of multiple scales was used to solve the ordinary differential equations of motion for cables subjected to in-plane distributed excitations, and the approximate analytical expressions of in-plane and out-of-plane primary resonance responses were obtained respectively. Then, the transient phase difference and its amplitude between the response and the excitation were obtained through the Hilbert transform. The rule and reason for the transient phase difference between the response and the excitation under different cable forces were studied. The results show that, the phase difference between the out-of-plane response and the excitation is constant, while for the in-plane one it is related to the elastic parameters and the sag of the cable. A small change in cable tension may result in a significant change in the transient phase-frequency characteristics. The main reason is that there are a twice-frequency term and a drift term in the approximate solution of the in-plane response, the former makes the transient phase of response appear twice positive-negative alternations in a single cycle, and the latter determines the maximum value and the variation law of the transient phase difference between the in-plane response and excitation.
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