Space elevator cable's oscillation caused in space thermal environment

Abstract

On the assumption that the tether's Young's modulus depends on the tether temperature, we analyzed the behavior of the space elevator tether with taking the tether's temperature change into account. The results show the tether has no vibration in the north-south direction, but a vibration in the east-west direction. This vibration's amplitude is about 40 km with a half-day cycle. Since the temperature change in most of the part of the tether has a half-day cycle, it is concluded that this vibration is caused by the temperature change through the expansion and contraction of the tether. Coriolis force generated by the expansion and contraction of the tether makes the tether vibrate by acting as an excitation force. The natural frequency was calculated assuming the space elevator to be a string. The first-order natural frequency is 1.59 [day−1] and the period is 0.628 [day], meaning there is a risk of resonance with the vibration (frequency; 2[day−1]). By changing the values of the two parameters (the length of the space elevator and the internal stress generated in the tether), the natural frequency of the space elevator can be changed. By increasing the tether length or decreasing the internal stress, the natural frequency can be shifted to the lower side. Contrarily, by shortening the tether length or increasing the internal stress, the natural frequency can be shifted to the higher side. For the actual operation of the space elevator, it is suggested that shifting to the higher frequency side is better. Then, the amplitude of the vibration was calculated when the natural frequency is changed by varying the internal stress or the tether length. When the internal stress is changed, the vibration amplitude peaks out when the natural frequency is around 1 [day−1], and when the tether length is changed, the shorter the tether length (the higher the natural frequency), the smaller the amplitude. From this result, it is concluded that the internal stress should be higher and/or the tether length should be shortened to shift the natural frequency to the higher side to suppress the vibration.