Investigation of temperature effects on the inplane subharmonic resonances of suspended cables

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Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (6) : 1-6.

ZHAO Yaobing 1, JIN Bo 2, HUANG Chaohui 1

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Abstract

A new thermal stressed configuration of suspended cables was generated under the effects of temperature variations which lead to some changes of the cable tension force and sag. The effects of temperature changes on the nonlinear equations of motion of a suspended cable are reflected by two nondimensional factors related to the cable tension and sag. On the basis of the nonlinear inplane vibration equations of the suspended cable under harmonic excitation where the temperature effects were taken into consideration, the Galerkin method was introduced to discretize the nonlinear partial differential equations firstly, then the multiple scales method was used to obtain the approximate solutions of 1/2 and 1/3 order subharmonic resonances, and the corresponding frequency response equations were obtained. Furthermore, the temperature effects on the resonance responses were investigated quantitatively and qualitatively by using numerical examples. The numerical results show that the effects of different temperature variations on the subharmonic resonances of the suspended cable are obvious, and these effects are closely related to the sagtospan ratio. As to the case of small sagtospan ratio, the nonlinear vibration characteristics would be varied by the temperature effects quantitatively and qualitatively, and the deflection and its degree of the frequency response curves are changed under the temperature effects, and the range of resonances and the response amplitudes are also affected. As to the case of large sagtospan ratio, only some quantitatively changes are induced by the temperature variations, and the response amplitudes are altered. Due to the initial tension force, the effects of warming and cooling on the nonlinear subharmonic vibration behaviors of the suspended cable are not symmetric.

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suspended cable / temperature variations / multiple scales method / sub-harmonic resonance / frequency response curves

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ZHAO Yaobing 1, JIN Bo 2, HUANG Chaohui 1. Investigation of temperature effects on the inplane subharmonic resonances of suspended cables[J]. Journal of Vibration and Shock, 2018, 37(6): 1-6

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