Inversion of dynamic displacement response of cable in the whole field based on single vibration measurement

Abstract

Aiming at the problem that the dynamic displacement at critical positions of the cable cannot be measured due to economic or difficult installation, this paper proposes a method to invert the dynamic displacement of the cable in the whole field by using the dynamic displacement of a single measuring point. The method can realize the inversion of the lateral dynamic displacement response (L-DDR) and angular dynamic displacement response (A-DDR). Firstly, the exact mode shape functions of the L-DDR and A-DDR, considering bending stiffness, sag, inclination angle, and boundary conditions, are derived from the cable vibration control differential equation. The exact mode shape functions are a closed-form solution; thus, it can accurately calculate the cable mode shape at any frequency in real time. Then, an inversion method of the dynamic displacement of the cable in the whole field is proposed based on the amplitude ratio of the exact mode shape. This method can be used to invert the dynamic displacement of the cable in the frequency domain and time domain. Finally, through a numerical simulation and an actual cable test, it is verified that the accuracy of the proposed method is satisfactory. The cable dynamic displacement components at modal and external load frequencies are the main contributors to the dynamic displacement of the cable.