Abstract
The dynamic motion of a span is coupled to the other spans in transmission lines. From the continuity conditions, force equilibrium conditions, and dynamical equations of every span conductor and insulator string, a close-form expression for the dynamic stiffness of a coupled two spans in harmonic motion is presented. Unlike some existing theories of single span conductor, the effect between the conductors and insulator strings is considered here. By means of example calculations, the validity of the dynamic stiffness of two-span is demonstrated by the consistency of the results determined by the ABAQUS. Meanwhile, the dynamic stiffness and natural frequency are discussed under variation of the span lengths ratio, Irvine parameter, and insulator string length. Moreover, the modal shape function corresponding natural frequency is derived, and the contribution of localization mode is studied. The results show that the contribution is either sensitive to or independent of transmission line parameters in certain parameter ranges. Finally, generalizing the work of two-span, the dynamic stiffness of arbitrary span number is obtained.
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