Vibrational Characteristics Of Overhead-line Equipment By Transfer Matrix Method
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Vibrational characteristics of overhead-line equipment cannot be solved analytically because the system constitutes neither a distributed constant system nor a concentrated constant one. Calculations have been carried out for &LIS system, by means of transfer matrix method to clarify the vibrational response of simple catenary equipment by point excitation. In the analysis, both the contact and messenger wires are assumed to be tensioned strings with their bending stiffness neglected. Therefore, each section of dropper spacing has four eigen functions and coefficicents, which are related to neighboring ones. By applying these relations of dropper spacing to the far away one step by step, the response of simple catenary equipment by point excitation is analytically gained. As a result, it is revealed that simple catenary equipment has two similar fundamental vibration modes. In one mode, the motive directions of contact wire of a span accord with those of others. In the other mode, the motive directions are opposite in every neighboring span. The former is defined as a ‘mode in the same phase’ and the latter as a ‘mode in the reverse phase’. Their frequency is about 1Hz under standard wire tensions. The fundamental mode in same phase is a little lower than that of reverse phase in frequency. The results of this paper are valid in the frequency range of 0Hz to about 30Hz,where, that is, a wire behaves as a string.