Determination of the inplane natural frequencies of multispan transmission lines by a transfer-matrix method

The dynamical equations of a `shallow¿ elastic catenary, oscillating in its own plane, are formulated and solved generally. Using the solutions, a transfer matrix is derived which is generally applicable to any shallow elastic catenary¿whether symmetrical with regard to its lowest point or not. The oscillations of composite systems comprising shallow catenaries can thus be treated by standard transfer matrix methods. On the assumption that the insulator strings hang vertically at equilibrium, a special transfer matrix of reduced order is obtained, and this can be used as the basis of the vibration analysis of a wide variety of multispan lines. The practical use of this matrix is illustrated by a computer calculation of the natural frequencies and normal modes of a symmetrical 3-span system. A successful comparison is made between these results and those obtained from a previous `lumped parameter¿ calculation. In an Appendix the frequency equations of symmetrical shallow elastic catenaries, under a variety of end conditions, are enumerated.