SAMS Subject Classification Number: 23

Overhead power lines are structures used to transmit and distribute electric power, as well as transmit electrical energy across large distances. A thin uniform rod with fixed ends is considered to represent a power line of unit length with minimal sag. A high voltage transmission line equation of motion will be derived using Lagrange Equation, with and without damping.

A change of variables is effected and then the Garlekin-Kantorovich method used to solved the resulting partial differential equation. It assumes that the solution to the partial differential equation is in trigonometric series form, like the one that can be found using the method of separation of variables. Thereafter, orthogonality of eigenfunctions is used, and the resulting system of coupled ordinary differential equations of initial value type is solved for both free and forced vibrations. For this study, MATHEMATICA is used in all computations and graphics because of its data handling and graphics capabilities.

Furthermore, this solution is approximated by using the numerical method of lines, which uses finite difference equations. This will be useful to check whether numerical method of lines can be applied to more complicated partial differential equations, extending to Rayleigh-Love, Rayleigh-Bishop and Mindlin-Hermann models.