Analytic approximation of natural frequencies of bent wire structures above ground

This paper deals with the analytic approximation of the natural frequencies of a long thin wire with a bend above ground. Therefore, an asymptotic approach from literature, that employs reflection coefficients at discontinuities, is used. The solutions for the reflection coefficients of a short circuit terminal and an open circuit one are taken from previous publications to calculate the natural frequencies for the wire bounded with those terminals in various combinations. Moreover, the reflection and transmission coefficients at the bend are used from literature as well. Lastly, a numeric double integration needs to be executed to obtain an approximation of the natural frequencies. The solution is compared to a purely numeric one. Therefore, an algorithm that extracts the singularities from an existing frequency response is explained and applied. Excellent agreement is found.