Approximate integral-operator methods for estimating the natural frequencies of coupled objects


  • John E. Ross,

  • Edward J. Rothwell,

  • Dennis P. Nyquist,

  • Kun-Mu Chen


Of central importance to the singularity expansion method (SEM) for analysis of conducting objects are the frequencies and currents for the natural modes of the object. When there is more than one object in proximity, the direct calculation of these quantities becomes difficult, and it is useful to have approximate methods to simplify the computations. This paper presents two approximate methods for calculating the natural frequencies for a group of coupled objects. The first method is a perturbational one, leading to a transcendental equation for the natural frequencies. It assumes weak coupling between objects so that the natural mode current distribution is only slightly perturbed from that existing on an isolated object. The second method is also perturbational and further assumes that the Green's function can be approximated by leading terms of a Taylor series expansion about the natural-mode frequencies of isolated objects Results are shown for the case of coupled thin wires and compared to more rigorous moment-method solutions as well as experimental results.