Electromagnetic scattering from vibrating penetrable objects using a general class of time-varying sheet boundary conditions

Calculation of electromagnetic (EM) scattering from vibrating penetrable cylinders of arbitrary cross-section is presented using a general class of time-varying sheet boundary conditions (SBCs) in conjunction with the method of moments (MoM). Sheet impedance and admittance expressions are first derived from the exact scattering solution for a penetrable circular cylinder with perturbed radius. Then, using the SBCs, integral equations are derived and solved numerically so that vibrating cylinders with arbitrary cross-section can be treated. Cylinder vibrations are assumed to be non-relativistic, allowing a simplified calculation of the scattered Doppler spectrum. A critical factor in the calculation of the potentially small Doppler components is that the time-varying nature of the cylinder boundary, contained within the sheet impedance and admittance expressions, can be isolated from the unperturbed terms in the scattered field. Comparison with exact and analytical perturbation solutions are presented to demonstrate the accuracy of the numerical solution.