Acoustic and electromagnetic wave interaction: Estimation of doppler spectrum from an acoustically vibrated metallic circular cylinder

Abstract

Abstract-The idea of using acoustically induced Doppler spectra as a means for target detection and identification is introduced. An analytical solution for the calculation of the bistatic scattered Doppler spectrum from an acoustically excited, vibrating metallic circular cylinder is presented. First the electromagnetic scattering solution of a slightly deformed circular cylinder is obtained using a perturbation method. Then, assuming the vibration frequency is much smaller than the frequency of the incident electromagnetic wave, a closed form expression for the time-frequency response of the bistatic scattered field is obtained which can be used directly for estimating the Doppler spectrum. The acoustic scattering solution for an incident acoustic plane wave upon a solid elastic cylinder is applied to give the displacement of the cylinder surface as a function of time. Results indicate that the scattered Doppler frequencies correspond to the mechanical vibration frequencies of the cylinder, and the sidelobe Doppler spectrum level is, to the first order, linearly proportional to the degree of deformation and is a function of bistatic angle. Moreover, the deformation in the cylinder, and thus the Doppler sidelobe level, only becomes sizeable near frequencies of normal modes of free vibration in the cylinder. Utilizing the information in the scattered Doppler spectrum could provide an effective means of buried object identification, where acoustic waves are used to excite the mechanical resonances of a buried object.

Electromagnetic scattering from a dielectric cylinder buried beneath a slightly rough surface

“…There are many difficulties associated with detecting objects beneath the ground due to the existence of clutter and low RF signal penetration into moist soil. Recently, the authors proposed an acousto-electromagnetic approach to enhance buried object detection by observing the scattered electromagnetic Doppler spectrum from an object vibrated at resonance [1] and [2]. In addition to the object vibration, the incident and scattered acoustic waves will perturb the interface above the buried object.…”

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

“…By equating (8) to the mode coefficients for the perturbed cylinder in (7) and keeping only first order terms in , we can solve for sheet impedance and admittance values that will yield an equivalent solution. Following some lengthy algebraic manipulation, and using the relationship from Bessel's equation, it can be shown that an equivalent solution (to first order in ) is obtained when (9) (10) (11) (12) Note that the sheet admittance expressions in (11) and (12) depend on the mode number and, as such, cannot be applied to a cylinder with non-circular cross-section. This mode dependence suggests that a higher order boundary condition should be used in place of (3).…”

“…None of these studies, however, consider arbitrary vibrations of the surface. More recently, an analytical study of EM scattering from metallic and dielectric circular cylinders with arbitrary vibration has been presented using a perturbation technique [12], [13], but the technique cannot be applied to objects of arbitrary cross-section. What is needed now is an efficient numerical method to calculate the EM scattering from a vibrating, penetrable object having arbitrary cross-section and arbitrary vibration.…”

Standoff Acoustic Modulation of Radio Frequency Signals in a Log-Periodic Dipole Array Antenna

“…A vibrating structure is known to modulate reflected RF signals producing a received signal comprising the originally transmitted signal and sidebands offset by the frequency of vibration. This Doppler modulation is exploited in land mine detection [12], [13], but can be detrimental as in modulation by rotating helicopter rotor-blades [14]. The use of a standoff acoustic tone to drive mechanical vibrations subsequently detected by an RF signal has also been explored [13], [15].…”