The complex phase gradient method: A new tool for the investigation of immersed elastic plate angular resonances

Abstract

The Phase Gradient Method applied to the complete characterization of the angular resonances of an immersed elastic plate, i.e., the angular poles of the plate reflection coefficient, was proven to be efficient, as far as the pole imaginary parts are not too large when compared to their real parts. This method consists of plotting the reflection coefficient phase partial derivative with respect to the sine of the incidence angle, considered as real, vs incidence angle. At the vicinity of an angular resonance, the plot exhibits a Breit–Wigner shape, whose minimum is located at the pole real part and whose amplitude is the inverse of its imaginary part. However, when the imaginary part is too large, this method does not give its value with a sufficient accuracy, compared to the exact calculation of the root in the complex angle plane. An improvement consists in plotting in 3D, in the complex angle plane, the angular phase derivative with respect to the real part of the sine of the incidence angle, considered as complex. When an angular pole is reached, the 3D curve shows a clear cut transition of very large amplitude, whose position is easily obtained.