High-frequency backscattering enhancements by thick finite cylindrical shells in water at oblique incidence: Experiments, interpretation, and calculations

Abstract

Impulse response backscattering measurements are presented and interpreted for the scattering of obliquely incident plane waves by air-filled finite cylindrical shells immersed in water. The measurements were carried out to determine the conditions for significant enhancements of the backscattering by thick shells at large tilt angles. The shells investigated are made of stainless steel and are slender and have thickness to radius ratios of 7.6% and 16.3%. A broadband PVDF ͑polyvinylidene fluoride͒ sheet source is used to obtain the backscattering spectral magnitude as a function of the tilt angle ͑measured from broadside incidence͒ of the cylinder. Results are plotted as a function of frequency and angle. These plots reveal large backscattering enhancements associated with elastic excitations at high tilt angles, which extend to end-on incidence in the coincidence frequency region. Similar features are present in approximate calculations for finite cylindrical shells based on full elasticity theory and the Kirchhoff diffraction integral. One feature is identified as resulting from the axial ͑meridional ray͒ propagation of the supersonic a 0 leaky Lamb wave. A simple approximation is used to describe circumferential coupling loci in frequency-angle space for several surface waves. The resulting loci are used to identify enhancements due to the helical propagation of the subsonic a 0Ϫ Lamb wave. © 1998 Acoustical Society of America. ͓S0001-4966͑98͒04302-1͔PACS numbers: 43.30.Gv, 43.20.Fn ͓DLB͔ INTRODUCTIONRecent high-frequency sonar images of truncated cylindrical shells indicate that the visibility of the ends of the shell can be improved by an elastic response of the shell.1 The enhancements are associated with a category of lth class of leaky ray shown in Fig. 1. The enhancement occurs when the tilt angle ␥ of the cylinder is close to the leaky wave coupling angle l ϭsin Ϫ1 (c/c l ), where c l is the phase velocity of the leaky wave and c is the speed of sound in the surrounding water. This ray is referred to as a meridional ray 2 since it is propagated along the meridian defined by the direction of the incident wave vector and the cylinder's axis. An analysis shows that the backscattering enhancement is associated with the vanishing of Gaussian curvature of the wavefront backscattered in the direction of the receiver. The enhancements reported 1 were for tilts in the vicinity of 18°and 35°corre-sponding to the excitation of symmetric and antisymmetric (s 0 and a 0 ͒ generalizations of leaky Lamb waves on the stainless steel cylinder used in those experiments. The purpose of the present paper is to document the existence of high-frequency backscattering enhancements for tilted cylindrical shells relevant to larger values of the tilt ␥ and in some cases, extending to ␥ϭ90°͑i.e., end-on incidence͒.The method of our investigation concerns the global response in the frequency-angle domain rather than the spatial responses emphasized in Ref.1. There are several reasons for identifying such high-frequency enhancement...

High-Frequency Material-Dependent Scattering Processes for Tilted Truncated Cylindrical and Disk-Shaped Targets

“…Of these waves, the a 0 wave has a phase velocity that depends significantly on frequency so that the tilt condition for the enhancement depends on frequency. This was confirmed by measuring the backscattering as a function of frequency over a wide range of scattering angles [6,10]. The a 0 wave studied was on the branch that is important above the coincidence frequency of the shell.…”

“…Away from the meridional ray coupling condition, qualitative measurements demonstrated that helical ray contributions can be significant [6,10,12,15]. A ray model for these enhancements was developed and confirmed with quantitative measurements of the backscattering of tone bursts [16] and the case of a water-filled shell was investigated [17].…”

“…The relevant meridian is in the plane containing the incident wave vector and the cylinder's axis. Since this type of scattering contribution was outside the scope of previous quantitative ray theories for scattering by shells (as well outside the scope of computational studies available at that time) Marston et al [4][5][6][7] extended quantitative ray theory for cylinders to include this type of backscattering enhancement. During the development of the ray theory, it turned out to be useful to test ray theory for the related case of scattering by tilted infinitely-long solid cylinders [4] and cylindrical shells [8].…”

“…Computations [6][7][8] show that at high frequencies, the relevant meridional rays for shells are typically associated with the lowest antisymmetric and symmetric generalizations of Lamb waves commonly designated respectively as a 0 and s 0 waves. Of these waves, the a 0 wave has a phase velocity that depends significantly on frequency so that the tilt condition for the enhancement depends on frequency.…”

“…The transient responses in the time-domain and time-frequency domains were also investigated [6,12,15].…”