Structural resonance contributions to scattering cross sections of cylindrical shells: Mode and frequency dependence

Abstract

H. Lamb’s compact formulation of resonance contributions to the scattered field of elastic, lossless spheres (1900) was generalized by P. W. Smith, Jr. to structurally damped scatterers of arbitrary shape (1962). Excluding axisymmetric modes, modal configurations of cylindrical shells are identified by a pair of axial/circumferential wave numbers associated with a predominantly flexural, poorly radiating resonance and two supersonic (membrane and shear) resonances. Implementing Smith’s solution for the latter two yields a simple expression for the familiar ‘‘chalice’’ resonance peak loci in the aspect/frequency plane. A peak’s height is proportional to the square of the ratio of the modal radiation resistance over the combined radiation and structural resistance. With increasing wave numbers, modal configurations gradually become tangential, thereby reducing radiation damping as compared to total damping (an effect overlooked in this speaker’s 1993 publication, which unrealistically neglected structural as compared to radiation resistance). Consequently, though associated with supersonic wave numbers, resonance peaks fade with increasing mode order and frequency. Results are compared with Rummerman’s (1993) detailed analysis and measurements. [Work sponsored by Naval Undersea Warfare Center.]