Fluid column resonances of water-filled cylindrical shells of elliptical cross section

Abstract

The acoustic resonances of a submerged fluid-filled cylindrical shell are analyzed as the shell cross section is deformed from circular to elliptical geometry. A schlieren visualization system is used to image standing wave fields within insonified water-filled shells of different eccentricities, and to locate the resonance frequencies of the fluid column. The acoustic behavior of elliptical cavities with infinite and finite surface impedances are modeled and the theory used to predict the resonance frequencies of the fluid column and calculate the pressure distribution in the acoustic field. As the symmetry of the circular shell is broken by deforming it to the more general ellipse the resonance spectrum changes; mode splittings and level crossings are observed as the eccentricity increases. The experimental observations of resonance patterns and frequency variation are in good agreement with the theoretical predictions.

Effects of fiber ellipticity and orientation on dynamic stress concentrations in porous fiber-reinforced composites

“…Analytic solutions to such structures require the computation of angular and radial Mathieu functions in the elliptical coordinate system. Examples of such applications include the solution of elliptical waveguide problems [52], optical fibers [53], scattering by mutilayered dielectric elliptic cylinders [54], free vibrations of elliptical membranes [55,56] and cavities [57], acoustic resonances of submerged fluid-filled elliptical cylindrical shells [58], and scattering of elastic and acoustic waves from elliptic cylinders [59][60][61][62][63]. Over the years many algorithms and programs have been developed to address the problem of computing Mathieu functions of integer and real arguments [52,[64][65][66][67][68][69].…”

Acoustic scattering by a rigid elliptic cylinder in a slightly viscous medium

“…Chinnery and Humphrey, 14 with an impedance boundary condition, give a solution in terms of Mathieu functions but add only experimental results. Leon et al 15 prefer to handle the multiple interactions in a Fourier modal method and give an extensive reference list.…”

Modal theory applied to the acoustic scattering by elastic cylinders of arbitrary cross section

“…14 Special attention has also been given to the resonances of water-filled cylindrical shells of elliptical cross section. 2 As the symmetry of the circular shell is broken by deforming it to the more general ellipse, the resonance spectrum changes. Mode splittings and level crossings are observed as the eccentricity increases.…”

“…Mode splittings and level crossings are observed as the eccentricity increases. 2 In connection with that, it would be of interest to study resonances from the T-matrix approach in the scope of the multichannel resonant acoustic scattering. 18 -20 The modal formalism developed in this paper can be considered as being rather similar to the T-matrix approach.…”

“…Experimental results are even fewer for this type of scatterers. 2,3 The aim of our paper is first to calculate the acoustic scattering by noncircular elastic cylinders with the use of a modal formalism and then to compare theoretical and experimental results in the case of elliptical elastic cylinders immersed in water.…”