Scattering from a cylindrical shell with an internal mass

Abstract

Perhaps the simplest approach to modeling acoustic scattering from objects with internal substructure is to consider a cylindrical shell with an internal mass attached by springs. The earliest analyses, published in JASA in 1992, by Achenbach et al. and by Guo assumed one and two springs, respectively. Subsequent studies examined the effects of internal plates and more sophisticated models of substructure. In this talk we reconsider the Achenbach—Guo model but for an arbitrary number, say J, of axisymmetrically distributed stiffeners. The presence of a springs-mass substructure breaks the cylindrical symmetry, coupling all azimuthal modes. Our main result provides a surprisingly simple form for the scattering solution for time harmonic incidence. We show that the scattering, or T-matrix, decouples into the sum of the T-matrix for the bare shell plus J matrices each defined by an infinite vector. In addition, an approximate expression is derived for the frequencies of the quasi-flexural resonances induced by the discontinuities on the shell, which excite subsonic shell flexural waves. Some applications of the model to shells with specified long wavelength effective bulk modulus and density will be discussed. [Work supported by ONR.]