Scattering and active acoustic control from a submerged spherical shell

Abstract

This paper is concerned with the scattering from a submerged (heavy fluid) bilaminate spherical shell composed of an outer layer of steel, and an inner layer of radially polarized piezoelectric material. The methodology used includes separation formulas for the stresses and displacements, which in turn are used (coupled with spherical harmonics) to reduce the governing equations to linear systems of ordinary differential equations. This technique uses the full equations of elasticity rather than any of the various thin-shell approximations in determining the axisymmetric scattering from a shell, normal modes of vibration for the shell, as well as voltages necessary for annihilation of a scattered pressure due to insonification of the shell by an incident plane wave.

Elastodynamics of radially inhomogeneous spherically anisotropic elastic materials in the Stroh formalism

“…We now consider U = A U A A and T = A T A A where A = P, B only, in which sense this case may be referred to as the 'in-plane' problem. It implies restricting attention to the upper 2×2 block of the matrices in (12).…”

“…It is also consistent with another framework that defines B mn and C mn without a normalization factor λ −1 . Note however that the symmetry G = TG + T of the system matrix in (12) is not preserved under any change of the definition (6) unless it implies multiplying all three harmonics A mn by the same factor. By (43), the sextet η η η (α) 0 (α = 1..6) for n = 0 contains only two non-zero modes which are the modes α = l1, l2 of the longitudinal (radially polarized) wave…”

Acoustic wave interaction with a laminated transversely isotropic spherical shell with imperfect bonding

“…Fan and Tang [13] constructed a method for estimating the viscoelastic material parameters by using the experimental data (form functions) associated with a double elastic spherical shell covered with damping materials in water. Scandrett [14] investigated the acoustic scattering from a submerged bilaminate spherical shell composed of an outer layer of steel, and an inner layer of radially polarized piezoelectric material. Gao et al [15] investigated effects of viscoelastic damping of an outer layer on acoustic scattering characteristics of an air-filled double-layered spherical shell immersed in water.…”

Cloaking of an acoustic sensor using scattering cancellation

“…15 Such an approach enables efficient numerical solution techniques to be used for related problems, such as the scattering from spherically isotropic layers 18 and active cancellation using a piezoelectric shell. 17 To include a spherically isotropic elastic shell into the analysis used for the bilaminate acoustic scattering cancellation cloak, a revised expression for the scattering matrix of the core can be obtained, 19 thus allowing for the determination of the necessary cloaking layer properties.…”

“…of the piezoceramic decouple, and the mechanical stresses and strains in the piezoceramic can be treated separately 17 and then used to calculate the voltage generated by the sensor by integrating the electric field over the shell thickness,…”