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

Abstract

An exact analysis is carried out to study interaction of a time-harmonic plane-progressive sound field with a multi-layered elastic hollow sphere made of spherically isotropic materials with interlaminar bonding imperfections. A modal state equation with variable coefficients is set up in terms of appropriate displacement and stress functions and their spherical harmonics, ultimately leading to calculation of a global transfer matrix. A linear spring model is adopted to describe the interlaminar adhesive bonding whose effects are incorporated into the global transfer matrix by introduction of proper interfacial transfer matrices. The solution is first used to correlate the perturbation in the material elastic constants of an evacuated and water submerged steel (isotropic) spherical shell to the sensitivity of resonances appearing in the backscattered amplitude spectrum. The backscattering form function, in addition to the acoustic radiation force acting on selected transversely isotropic spherical shells with distinct degrees of material anisotropy, is subsequently calculated and discussed. An illustrative numerical example is given for a multi-layered hollow sphere with two distinct interlaminar interface conditions (i.e., perfectly and imperfectly bonded layers). Limiting cases are considered and fair agreements with solutions available in the literature are established.

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

“…The establishment of the Stroh format for the elastodynamic equations in spherical coordinates opens the door for applications to various boundary value and scattering problems. For instance, solutions for acoustic and elastic wave scattering from solid spheres and shells, which have been limited to isotropic materials (see Martin 2006, §4.10 for a review) or transversely isotropic shells with m = 0 (Hasheminejad & Maleki 2009), can be generated for arbitrarily layered shells and solids using standard solution techniques outlined in §6b. Other possible approaches that can be explored with the Stroh formalism include impedance matrices for spherical shells and solids, the use of which simplifies the formulation of boundary value problems, such as determining modal frequencies, solving radiation and scattering problems.…”

“…In view of eqs. ( 10)- (11), the first problem implies answering the following question: given the ansatz U = U (r), what symmetry yields simultaneous conditions T = T (r) and Γ Γ Γ = Γ Γ Γ (r)? Direct calculation of T A = t r • A from (2a) with u = A U A (r) A shows that T = T (r) holds for tetragonal, cubic and transversely-isotropic symmetries if their principal axes are parallel to e r , but it is invalid for any other cases including the above symmetries with non-radial principal axes, the trigonal symmetry and certainly any lower symmetries.…”

“…A state space system was developed for radially inhomogeneous TI by Shul'ga et al (1988), who also identified two distinct types of wave motion solutions: an uncoupled pure shear motion and a coupled radialangular solution pair. The state vector approach has been applied to vibrations of thick-walled TI shells (Chen & Ding 2001;Hasheminejad & Maleki 2009) and further developed for piezoelectric shells (Scandrett 2002). Lower symmetry can support specific types of kinematically restricted deformation.…”

Effect of the Non-Homogenity on Wave Propagation in the Composite Infinite Cylinder

“…Information about the behavior of inhomogeneous materials is an important in understanding the response to a dynamical input of composite materials and materials with local impurities for this reason. This mater has attracted the attention of many researchers such as Abd-Alla et al [1][2][3][4][5][6] The recent trend of research concerning non-homogeneous elasticity may be found in the works of all Marin et al 7 Hasheminejad, Maleki, 8 Daouadji et al 9 Marin, 10 Ding et al 11 12 Stress concentration in elastic bodies, i.e., local accumulation of stresses arise in the presence of material discontinuities such as those due to inclusions of materials with elastic properties which differ from those of the surrounding matters, may be found in the works of Mahmoud et al [13][14][15][16][17][18] a more general model has been proposed in which, the Young's module and density of the orthotropic materials of the shells are assumed to vary continuously and piecewise continuously in the thickness coordinate and have solved the static and dynamic stability problems of single-layer and laminated orthotropic cylindrical and conical shells with simple or freely supported edges. * Author to whom correspondence should be addressed.…”

Cloaking of an acoustic sensor using scattering cancellation

“…Therefore, application of the scattering cancellation approach to a piezoelectric shell requires the calculation of the field scattered by a coated spherically isotropic elastic shell. 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.…”