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

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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.

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  1. Acoustics Research Laboratory, Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, 16844, Iran

    Seyyed M. Hasheminejad & M. Maleki

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Correspondence to Seyyed M. Hasheminejad.

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Hasheminejad, S.M., Maleki, M. Acoustic wave interaction with a laminated transversely isotropic spherical shell with imperfect bonding. Arch Appl Mech 79, 97–112 (2009). https://doi.org/10.1007/s00419-008-0212-y

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