×

zbMATH — the first resource for mathematics

A sextic formalism for three-dimensional elastodynamics of cylindrically anisotropic radially inhomogeneous materials. (English) Zbl 1058.74044
Summary: We consider elasticity of arbitrary cylindrically anisotropic radially inhomogeneous media. The system of six first-order ordinary differential equations describing time-harmonic cylindrical waves propagating along the cylinder axis is obtained. The matrix of the system coefficients has a specific algebraic symmetry underlying the structure of the formalism. We discuss the matrix solution in the form of Peano expansion. The Wentzel-Kramers-Brillouin approximation is derived. Algebraic features of the solution are analysed, and their physical content is elucidated. The dispersion equation for waves in a hollow cylinder with free or clamped lateral surfaces is formulated in terms of impedance/admittance matrices. Their analytical properties are established, which are useful for analysis of the resulting frequency spectrum. The theory is extended to anisotropic radially inhomogeneous piezoelectric cylinders, for which an octet generalization of the formalism is developed and studied.

MSC:
74J10 Bulk waves in solid mechanics
74E10 Anisotropy in solid mechanics
74F15 Electromagnetic effects in solid mechanics
74H05 Explicit solutions of dynamical problems in solid mechanics
74J05 Linear waves in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI