Wave propagation in a piezoelectric two-layered cylindrical shell with hexagonal symmetry: Some implications for long bone

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Abstract
Harmonic wave propagation is considered in a 2-layered cylinder of dissimilar but transversely isotropic materials such as bone. The model includes the approximate piezoelectric behavior of long bone and the frequency equation is shown to constitute a 16th-order determinant. A frequency equation is also derived for the nonpiezoelectric case. Though the frequency equations are much too complicated to be treated analytically, they are shown to lead to simpler forms for the special cases of axial symmetry, very long and very short wavelengths. in the absence of established values for the piezoelectric moduli of bone and of the elastic constants of the inner spongy layer, a numerical solution to the model does not seem worthwhile at present.

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