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This paper deals with radial vibrations of dissipative poroelastic spherical shell
embedded on the elastic foundation. The case of dissipation results in a transcendental,
complex valued frequency equation, and the numerical results are not possible. Hence, the
limiting case is considered. When the argument is small, the asymptotic expansions of Bessel
functions can be employed and consequently frequency equation can be separated into two
real valued equations which in turn give phase velocity and attenuation. In this case, a thick
walled hollow spherical shell becomes a thin spherical shell. Phase velocity is computed as a
function of the wavenumber, and attenuation is computed against the ratio of outer and inner
radii. The results with the elastic foundation are compared with that of without elastic
foundation. In the absence of dissipation, the phase velocity is computed and the comparison
is made between the present work and earlier works.
Keywords: poroelastic spherical shell, frequency equation, phase velocity, attenuation, elastic foundation |
full paper (pdf, 864 Kb)