The spectrum of acoustic vibrational modes of an inhomogeneous elastic continuum is analyzed with application to a spherical nanoparticle embedded in an infinite glass block. The relationship of these modes to the discrete vibrational spectrum of a free sphere is studied. The vibrational modes of a sphere with a fixed surface are relevant in some situations. Comparisons are also made to calculations of mode frequency and damping based on complex-valued frequency.
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Murray et al. (2004) studied this question.
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