The influence of shape and material anisotropy on the vibrational modes of free particles

The influence of specimen geometry and material anisotropy on the vibrational modes of free-standing particles is investigated using a variational method applied to the traction-free vibration of elastic solids. The geometric shapes of spheres, cubes, and pyramids with both isotropic and cubic material symmetry are explored for a variety of compounds. It is shown that the shape and inclusion of anisotropy in the elastic stiffness tensor are both critical parameters in the frequency spectra, and that these features must be modeled for an accurate representation of both free and embedded particles.