Determination of elastic modulus for hollow spherical shells via resonant ultrasound spectroscopy

•The axisymmetric frequency equation of an isotropic hollow two-layer sphere is deduced by three dimension elasticity theory and global matrix method.•The simulated results demonstrate that the natural frequencies of a hollow sphere are more strongly dependent on Young’s modulus than Poisson's ratio.•The Young’s moduli of polymer capsules with an sub-millimeter inner radius are measured accurately with an uncertainty of ∼10%.