Investigation of natural frequencies of laser inertial confinement fusion capsules using resonant ultrasound spectroscopy

•The frequency equation of isotropic multi-layer hollow spheres was derived using three-dimension (3D) elasticity theory and transfer matrix method.•The natural frequencies of the capsules with a millimeter-sized diameter are determined experimentally using resonant ultrasound spectrum (RUS) system.•The predicted natural frequencies of the frequency equation accord well with the observed results.•The theoretical and experimental investigation has proved the potential applicability of RUS to both metallic and non-metallic capsules.