Dynamic response of a viscoelastic cylinder with ablating inner surface

The effects of ablation and viscoelasticity on the vibratory response of a hollow cylinder are investigated. The cylinder is subjected to a time-dependent internal pressure. Solutions are presented for the circumferential stress at the eroding inner surface and for the displacement in radial direction. It is found that, due to ablation, frequencies decrease and amplitudes increase. The increases in amplitudes due to ablation are counteracted by viscoelastic damping. In this analysis, it is assumed that the material is incompressible in bulk and viscoelastic in shear.