Reconstruction of the shear modulus of viscoelastic systems in a thin cylinder: An inversion scheme and experiments

We consider a problem of reconstructing the shear modulus of an viscoelastic system in a thin cylinder from the measurements of displacements induced by torques applied at the bottom of the cylinder. The viscoelastic system is a mathematical model of a pendulum-type viscoelastic spectrometer (PVS). We first compute in an explicit form the solution of the viscoelastic system, and then derive with an error estimate the leading order term of the average of the solution. This leading order term yields a nonlinear inversion scheme to determine the shear modulus from the measurements of displacements. We apply the inversion scheme to determine the shear modulus using experimental data acquired from a PVS system.