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Results from the application of three nonlinear stiffness reconstruction algorithms to two simple cylindrical geometries are presented in this paper. Finite-element simulated harmonic motion data with added noise were initially used to represent a measured surface displacement dataset for each geometry. This motion was used as input to gradient-descent, combinatorial optimization, and hybrid reconstruction algorithms that aimed to reconstruct two shape-based parameters describing the internal stiffness of the geometry. Both the combinatorial optimization and hybrid algorithms showed significant advantages in reconstructed parameter accuracy when compared with the traditional gradient-descent approach, with success metrics improving by 13-28%. Results from the hybrid algorithm applied to silicone phantom displacements demonstrated for the first time the ability of this type of algorithm to reconstruct internal stiffness using only experimentally measured surface motion data. Improvements in the sophistication of the hybrid approach should lead to improved accuracy in reconstructed solutions, as well as enabling reconstructions where the geometry is less straightforward.