Strategies for characterizing damping and restitution in compliant impacts while eliminating the force discontinuities associated with the standard Kelvin-Voigt model are examined within the framework of linear viscoelasticity. A modification of the Kelvin-Voigt model as well as higher-order (Maxwell and standard linear) models are studied in an effort to satisfy the expected force-displacement boundary conditions. The restitution coefficients, energy losses per cycle, and equivalent linear damping ratios are then obtained analytically as functions of the dimensionless viscoelastic parameters which may be easily related to and obtained from experimentally measured restitution coefficients.

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