The paper deals with a new approach to modeling the non-conservative behavior of hard rubbers in damping structures operating under quasi-harmonic, low-frequency conditions and in the large deformation regime. In particular, a hyperelastic proportional damping (HPD) model is proposed based on experimental research of dynamic responses of cylindrical specimens to torsion excitation. The HPD model depends on two ingredients. First, it relies on the integration of the dissipated energy of an experimentally obtained steady hysteresis loop. And second, this hysteresis loop is employed to construct a so-called skeleton curve, which is utilized to obtain the parameters of a generalized Rivlin model of the hyperelastic material. In addition, attention is paid to the HPD model's dependence on the frequency and amplitude of the torsional excitation. Finally, the problem of nonlinear transient vibration of a viscoelastic cylinder is formulated and numerically solved by the finite element method. The results obtained from finite element analyses are in accord with experimental data and validate the proposed HPD model for material damping evaluation.
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