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This paper provides a comprehensive understanding of the amplitude- and frequency-dependent characteristics of rubber springs. The dynamic nonlinear inelasticity of rubber is a key academic problem for continuum mechanics and a bottleneck problem for the practical use of rubber structures. Despite intensive efforts witnessed in industrial applications, it still demands an unambiguous constitutive model for dynamic nonlinear inelasticity, which is known as the Payne effect. To this end, three types of rubber springs (shear-type (ST), compression-type (CT) and shear-compression-combination-type (SCCT)) were tested with amplitude and frequency sweeps in different conditions. We investigated and present changes in dynamic stiffness and loss factor with amplitude, frequency and the hysteresis loops of different rubber springs. We also propose a hypothesis and research strategy to study a constitutive model involving multiple factors of hyperelasticity, the Mullins effect, viscoelasticity and the Payne effect, which we hope will provide new ideas for the establishment of a constitutive equation. [ABSTRACT FROM AUTHOR]