Empirical formulas for predicting the energy attenuation behavior of primary stress waves in 1D composite chain of viscoelastic spheres

One-dimensional composite chain of viscoelastic spheres are potential candidates for novel impact buffers. Understanding the energy attenuation behavior of primary stress waves in the composite chain of viscoelastic spheres is the premise for high-performance impact buffers design. Although the current research included viscoelasticity into the motion equations of spheres, most of them were limited to homogeneous chains. Moreover, the models of discrete system could not give the explicit expressions of the key factors governing the energy attenuation of primary stress waves. The absence of explicit formulas for the key factors hindered efficient optimization design of impact buffers constructed by one-dimensional composite chain of viscoelastic spheres. In this study, empirical formulas for predicting the input amplitude, the attenuation coefficient of the contact force and the transmission coefficient at the interface were constructed. Multivariate nonlinear regression method and dimensional constraint were applied to ensure that all the empirical formulas only employ the impact velocity and the parameters of the used spheres as independent variables. Intermediate factor was introduced for individual key factor to evaluate the accuracy of the empirical formula. Though the groups of empirical formulas have degraded performance in the low range of the intermediate factors, their accuracy in quantitatively predicting the energy attenuation behavior of the stress waves in one-dimensional composite chain of viscoelastic spheres deserves satisfactory.