Acceleration spectrum analysis of hyperbolic tangent package under random excitation

Abstract

AbstractMany packaging cushion materials follow the hyperbolic tangent type of constitutive relation, so a hyperbolic tangent stiffness non‐linearity was derived to describe the stiffness property of the package. Transport package was modelled as the single degree of freedom (SDOF) of hyperbolic tangent spring–mass–damping (SMD) system. The displacement and velocity responses of the system were obtained by Fokker–Planck–Kolmogorov (FPK) equation. Based on the kinematic equation and integral transforming, the approximate analytic solution of the acceleration response power spectral density (PSD) of the hyperbolic tangent package was established for the first time, and the influences of system non‐linearities on the acceleration response PSD were investigated. Validation experiment with a complete packaged computer was carried out to verify the proposed approach. Non‐linearity of the stiffness influenced the acceleration response PSD through the effect of parameter γ and statistical moment mi0. The frequency corresponding to acceleration response peak was determined by the damping correlation coefficient α and parameter γ, which was determined by system characteristic parameter β, frequency parameter ω0 and statistical moment mi0. The proposed approach can be used to predict the acceleration response PSD of transport package, and the analysis has important value for packaging optimization design.