Acceleration spectrum analysis of hyperbolic tangent package under random excitation

Abstract

Many 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.

A new approach for non‐Gaussian vibration analysis of hyperbolic tangent package with a critical component

“…Qiu et al 32 studied the solutions of the neutral dynamic equations for a class of third‐order nonlinear oscillation. Yang and Wang 33,34 established the acceleration response spectrum theory of the HTPS under Gaussian excitation, verified the correctness of the proposed method through a complete packaging computer vibration experiment, and analyzed the HTPS specific nonlinear effects caused by soft spring stiffness.…”

Reliability analysis for product package via probability density function of acceleration random response

“…In order to study the packaging stochastic dynamics, generally, the above model is always simplified as the single degree of freedom (SDOF) spring–mass–damping (SMD) system (Yang and Wang, 2021), as shown in Figure 1(d). m represents the mass of the product, c is the damping of the cushion packaging material, x presents the displacement of the product, u denotes the external displacement excitation under random vibration, and f(x) represents the stiffness restoring force.…”

“…Analytical PDF of acceleration random response for cubic nonlinear product package has seldomly been investigated due to the difficulty of solving nonlinear random problem and less attention paid to the acceleration response. Therefore, on the basis of the acceleration response spectrum study for the nonlinear packaging system (Yang and Wang, 2020, 2021), this paper focused on the approximate analytical solution of acceleration response PDF for cubic nonlinear product package under random vibration.…”