Package response characteristics analysis under non-Gaussian loads

In many cases, the package is excited by non-Gaussian random vibration loads. In circumstances where the packaging system optimization and package parameters optimization are performed, the package acceleration response statistical characteristics and the vibration reliability need to be determined repeatedly. Aiming at this disadvantage, an efficient and accurate analytical method was proposed to determine the statistical characteristics of nonlinear package acceleration responses. By use of non-Gaussian Karhunen - Loeve expansion, the stationary non-Gaussian random vibration was expressed as the linear combination of uncorrelated non-Gaussian random variables, and the package acceleration response was approximated by using first order Taylor expansion, so that the statistical characteristics of the package acceleration response were able to be calculated analytically. The probability density function ( PDF) and cumulative distribution function (CDF) of the package acceleration response were determined using the saddlepoint approximation method, based on the first four statistical moments of the package acceleration response. Since the linear combination of non-Gaussian variables was used to express the excitation, the nonlinear transformation of random variables was avoided. It is shown the first order Taylor expansion approximation for the response has good accuracy. The PDF and CDF of the package response were determined analytically by use of saddlepoint approximation, so, the Monte Carlo (or Quasi Monte Carlo) simulations were avoided, and it is also shown the analysis efficiency is improved greatly. © 2023 Chinese Vibration Engineering Society. All rights reserved.