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The Statistical Characteristics of Maxima of Contact Force in Stacked Packaging Units under Random Vibration
Author(s) -
Fang Ke,
Wang ZhiWei
Publication year - 2018
Publication title -
packaging technology and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.365
H-Index - 50
eISSN - 1099-1522
pISSN - 0894-3214
DOI - 10.1002/pts.2313
Subject(s) - maxima , spectral density , probability density function , vibration , maxima and minima , random vibration , gaussian , contact force , materials science , structural engineering , mechanics , mathematics , acoustics , engineering , mathematical analysis , physics , statistics , classical mechanics , art , performance art , art history , quantum mechanics
Stacked packaging units are the major form when transporting packaged products. In these stacked packaging units, the maxima of contact force between boxes are closely related with fatigue, the main failure form of packaged products during transportation, which can be simulated by random vibration. Therefore, this paper proposes a probability density function (PDF) of maxima for stationary Gaussian random signal with non‐zero mean and non‐unit variance to study the statistical characteristics of the maxima of contact force in three‐layer stacked packaging units, which is of vital importance to the fatigue evaluation. The proposed PDF of maxima is controlled by three parameters: spectral width parameter ϵ , mean value μ x and variance σ x . These three parameters are obtained respectively under three different impact factors, namely, constraint, acceleration excitation and location of contact surface. Power spectrum density (PSD) of contact force and PSDs' Q factors are also calculated. Relations and variations of the three parameters of PDF of maxima, PSD and PSD's Q factor under different impact factors are discussed in detail. It is found that the system of the three‐layer stacked units with a wide‐band excitation ( ϵ → 1) as input and contact force ( ϵ < 1) as output can be regarded as a relatively narrow band system. And the proposed PDF of maxima proves to be an effective method to investigate the statistical characteristics of the maxima of contact force between boxes in the stacked packaging units. Copyright © 2017 John Wiley & Sons, Ltd.