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### Influence of Jumping Phenomenon on Response of Package Under Random Vibration

#### Abstract

Since asymmetric contact is characteristic of the package surface, jumping phenomenon may happen under strong random vibration. To study the influence of jumping phenomenon on package response, a piecewise linear random vibration model is established. By applying Fokker-Planck-Kolmogorov (FPK) equation method, distribution of displacement composed of Gaussian distribution and exponential distribution is obtained. After that, distribution of maxima of displacement composed of Rayleigh distribution and exponential distribution is obtained. The proportion of time taken by loss of contact in a single cycle is studied under different peak of displacements. When the peak of displacement is from 1 to 3, the period is from 2 to 2.56, and proportion of time taken by loss of contact is from 0 to near 50%. By applying the relation between peak of displacement and contact force, distribution of maxima of contact force can be obtained as translational Rayleigh distribution, which is also proved by numerical simulation and experiment respectively. Moreover, by numerical simulation, distribution of acceleration and time history of modified displacement are obtained. It is found that when RMS value of displacement signal increases, probability of loss of contact becomes greater, and the time cost by the same number of cycles will be prolonged. By experiment, distribution of acceleration and acceleration PSD are obtained. It is found that when random excitation increases, the probability of –g increases and the frequency corresponding to peak of acceleration PSD declines. It indicates that the loss of contact causes the decline of the central frequency.

#### Keywords

piecewise linear; loss of contact; random vibration; FPK equation; central frequencyText

DOI

10.12783/iapri2018/24371

10.12783/iapri2018/24371

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