Study On Dynamic Responses Properties Of Packaging System Under Different Spectral Excitation

Packaging system is usually a nonlinear system,and there is a jumping phenomenon of packaged product during transportation.More research is needed into the impact of excitation of the resonance region on the responses of packaging system.Respectively,taking single-layer,twolayer and three-layer stacked packaging system for research objects,the sine sweep vibration experiments were carried on packaging system under unconstrained,elastic and fixed constraints conditions.According to the results of sweep vibration experiments set up two types of acceleration random vibration power spectral density(PSD)excitation,which had the same spectrum excitation in the vicinity of the resonance frequencies and the different spectrum excitation in the vicinity of the non-resonance,investigated the influence of the above-mentioned random vibration excitation on the acceleration responses and the dynamic contact force responses of nonlinear packaging system with three kinds of constraints and input vibration intensities.The dynamic contact force responses were merely investigated for single layer packaging system.In random vibration experiments,the acceleration responses of product and dynamic contact force responses of packaged product were collected and compared for three kinds of packaging systems of stacking layers under different constraints and vibration intensities conditions.The acceleration responses included the acceleration response PSDs,the time series of acceleration responses,the probability density function(PDF)of acceleration response,the skewness,kurtosis,mean and standard deviation of acceleration responses.The dynamic contact force responses included the dynamic contact force response PSDs,the PDF of the peak of dynamic contact force response,the mean,standard deviation,the number of mean value crossings,the number of maxima of dynamic contact force,and bandwidth coefficient.Comparing the results of responses under the two types of spectrum excitation: under the same constraint and vibration intensity condition,the acceleration PSDs of product and dynamic contact force PSDs of packaged product were basically consistent around the resonance frequencies.However,when the vibration intensity was higher,the response PSDs had a certain deviation in a small range of the resonance point due to the influence of the damping for single packaging system and bottom product in high order resonance frequency region for two-layer and three-layer stacking packaging system.The time series of acceleration responses and the PDF of acceleration responses almost showed no difference under the different spectral excitation,the mean,standard deviation,skewness and kurtosis were close.There were some differences between the PDF of the peak of dynamic contact force,and the distributions in the spectrum 1 were narrower and higher than that in the spectrum 2,however,the mean,standard deviation,the number of mean value crossings,the number of maxima of dynamic contact force,and bandwidth coefficient were close.Due to the influence of nonlinearity of cushioning materials and jumping of packaged product,the PDF of acceleration responses deviated the Gaussian distribution and the PDF of the peak of dynamic contact force deviated the PDF of the linear peak of dynamic contact force by a Gaussian excitation signal.Excitation of resonance region controls the responses of the whole nonlinear packaging system,and excitation of non-resonance region has little influence on the system response.The product packaging protection design should pay more attention to the resonance area.