Random Vibration Analysis For Stacked Packaging And Monitoring System For Logistics Environment

Stacked packaging unit is the major form of distribution of products.Due to irregular pavement,stacked packaging can be subjected to random vibration during transportation.The product in the packaging is often damaged due to the excessive acceleration.At the same time,the dynamic contact force between stacked packaging is much larger than static contact force,and the continuous action of dynamic contact force can have fatigue cumulative effect on the packaging.Therefore,the response of acceleration and dynamic contact force is of particular importance to the design of the packaging.In the packaging dynamics,the response of a single package has been deeply studied.However,there are very few results of response of stacked packaging.Research of stacked packaging under random vibration focuses on the response of acceleration in time domain,but less research on the response of acceleration in frequency domain.Therefore,dynamic contact force between stacked packaging has not been systematic studied.To this end,this paper mainly studies the response rule of stacked packaging under random vibration,and studies from the following four aspects:(1)The contact force is non-zero mean non-unit variance when the stacked packaging unit is subjected to random vibration because of static force.PDF(Probability Density Function)of maxima of non-zero mean non-unit variance stationary Gaussian random signal is derived,namely expanded PDF of maxima of random signal.The expanded PDF is controlled by three parameters,spectral width parameter ,mean value and variance .This expanded PDF is applied to the study distribution of the maxima of dynamic contact force.(2)The response of two types of package under random vibration is studied.Firstly,the asymmetrical cubic non-linear random vibration system is studied.The PDF of displacement and PDF of peak of displacement are obtained.When stiffness is symmetrical,the PDF is Gaussian.When stiffness of one side is larger,the PDF of the side is smaller.PDF of peaks is only decided by stiffness of one side.Secondly,jumping phenomenon is considered,and a SDOF(single degree of freedom)non-linear random vibration system with jumping phenomenon is established.PDF of displacement can be obtained by similar steps.The impact to period by jumping phenomenon is analyzed.PDF of maxima of contact force is deduced as a translational Rayleigh distribution.Finally,numerical experiment and random vibration experiment is carried out to verified the PDF of maxima of contact force.(3)Random vibration of stacked packaging is carried out.Two kinds of input are set,namely band-limited white noise and band-limited ASTM D4169 Truck,which have 4 levels respectively.Acceleration PSD(Power Spectral Density)of products,contact force PSD,PDF of level crossing of contact force,PDF of maxima of contact force are obtained.By experimental data fitting,it can be seen that the PDF of force level-crossing is more close to Weibull distribution than Gaussian distribution and Rayleigh distribution.The expanded PDF of maxima has a good fitting with experiment data under low excitation level,while under high excitation level particularly with no fixed constraint,non-Gaussian contact force appears so that the proposed PDF of maxima deviates from the experiment data.The three parameters are obtained respectively under three different impact factors including constraint,acceleration excitation and location of contact surface.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.(4)Since container is sealed in transportation,in order to know the status of product during transport,this paper constructs a monitoring system for logistical containers.A measuring device for dynamic force is designed.Vibration intensity of container(acceleration and spectrum data),temperature,humidity,oxygen and ethylene concentration also can be measured.The system has already been put into use in some trucks and performs quite well.