Study On The Propagation Of Stress Wave In Viscoelastic Medium Based On Laplace Transform

Foam,rubber and other polymers are widely used as the materials that can buffer and reduce noise due to their light weight and high damping properties.These materials will receive hit,collision,etc while in use,so it is very important to obtain their dynamic mechanical properties.In order to obtain those properties,scholars have conducted much research on viscoelastic wave propagation.This paper,based on the stress wave propagation test in viscoelastic medium,studies the stress wave fluctuation in viscoelastic medium,and compares the experiment and theoretical waveform to verify the correctness of the theoretical algorithm.First,this paper introduces several methods from both home and abroad for anal-yzing the propagation of stress waves in viscoelastic media.At the same time,it compares and analyzes the using conditions,application range,and their respective advantages and disadvantages of the methods before describing the mathematical principle and basic theory of Laplace transform and its application in the analysis of stress wave propagation.Then,the experiment of stress wave propag-ation in viscoelastic medium is designed to analyze the impact of different impact speed and different projectile length on the stress waveform.The results show that the length of the projectile affects the wave width of the waveform,which is that the longer the projectile is,the wider the wave is;the peak value of the waveform is related to the impact speed of the projectile,which is that the faster the impact velocity is,the larger the wave peak value is.This finding also provides a basis for the verification of Laplace transform theory in waveform prediction.In order to obtain the constitutive parameters of the material,the room temperature compression creep test is used to obtain the creep curves of the four viscoelastic materials.The creep curve is subjected to nonlinear curve fitting.According to the fitting error,the optimal constitutive model is selected and its results show that the Burgers model has the best description of the creep performance of the four materials.Then,this paper analyzes the influencing factors that affect the Laplace transform method to predict the waveform results and determines the initial conditions,boundary conditions,loading waveforms,constitutive model and constitutive parameters.The researchers used MATLAB to program the Laplace transform theoretical method calculation process,substituted the initial data determined above into the program,and obtained the predicted waveform of stress wave propagation in the viscoelastic medium,also compared with the test waveform to verify the correctness of the Laplace transform method.The analysis results show that the Laplace change method is correct and can accurately describe the stress fluctuations in PC materials,but cannot describe the stress fluctuations of PE,PMMA and PA.Finally,this essay analyzes the level of impact speed and projectile length on the predicted waveform results.The analysis shows that the larger the impact velocity of the projectile is,the larger the peak error of the first waveform is,and the smaller the peak error of the second waveform is.If the projectile is longer,the same result will also happen.