Study On Properties Of Wave Propagation In The Bar And Plate Based On Peridynamics

It's supposed that studying the wave propagation in the structure for the actual engineering,especially the propagation characteristics of the wave in the bar,as well as aerospace engineering,seismic engineering,structural engineering,have deeper significance and value,and also practical guidance in engineering protection.Based on the basic theory of peridynamics,a new theory of solid mechanics was based on the thought of non-local action,the corresponding stress and strain concepts and continuity assumptions were simplified to study the wave propagation characteristics and laws in medium.This paper has studied the propagation characteristics and law of wave in the bar.Firstly,the development status of the peridynamics theory at home and abroad,the basic theory and numerical algorithm are introduced.By means of the theory of elastic deformation and strain in the material mechanics and elasticity,the micromodulus and critical elongation of the peridynamics' model is derived for basic parameters.In addition,it might use the peridynamics theory to establish the peridynamics of the bar model,and the propagation of one-dimensional stress longitudinal wave was deduced,according to the established mechanical model,and might convert into the corresponding mathematical model,and establish basic motion equations for the propagation of longitudinal wave and perform parameter variable conversion and the numerical calculation,and obtain the relationship between wave velocity ratio and wavelength;obtaining numerical calculation and transformation,which has used classical methods for a comparison,the results showed that the wave speed gradually decreased with the increase of the peridynamic radius during the propagation process,and the energy in it was also attenuated,which was consistent with the laws in classical mechanics and wave theory;it was close to 1,which was consistent with the theoretical analysis given by the corresponding relationship.In addition,the larger the peridynamic radius,the larger the value of the ratio of wavelength to distance between points in the same wave velocity ratio.The motion equation of the traditional finite element method was equivalent to the time about 1 times pitch peridynamic radius equation of motion,and the basic laws were the same.At the last time,the two-dimensional plain plate model is verified and compared respectively.The result of the two methods are compared and analyzed,and the peridynamics' method and the model were further verified about the correctness and validity,the wave speed gradually decreased with the increase of the peridynamic radius during the propagation process,and the energy in it was also attenuated,which was consistent with the laws in classical mechanics and wave theory;it was close to stable value,the final approximation has approached a stable value,and this value was related to the relative position,the relative position of the bond.The extended model has also been verified and analyzed,what was different from the previous model was that within a certain range,the larger the peridynamic radius,the smaller the value of ratio,which could more accurately reflect the effect of the distance between material points on non-local forces,the effect of wave propagation speed and verify the accuracy and the feasibility of the peridynamics' theory.