Propagation And Attenuation Of Stress Waves In Heterogeneous Viscoelastic Rods

The rock mass in nature has viscoelasticity and inhomogeneity,and the attenuation phenomenon will occur when the stress wave propagates in the geological rock mass due to the influence of the internal material properties and structure of the rock mass.With the development of deep mining and tunnel engineering,people pay more attention to the propagation of stress waves in heterogeneous viscoelastic bodies.In this paper,the propagation and attenuation of stress waves in heterogeneous one-dimensional viscoelastic bodies are studied,and the effects of inclusions and viscoelasticity on the propagation of stress waves are analyzed.The main research content is divided into the following three parts:(1)Based on the classical elastic theory and wave theory,the propagation and attenuation of stress waves in an elastic rod with multiple elastic inclusions are studied.The displacement solution of any region in a heterogeneous rod with n inclusions is obtained by using the traveling wave method,and the reflection coefficient,transmission coefficient and attenuation coefficient of the wave passing through the inclusion are obtained.Then the finite element software COMSOL 6.0 is used to calculate the influence of incident wave wavelength and the number of inclusions on stress wave propagation.The results show that the numerical solution is consistent with the theoretical solution;the material parameters,incident wavelength and the number of inclusions will affect the wave attenuation coefficient;the more the number of inclusions,the more obvious the attenuation phenomenon.(2)Based on viscoelastic theory and wave theory,the propagation and attenuation of stress waves in an elastic rod with multiple Kelvin-Voigt viscoelastic inclusions are studied.The displacement solution of stress wave propagation in the rod is obtained by harmonic trial method,and the reflection coefficient,transmission coefficient and attenuation coefficient of viscoelastic inclusion to wave are obtained.The effects of dimensionless factor μ(related to viscosity coefficient η)on reflection coefficient and transmission coefficient and attenuation coefficient are analyzed,and then the effects of inclusion thickness and number on wave propagation are calculated by finite element software COMSOL 6.0.The results show that the numerical solution is consistent with the theoretical solution,the reflection coefficient increases with the increase ofμ;and with the increase of,u,the transmission coefficient first decreases,then increases,and finally decreases;the more the number of inclusions and the greater the thickness,the more obvious the attenuation of stress wave.(3)Based on viscoelastic theory and wave theory,the propagation and attenuation of stress waves in Kelvin-Voigt viscoelastic rod with multiple Kelvin-Voigt viscoelastic inclusions are studied.The propagation of stress wave in semi-infinite viscoelastic rod is analyzed by creep function,and the displacement of stress wave in each region of heterogeneous viscoelastic rod is obtained by harmonic trial method.The finite element software COMSOL 6.0 is used to analyze the propagation of stress waves in heterogeneous viscoelastic rods.The results show that the numerical solution is consistent with the theoretical solution,and the thicker or more the inclusion,the more serious the attenuation of the stress wave.The study of this paper has a certain guiding significance for solving the problem of stress wave propagation in complex rock mass.Stress wave has a broad application prospect in natural exploration and technical development,and the study of wave problems in heterogeneous bodies is of great significance in many engineering fields.Such as the exploration of oil,coal and ore,and the construction of underground structures such as subways and highway tunnels,the propagation,reflection and refraction of stress waves can also be used to study the internal structure of rock mass.