Research Of Elastic Waves In The Inhomogeneous Medium And Soil Structure

The researches of elastic waves in solid mediums have crucial theoretical significance.The results of these researches help people to understand the properties and geometrical structure of medium more precise all the time.Under the hypothesis of the homogeneous medium,the propagation of elastic waves in single or muti-phase medium have been well studied.However,in some engineering applications,gradient model is more accurate to describe the material in-homogeneity.Therefore,in the problem of elastic waves and dynamic response,the influence of in-homogeneity should be further studied.In this thesis,based on the summary of the basic theories and methods of the propagation of elastic waves in all kinds of mediums,the wave propagation equations in elastic,saturated and unsaturated inhomogeneous mediums have been solved by power series method and special function method.We investigate four problems as follows,circumferential SH waves on cylinder with subsurface damage,Love waves propagation of inhomogeneous layered saturated soil half-space,propagation and scattering of SH wave in the inhomogeneous unsaturated soil with circular cavity,and Lamb waves in functionally graded composite plate with non-integral power function volume fractions.1.We analyze the propagation of circumferential SH waves on cylinder with subsurface damage.The control equations of circumferential SH waves in inhomogeneous elastic medium on cylindrical coordinate system have been deduced.The power series method and special function method are used to solve the equations.Then,we discuss the influences of SH waves propagation properties with inhomogeneous.The results provide the theoretical guidance in nondestructive evaluation for cylinder structure with subsurface damage.2.Based on the Biot theory,the Love waves propagation in inhomogeneous layered saturated soil half-space is analyzed in analogy with the wave propagation in functional graded material.We introduce the graded parameter to illustrate the inhomogeneous of saturated soil.The control equations with variable coefficient are solved by power series method.The effects of graded parameter with Love waves dispersion and attenuation have been researched.3.Based on the constitutive relation of Bishop effective stress theory,we deduce the wave propagation equations of unsaturated soil.The propagation of SH waves in inhomogeneous unsaturated soil with the variety of material parameters as exponential function has been discussed.Using the mirror method and transformation of coordinates method,we investigate the problem of scattering and dynamic stress concentration of SH wave in the inhomogeneous unsaturated soil with circular cavity with different homogeneous and saturability.4.Based on the theory of elastokinetics,the propagation of Lamb waves in functionally graded composite plate with non-integral power function volume fractions has been studied.We establish the differential control equations with variable coefficient.The series solutions of these equations are obtained by substitution method and Taylor series expansion method.Then,we discuss the relationship of dispersion of Lamb waves and inhomogeneous of non-integral power function graded material.The graded properties of Lamb waves dispersion have been researched,and the effectiveness of power series method on non-integral power problems has been verified.In this thesis,we analyze the propagation and scattering of elastic waves in inhomogeneous mediums and soil with difference structure and material properties.The wave equations with variable coefficient are solved by power series method,and the influence of inhomogeneous and saturability to elastic wave propagation is discussed.The results of these problems,enrich the fundamental theories of wave propagation in all kinds of mediums,especially in inhomogeneous and unsaturated soil.Then,we explore the effective methods of these problems and offer the farther theoretical gist of nondestructive evaluation and geophysical prospecting for inhomogeneous medium and unsaturated soil.These results have certain practical application values.