Study On Propagation Characteristics Of Several Elastic Guided Waves In Functionally Graded Viscoelastic Structures

In recent years,functionally graded materials have been widely used in various fields such as national defense,aerospace,biomedical engineering and so on.The properties of specific parts of functionally graded materials have also been significantly enhanced.To detect new type of materials by using ultrasonic nondestructive testing,the elastic guided waves in functionally graded viscoelastic structures are studied in this paper.The main contents include three parts:First,the propagation characteristics of Lamb wave in functionally graded viscoelastic plate are analyzed by power series method.Based on the basic equations of elastic dynamics,the field control differential equations expressed by displacement function are deduced.The dispersion equation is obtained by combining the boundary conditions.The viscous properties of materials make the dispersion equation into complex transcendental equation.A minimum modulus approximation method is proposed for this equation and the optimization is carried out.The results show that the phase velocity and attenuation of Lamb wave are almost invariable when the material gradient parameters change with the same law,but the wave structure and ellipticity of surface particles change obviously.The phase velocity and attenuation characteristic of Lamb wave are affected by the variation of material parameters.Viscosity is an important factor in wave attenuation.Second,the propagation of Love waves in viscoelastic half space with subsurface damage is studied,with the damage layer considered as a functionally graded viscoelastic film.The field control differential equation is established,and the material parameters of gradient damage layer and the homogeneous viscoelastic half space are in the form of power series and exponent respectively.According to the boundary,continuity and attenuation conditions,the dispersion and attenuation curves of Love waves in viscoelastic half space with sub-surface gradient damage are obtained.The results show that the it does not attenuate when the viscosity is zero.In addition,the phase velocity and the absolute value of imaginary part of Love wave velocity increase with the increase of the elastic parameters of the damage layer.This method proves that it is feasible to consider the damage area of the material as a the functionally graded layer.Final,by extending the viscous characteristics from solid to liquid,the propagation of leaky Lamb waves in an elastic plate covered by viscous liquid with sub-surface gradient damage is investigated.Based on the previous theoretical basis and the assumption of damage layer,the field control differential equation is established,in which the field control equation in viscous liquid layer is expressed by displacement potential function.The numerical example shows that the phase velocity and attenuation of wave propagation are affected by the change of material parameters of the sub-surface damage layer.The viscosity of liquid has only effects on the attenuation characteristics of wave,but not on the phase velocity of wave propagation.The attenuation extreme point of Mode 2 can provide a new idea for non-destructive detection of liquid structures.By studying the propagation characteristics of three kinds of elastic guided waves in functionally graded viscoelastic structures,an effective method to solve the problem of wave propagation in inhomogeneous materials is proposed.It opens up a new method for ultrasonic nondestructive testing of viscoelastic heterogeneous materials and also provides reference and theoretical guidance for the development of SAW devices.