| At present,the research on elastic waves in cylinder structures mainly includes circumferential waves and axial waves.Many researchers focus on the effects of material parameters and boundary conditions on the elastic wave propagation characteristics,and the displacement and stress distribution of elastic waves in cylinder structures.Based on previous research,this thesis is carried out several typical problems of elastic wave propagation in functionally graded materials(FGM)cylinder structures as follow:Firstly,the circumferential SH waves in several typical single-layer and multi-layer cylinder structures are compared and analyzed.The exact analytical solution of displacement function is obtained by Bessel function for homogeneous material layer,and the asymptotic analytical solution of displacement function is obtained by power series method for functionally graded material layer.Substituting the displacement function solution into the boundary conditions,the dispersion equations of the circumferential SH wave in the cylinder structures are obtained.The energy distribution of the circumferential SH wave in the cylinder structures are discussed.It is founded that the energy of SH wave is concentrated on the outer surface or sub-outer surface of a cylinder structure.circumferential SH surface wave cannot propagate in the cylindrical cavity.Secondly,the axial waves in functionally graded piezoelectric semiconductor materials cylinder shells are studies.Based on the theory of elastic dynamics and piezoelectric semiconductor,the asymptotic solutions of axial wave displacement function,potential function and disturbed carrier concentration function are obtained by power series method.Through numerical examples,the influence of material parameters,steady state carrier concentration and circumferential wave number on the dispersion and attenuation of axial waves were discussed.It is founded that the increase of steady state carrier concentration will decrease the phase velocity and the increase the attenuation.The increase of circumferential wave number will increase the phase velocity and decrease the attenuation.Finally,the cut-off frequencies of longitudinal wave propagating in functionally graded piezoelectric-piezomagnetic materials cylinder shells is investigated analytically.The asymptotic solution of the cut-off frequencies of the longitudinal waves propagating in the functionally graded piezoelectric-piezomagnetic materials(FGPPM)cylinder shell is obtained based the WKB method.If the material is homogeneous we discover the exact analytical solution based the Bessel function can be obtained.A comparison of WKB solution and exact analytical solution proves the accuracy of the WKB method.The influence of material parameter gradient variation and cylinder shell thickness variation on the cut-off frequencies of longitudinal waves were discussed.It is founded that the set of cut-off frequencies of longitudinal wave is a union of two series of approximate arithmetic progression.The gradient variation of material parameters has a significant impact on the cut-off frequencies of longitudinal waves.The cut-off frequencies of longitudinal wave decrease with the increase of cylinder shell thickness.This thesis enriches and improves the research for the elastic wave propagation characteristics in FGM cylinder structures.These conclusions provide a theoretical guidance for ultrasonic nondestructive testing of cylinder structures and the design of surface acoustic wave devices base on cylinder structures. |
