Research On The Wave Characteristics Of Functionally Graded Waveguides With Rectangular And Sector Cross-sections

As a kind of special nonhomogeneous materials,functionally graded materials(FGM)have a lot of advantages,such as reduceing the residual stress,easing the stress concentration.So FGM have good application prospect in various fields,such as electronics,chemistry,optics,biomedicine,acoustics,nuclear engineering,civil engineering and the like.Reliable methods for non-destructively measuring the material properties and flaws in FGM structures are needed.Ultrasonic technology is a very promising technique for the inspection of FGM.The effective use of ultrasonic for such a purpose depends on a good understanding of wave propagation in FGM.The inhomogeneity of FGM makes it very difficult to analyze wave characteristics of the FGM structures.So far,various numerical methods are mainly used by scholars to solve wave problems.The double orthogonal polynomial series expansion method,an analytic method,is employed in this paper to investigate guided wave propagation in various FGM structures,such as FGM,graded piezoelectric material and graded piezoelectric-magnetic material bars with rectangular cross-sections,FGM and graded piezoelectric cylindrical structures with sector cross-sections,which are detailed as follows:First,the guided wave propagation in FGM,graded piezoelectric material and graded piezoelectric-magnetic material bars with rectangular cross-sections are investigated by using the double Legendre polynomial approach,and the effect of graded index,width to height ratio and polarization on wave characteristics are discussed.The results show that both of them have significant effect on wave characteristics;the symmetry of displacement,electrical potential and magnetic potential has a close relationship with geometry and material distribution;High frequency waves propagate predominantly around the side with the material having the lower wave speed.Investigation results have significant guidance on the design,manufacture and optimization of transducers.Then,guided wave propagation in FGM cylindrical structures with sector cross-sections are studied by introducing the double orthogonoal polynomial series method into the cylindrical coordinate system.Influence factors of the covergence of the double Legendre polynomial approach are analyzed,and the influences of the variation of radius to thickness ratio,angular measure and gradient index on guided wave characteristics are also discussed.Results show that displacement distributions,Poynting vectors are symmetric or antisymmetric with respect to the variable ?,not to the variable r.Investigation results lay the basis for non-destructively test of this kind of structures.Then,guided wave propagation in graded piezoelectric cylindrical structures with sector cross-sections are also studied.And the influences of the variation of radius to thickness ratio,angular measure and gradient index on guided wave characteristics are also discussed.Results show that Poynting vectors mainly distribute in the region with the material having the lower wave speed when the wavenumber is much bigger.Investigation results have significant guidance on the design and optimization of cylindrical transducers.