Research On Characteristics Of Evanescent Wave In Functionally Graded Plates And Curved Waveguide Structures

Ultrasound guided wave detection technique has been widely used in nondestructive evaluation of various engineering structures due to its rapid,high efficient and sensitive features.In recent years,ultrasonic guided wave detection technique is no longer limited to the location detection of defects in structures,and the detection of shape and size of defects has also attracted much attention.In the waveguides,the boundary and the wave field near the defect and load represent a diverse superposition of guided propagating waves,guided evanescent waves with exponential attenuation and guided evanescent waves with damped attenuation.Investigating guided evanescent waves is necessary to exactly understanding the complicated interactions between guided wave and defects,and is the base of evaluating the shape and size of defects.In the field of elastic wave theory and its application,many aspects such as acoustic wave sensing,structural analysis of resonant devices,involve the solution of dispersion equation in complex wavenumber domain.Dispersion equation relating the wavenumber to the frequency,a transcendental equation,is difficult to obtain the complete spatial dispersion curves,and various iterative methods are often adopted to solve the problem.In this paper,an analytical method based on Legendre orthogonal polynomial series is presented to deal with the complex dispersion characteristics of guided waves.The presented method can transform the complex wave propagation problem into an eigenvalue matrix equation whose eigenvalues are wavenumbers,and can avoid the shortcomings of the iterative methods such as many times of circulation,huge quantity of calculation,lower accuracy.The propagation and evanescent wave characteristics of functionally graded plates,cylindrical and spherical curved structures are calculated by the presented method.The results are compared with those of the existing literatures,and the correctness and effectiveness of the presented method are verified.Firstly,the guided wave characteristics of functionally graded plate,functionally graded piezoelectric plate and functionally graded piezoelectric-piezomagnetic plate are investigated.The effects of different graded fields,piezoelectric properties of materials and electrical boundary conditions on the characteristics of propagating and evanescent wave are illustrated.The displacement and stress distributions are calculated and the characteristics of evanescent wave are analyzed.The results indicate that SH evanescent wave only has purely imaginary wavenumber modes,which attenuates with a exponential shape.Lamb evanescent wave has two kinds of modes,namely purely imaginary wavenumber modes and complex wavenumber modes.Complex modes attenuate with a sinusoidal shape.Specially,some complex modes with very small imaginary part can propagate a very long distance.With the increase of frequency,mode conversion will occur.Evanescent wave will convert into a propagating wave at a certain frequency.In piezoelectric structures,there are some evanescent wave modes with high velocity and very small attenuation at high frequencies.Secondly,the presented method is introduced into the cylindrical coordinate system to study the guided wave characteristics of anisotropic,piezoelectric and functionally graded piezoelectric cylindrical curved plates.The effects of different radius-thickness ratios,graded fields,elastic constants of material and boundary conditions on the characteristics of propagation wave and evanescent wave are illustrated.The results show that the attenuation of evanescent wave in the cylindrical curved plate with a large radius-thickness ratio is faster than that with a small radius-thickness ratio.With the increase of frequency and mode order,the effect of graded field on complex wavenumber branches of circumferential Lamb-like wave is more significant.The elastic constants of material,piezoelectric properties and mechanical and electrical boundary conditions have significant effects on complex dispersion characteristics of guided wave in cylindrical curved plate.Finally,the presented method is introduced into the spherical coordinate system to study the guided wave characteristics of anisotropic,piezoelectric and functionally graded spherical curved plates with different radius-thickness ratios and graded fields.The convergence of the presented method is discussed.The results show that this method has a good convergence.The purely real wavenumber mode is easier to converge than the purely imaginary wavenumber one,and the purely imaginary wavenumber mode is easier to converge than the complex one.For the anisotropic structure,Lamb-like wave and SH wave is coupled,and the dispersion curves become very complicated.The effect of radius-thickness ratio and graded field on dispersion characteristics is similar to that in cylindrical curved plate.