Research On Ultrasonic Guided Wave Characteristics In Unidirectional Composite And Functionally Graded Composite Structures

Composite materials with different functions, such as fiber-reinforced composite, functionally graded material and piezoelectric-piezomagnetic composite, have received considerable research and been widely used in many fields in recent years. The rapid development and application of advanced composites put forward a new challenge to the nondestructive testing technology. Due to the long distance propagation and fast features, the ultrasonic guided wave technique has a good application prospect in the nondestructive detection for composite structures. However, some mechanism and characteristics of guided waves are still not very clear. The effective use of the ultrasonic guided wave technique for such a purpose depends on a profound understanding of the wave propagation in composites.Initial stress is present during the composite manufacturing process, and it is well known that an initial stress state in a body can significantly affect its wave characteristic. Body wave and surface wave considering initial stress have received much research, but the guided wave under initial stress is still very limited. The Legendre polynomial series expansion approach proposed by Lefebvre et al. to solve the wave propagation in multilayered plates is an asymptotic solution method, which can convert the variable coefficient differential equation of the composite structure into a matrix eigenvalue problem. Using this method, the guided wave propagation in various composite structures including the composite plate, hollow cylinder, bar with rectangular cross-section, ring with rectangular cross-section and multilayer hollow cylinder with initial stresses are studiedFirstly, the guided wave propagating in the unidirectional composite plate with initial stress is investigated using the Legendre polynomial approach based on the “Mechanics of Incremental Deformations”. The effects of the initial stresses in different directions on the dispersion curves and on the displacement and stress distributions are illustrated. In the context of the GN generalized thermoelastic theory, the thermoelastic wave propagating in functionally graded plate is investigated. The effects of different gradient fields on the wave characteristics of elastic modes and thermal modes are discussed. The results indicate that initial stress does not affect the wave decomposition for the plate, and it has significant effects on Lamb wave and SH wave, but the influence pattern of the initial stress on them is very different. The thermoelasticity has little effect on the elastic modes in functionally graded plate, and SH wave is not in?uenced by the thermoelasticity. The gradient field has significant effects both on elastic modes and on thermal modes.Secondly, the wave equations of various composite structures including hollow cylinder and cylindrical curved plate and multilayered hollow cylinder with initial stress are derived. The effects of initial stress on the dispersion curves are illustrated using the Legendre polynomial approach. The results indicate that the effect of the compressive stress is usually contrary to that of the stretch stress. The effects of the initial stress on longitudinal modes are different from that on torsional modes, and the latter is very regular. The influence pattern of the radial initial stress is different from that of the axial initial stress. The gradient field also has a significant effect on the guided wave.Thirdly, a double orthogonal polynomial approach is proposed to solve wave propagation in 2D structures due to the Legendre polynomial approach can only deal with the wave propagation in one dimension structures, i.e. structures having a finite dimension in only one direction, such as horizontally infinite flat plates and axially infinite hollow cylinders. The proposed approach is validated by the specific numerical example. The guided waves propagating in the unidirectional composite bar with initial stress and piezoelectric bar are investigated. The effects of anisotropic and initial stress on the guided wave propagation in unidirectional composite bar are illustrated. The dispersion curves of piezoelectric bars with various width to height ratios and different polarization directions are analyzed. The effect of the piezoelectricity on the guided wave is discussed. The results indicate that width to height ratio and initial stress and polarization direction have obvious effects on the guided wave propagation in bar.Finally, the proposed double orthogonal polynomial approach established in the Cartesian coordinate is introduced in the cylindrical coordinate system to investigate the guided waves propagating in the unidirectional composite ring with initial stress and piezoelectric ring and functionally gradient piezoelectric-piezomagnetic ring. The results indicate that width to height ratio and radius to thickness ratio and initial stress all have significant effects on dispersion curves. The displacement distributions of the unidirectional composite ring are symmetric or antisymmetric. The phase velocity decreases with the radius to thickness ratio increasing. The effect of the piezoelectricity on the dispersion curves increases with wavenumber and mode order increasing. For the functionally gradient piezoelectric-piezomagnetic ring, the polarization direction and gradient field both have significant effects on guided wave characteristics, and high frequency waves propagate predominantly around the side with more material having lower wave speed.