Generation of Low-Attenuation Lamb Wave Modes in Three-Layer Adhesive Joints

Abstract

In this paper, the attenuation of lamb waves in three-layer adhesive joints, including two elastic plates bonded together by a viscoelastic adhesive layer, is investigated using the global matrix method and then a suitable incidence angle is calculated to generate a low-attenuation lamb wave using an angle beam transducer. The theoretical boundary value problem in adhesive joints with a perfect bond and traction-free boundary conditions on their outer surfaces is solved to find a combination of frequencies and modes with lowest attenuation. A characteristic equation is derived by applying continuity and boundary conditions in adhesive joints using the global matrix method. Phase velocity and attenuation dispersion curves are obtained with numerical solution of this equation by a computer code for a three-layer joint, including an aluminum repair patch bonded to the aircraft aluminum skin by a layer of viscoelastic epoxy adhesive. To validate the numerical solution results, wave structure curves are plotted for a special mode in two different frequencies in the adhesive joint. Also, the transducer incidence angle is calculated in terms of frequency to generate lamb wave modes with low attenuation level using the theoretical method.

Prediction of frequency and spatially dependent attenuation of guided waves propagating in mounted and unmounted A380 parts made up of anisotropic viscoelastic composite laminates

“…Finally, the displacement and stress mode shapes of the laminate can be portrayed along the plate thickness direction through equations ( 8) and (9). For some composite aeronautic laminates that have symmetry in terms of stacking sequence, the solution points ðω,k * ,θÞ in equation ( 19) can be further classified into symmetric and anti-symmetric modes by checking the symmetry condition 42 of the computed displacement and stress mode shapes at the midplane of the whole laminate, as presented in equation (20) ( ½u 3 ,σ 23 ,σ 13 midplane ¼ ½0; 0; 0 symmetric modes ½u 1 ,u 2 ,σ 33 midplane ¼ ½0; 0; 0 anti À symmetric modes (20) With the solved dispersion relation between ω and k * at a specified θ 0 , phase velocity c p is computed from equation (21). If the damping effect is slight, that is, k i ( k r , meanwhile if the structure is quasi-isotropic, group velocity c g can be computed through equation (22), which is an isotropic model.…”

“…The two combinations of damping models are further employed to predict the dispersion curves in the 3D space ðf ,k r ,k i Þ at the fixed propagation angle θ ¼ 90 °as depicted in Figures 22(a) and (b) for HR+BT and KV+BT models, respectively. These modal curves are classified into symmetric and anti-symmetric modes by checking the symmetry conditions of the displacement mode shapes based on equation (20), which are not presented in this paper for the sake of brevity. For a certain combination of damping model, the 3D curves in Figures 22(a) and (b) are projected onto the ðf ,k r Þ plane and the ðf ,k i Þ plane to make a comparison of the two combinations of damping models.…”

“…15,16 The partial wave superposition approach (PWSA) is generally employed to derive the DEs of the single-layer anisotropic viscoelastic plate. 17,18 For the multi-layered system, PWSA is extended to a class of matrix-based methods, for example, transfer matrix method (TMM) 19 and global matrix method (GMM), 20 which are based on the linear 3D elasticity theory and thus become the standard manner to derive the analytical DEs of this system. However, solving these equations is not an easy task and it usually requires Lowe’s dual-variable root-finding method 21 or Zhu-Qian’s 2D Module Ratio Convergence Method (2D MRCM).…”

Application and Challenges of Signal Processing Techniques for Lamb Waves Structural Integrity Evaluation: Part A-Lamb Waves Signals Emitting and Optimization Techniques

“…Degertekin et al [31] added hertzian contacts between the plates and the end of specially designed quartz rods, which guide anti-symmetric modes generated by PZT-5H transducers bonded at their other end. For an angle beam transducer, a low-attenuation Lamb waves mode was generated by setting the incidence angle [32]. Other literatures studied theoretical model of the PWAS-related Lamb waves to identify the single mode emitting frequency, then adopted the post-process technique, such as time reversal, to enhance the mode purity [33,34].…”

Theoretical determination of the criteria for bonding quality characterization inside a multilayer by ultrasonic echo-pulse method

“…Components that have a tangential displacement seem to be more sensitive to this parameter, which is why research has been directed since the nineties towards the study of longitudinal or transverse waves under oblique incidence [2,3,4] and Lamb guided waves when the sheets to be bonded are thin plates [5,6,7,8]. The characterization of the bonding quality by Lamb waves requires a more in-depth study to define the modes most sensitive to the adhesion conditions of the interfaces [9,10]. When two solid media are viscoelastically or rigidly coupled together, the mechanical behavior of the system can be studied by measuring the reflection [11] or transmission [12,13,14] coefficients of a longitudinally or transversely polarized acoustic beam.…”