Reflection and transmission characteristics of Lamb waves at an adhesive lap joint of plates

The reflection and transmission characteristics of Lamb waves at an adhesive single lap joint of plates are examined theoretically by the hybrid finite element method. The adhesive joint is modeled by a linear spring-type interface, which is characterized by normal and tangential stiffnesses. For the incidence of the lowest-order antisymmetric (A0) Lamb mode in a low frequency range, it is shown that the reflection and transmission coefficients of the A0 mode take local maxima and minima at multiple frequencies. This behavior results from the interference of waves originating from the lowest-order antisymmetric guided wave mode in the overlap region. The peak frequencies of the transmission coefficient increase monotonically with increasing tangential stiffness, but are almost invariant with the normal stiffness of the adhesive joint. Furthermore, time-domain numerical simulation using the finite element method is carried out to discuss the theoretical results. As a result, for the A0 mode incidence, the reflection and transmission waveforms of the A0 mode from the lap joint are found to show long-oscillation tails. The spectral analysis for the obtained waveforms shows that these tails are necessary to identify the frequencies at which the reflection and transmission coefficients take local maxima and minima.Naoki Mori and Takayuki Kusaka, "Reflection and transmission characteristics of Lamb waves at an adhesive lap joint of plates", The Journal of the Acoustical Society of America 145, 3075-3085 (2019) https://doi.org/10.1121/1.510909

The number of 44-cycles and the cyclomatic number of a finite simple graph

Let $G$ be a finite connected simple graph with $n$ vertices and $m$ edges. We show that the number of $4$-cycles contained in $G$ is at most $\binom{m-n+1}{2}$ when $G$ is not bipartite. We further provide a short combinatorial proof of the bound $\binom{m-n+2}{2}$ which holds for bipartite graphs.Comment: 16 pages, writings are improved (sections number is changed). References are adde

Harmonic generation at a nonlinear imperfect joint of plates by the S0 Lamb wave incidence

Nonlinear interaction of Lamb waves with an imperfect joint of plates for the incidence of the lowest-order symmetric (S0) Lamb wave is investigated by perturbation analysis and time-domain numerical simulation. The imperfect joint is modeled as a nonlinear spring-type interface, which expresses interfacial stresses as functions of the displacement discontinuities. In the perturbation analysis, under the assumption of weak nonlinearity, the second-harmonic generation at the joint is examined in the frequency domain by the thin-plate approximation using extensional waves. As a result, the amplitude of the second-harmonic extensional wave is shown to be in good agreement with the result of the S0 mode in a low-frequency range. However, it is found that the thin-plate approximation does not reproduce the amplification of the second-harmonic S0 mode, which occurs due to the resonance of the joint. Furthermore, the time-domain analysis is performed by the elastodynamic finite integration technique (EFIT). When the amplitude of the incident wave is relatively large, the fundamental wave and the second harmonic exhibit different behavior from the results by the perturbation analysis. Specifically, if the incident amplitude is increased, the peak frequency of the second-harmonic amplitude becomes low. The transient behavior of the nonlinear interaction is also examined and discussed based on the results for the weak nonlinearity

Effect of interfacial adhesion on the ultrasonic interaction with adhesive joints: A theoretical study using spring-type interfaces

The effect of interfacial properties on the reflection and transmission characteristics of ultrasonic waves at adhesively bonded joints is theoretically investigated. An adhesive joint is modeled as a double-interface model, namely, a homogeneous layer coupled to adherends by two spring-type interfaces with different interfacial stiffnesses. For the normal incidence of a one-dimensional longitudinal wave, theoretical results are obtained and validated by finite element simulation. When the thickness of the adhesive layer is sufficiently small compared to the wavelength, the amplitude reflection and transmission coefficients show monotonic dependence on frequency, which can be explained by the theoretical relation of the double-interface model to a single spring-type interface model. The reflection and transmission behavior is invariant if the values of the two interfacial stiffnesses are interchanged. For a relatively thick adhesive layer, on the other hand, the reflection coefficient shows local minima at multiple frequencies. As one interfacial stiffness decreases, the local minimum frequencies decrease and the local minima increase. If the values of the two interfacial stiffnesses are interchanged, the reflection coefficient remains invariant but the reflection waveform shows different features. The obtained reflection and transmission characteristics are discussed in light of the characterization of the interfacial adhesion.Naoki Mori, Naoki Matsuda, and Takayuki Kusaka, "Effect of interfacial adhesion on the ultrasonic interaction with adhesive joints: A theoretical study using spring-type interfaces", The Journal of the Acoustical Society of America 145, 3541-3550 (2019) https://doi.org/10.1121/1.511185