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A tube-block structure is proposed to realize tunable elastic wave transmission and resonance, consisting of periodically aligned circular tubes sandwiched and joined by two blocks. Finite element simulations for a unit structure are carried out to reveal the frequency dependence of the transmission behavior for the normal incidence of longitudinal and transverse waves in the tube-block structure. As a result, the transmission ratios are found to take multiple local maxima at different peak frequencies. Eigenfrequency analysis shows that the local resonances of the tube and the block surfaces occur at the peak frequencies in the transmission ratios. The peak frequencies originating from the local resonance of the tube depend on its radius and thickness, while those from the resonance on the block surfaces are in good agreement with the theoretical relation between the interval of the periodically aligned tubes and the wavelength of the Rayleigh wave. Furthermore, when the tube-block structure is subjected to compressive loading, the deformation shifts the peak frequencies of the transmission ratio corresponding to the local resonance of the tube. This result implies that the proposed structure has the potential to serve as a tunable meta-interface between solid blocks. [ABSTRACT FROM AUTHOR]

The second-harmonic generation of the fundamental antisymmetric Lamb wave at a closed parallel crack in an elastic plate is studied by numerical analysis. The closed crack is modeled as a spring-type interface with quadratic nonlinearity. Based on a perturbation method, the problem of nonlinear Lamb wave scattering is decomposed into two linearized problems, i.e., for the linear reflection/transmission of the incident Lamb wave at the crack and for the generation/radiation of the second-harmonic Lamb waves due to the contact nonlinearity. The reduced problems are solved by the finite element method in the frequency domain. Numerical results demonstrate significant effects of the crack resonance on the linear and nonlinear Lamb wave scattering responses, which appear as sharp peaks/dips in the reflection/transmission spectra and enhanced second-harmonic amplitudes at some frequencies. Two simple frequency selection rules are established which explain the enhanced generation of the second-harmonic Lamb waves. The time-domain analysis is also carried out to supplement the frequency-domain analysis, which confirms that the incident Lamb wave interacts with the crack at some specific frequencies in its bandwidth in a selective manner and enhances the generation of the second-harmonic components. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The reflection and transmission of Lamb waves at an imperfect joint of plates are analyzed numerically by the modal decomposition method and the hybrid finite element method. The joint is modeled as a spring-type interface characterized by distributed normal and tangential stiffnesses. The analysis is focused on a low-frequency range where the lowest-order symmetric and antisymmetric Lamb waves are the only propagating modes. The frequency-dependent reflection and transmission characteristics of these Lamb modes are computed for different interfacial stiffnesses, together with the generation behavior of localized, non-propagating higher-order Lamb modes. As a result, S0-mode Lamb wave is shown to exhibit the reflection and transmission characteristics which are monotonically frequency-dependent. On the other hand, A0-mode Lamb wave shows complicated and non-monotonic frequency dependence in the reflection and transmission characteristics. The obtained Lamb wave characteristics are discussed in the light of approximate one-dimensional models constructed based on classical plate theories. As a result, the reflection and transmission coefficients of S0-mode Lamb wave are accurately reproduced by a simple model of longitudinal wave in thin plates, while those of A0-mode Lamb wave are well described by the Mindlin plate model of flexural wave. It is also shown that stiffness reduction at the corners of the contacting edges of plates has only minor influence on the reflection and transmission characteristics. [ABSTRACT FROM AUTHOR]

Resonance behavior of an imperfect joint of elastic plates subjected to the incidence of the lowest-order symmetric (S0) Lamb mode is numerically analyzed in the frequency domain by the hybrid finite element method. To this purpose, the reflection and transmission characteristics of the S0 mode are calculated for the frequency range in which the S0 mode is the only symmetric mode that can propagate in the plates. The imperfect joint is modeled as a linear spring-type interface characterized by the normal and tangential stiffnesses. As a result, it is shown that the imperfect joint of plates has two resonance frequencies at which the out-of-plane displacement amplitudes at the joint are remarkably increased. One resonance frequency depends only on the normal stiffness, and the other only on the tangential stiffness. Each resonance frequency coincides with that of a free edge of a plate, and monotonically increases with the corresponding joint stiffness. Furthermore, it is also shown that the reflection and transmission behavior of the S0 mode at the imperfect joint of the plates can be well reproduced by the one-dimensional thin-plate approximation of extensional waves when the frequency is sufficiently small compared to the resonance frequencies.