Xuwei Cao

T-bars, as a type of complex-shaped structures, are widely used in various engineering fields. To enable early detection of structural damage, this study proposes a guided wave-based method for locating damage in T-bars. First, the group velocity curves of guided waves in T-bars are calculated using the semi-analytical finite element method, and an appropriate mode is selected for inspection. Since time-domain signals obtained in measurements are often contaminated by interference modes and noise, a novel mode enhancement technique based on the phase coherence of full matrix data is proposed in this study. This method calculates phase-weighted signals to suppress noise and enhance the desired signal components effectively. Furthermore, damage located on the top or either side of the T-bar can be distinguished using two appropriate frequency-mode combinations, although it remains difficult to differentiate between damage at the left and right bottom edges. To address this limitation, a subarray beamforming method is proposed. The acquired signals are divided into left and right subarrays based on the symmetry axis of the T-bar. Each subarray is separately summed and weighted, and the damage location on the left or right edge is determined by comparing the signals from the two subarrays. This method can identify damage locations in structures with geometric symmetry.

The guided waves in the uniform waveguide of rectangular cross-section exhibit complicated propagation and scattering characteristics due to the diversity of vibration modes. This paper focuses on the mode conversion of the lowest Lamé mode at a part-through or through-thickness crack. Firstly, the Floquet periodicity boundary condition is applied to derive the dispersion curves in the rectangular beam, which relates the axial wavenumber to the frequency. On this basis, the frequency domain analysis is conducted to investigate the interaction between the fundamental longitudinal mode in the vicinity of the first Lamé frequency and a part-through or through-thickness vertical or inclined crack. Finally, the nearly perfect transmission frequency is evaluated by extracting displacement and stress harmonic fields throughout the cross-section. It is shown that this frequency originates from the first Lamé frequency, increases with the crack depth, and decreases with the crack width. Between them, the crack depth plays a major role in the frequency variation. In addition, the nearly perfect transmission frequency is negligibly affected by the beam thickness, and such a phenomenon is not observed for inclined cracks. The nearly perfect transmission may have potential applications in the quantitative evaluation of crack size.

A thorough understanding of the scattering mechanism of Lamb waves at discontinuities is of interest for quantitative evaluation of structural properties and mode control. This study extends the generalized scattering matrix method to investigate the interaction of straight crested Lamb waves with multiple cascaded rectangular notches. Based on the orthogonality and completeness of Lamb modes, the mode matching method is utilized to determine the scattering matrices of downward and upward step discontinuities. After that, the generalized scattering matrix method is employed to determine the scattering matrices of a single rectangular notch and the recurrence relations between the scattering matrices of n + 1 cascaded notches and those of n cascaded notches. Finally, the scattering matrices of multiple cascaded notches can be easily obtained taking advantage of the recurrence relations. As the number of cascaded notches increases, more and sharper peaks appear in the scattering coefficient curves. The finite element simulations conducted in the time domain validate the theoretical results for cascaded notches with identical or different depths, which demonstrate that this method can be applied to find the scattering coefficients at piece-wise periodic or nonperiodic waveguides. The generalized scattering matrix method may have potential applications in quantitative nondestructive evaluation and mode control.

The accurate information of Lamb wave packets, such as amplitude, time of flight, and waveform, are essential for damage detection and evaluation. Due to the dispersive, multimodal, and attenuative characteristics of Lamb waves propagating in viscoelastic media, the desired mode component is difficult to be extracted from response signals. To address this issue, a technique based on the viscoelastic propagation model of Lamb waves is proposed in this article. Different from the conventional frequency–wavenumber domain filtering, the proposed technique achieves mode extraction by estimating the parameters of the viscoelastic propagation model, that is, complex amplitude a_m( r, ω) and effective complex wavenumber ξ_m( ω). Benefiting from that, it enables to decompose and reconstruct the desired mode from spatial–temporal measurement data. First, the frequency-dependent effective complex wavenumbers are extracted using the matrix pencil method, where the real parts represent the dispersion and the imaginary parts represent the effective attenuation. After that, the complex amplitudes are obtained by solving linear least-square equations. Finally, the complex amplitude, effective complex wavenumber, and frequency range of the desired mode are picked out to reconstruct the mode component in the time domain. The finite element simulation and experimental results verify the effectiveness of our technique. Furthermore, the performance of the proposed technique in noisy circumstances is analyzed through synthetic signals, which shows a small reconstruction error and a good convergence.

Accurate knowledge of dispersion relations is of vital importance for Lamb wave-based damage detection. In this paper, an experimental technique is proposed to obtain the Lamb waves phase velocity dispersion without prior knowledge of material properties. It requires measurements at only two neighboring positions, and can evaluate phase velocity dispersion over a wide frequency range. In that technique, the short-time chirp-Fourier transform is first applied to the Lamb wave signals to achieve a concentrated time–frequency representation. On this basis, ridge tracking is completed and the group delay (GD) of the interested modes is estimated accurately. Subsequently, the Vold–Kalman filter is introduced to extract these wave modes, and the instantaneous phase is estimated from each individual wave mode via Hilbert transform. Lastly, the phase velocity is obtained as a function of the propagation distance, GD and phase shift. The proposed technique is investigated in two different mediums: simulated signals as Lamb wave propagating in an aluminum plate and experimental signals as that in a carbon fiber-reinforced polymer laminate. The results demonstrate its effectiveness and efficiency.