Tone-burst Excitation Research Articles

A Crack Size Quantification Method Using High-Resolution Lamb Waves.

Traditional tone burst excitation cannot attain a high output resolution, due to the time duration. The received signal is much longer than that of excitation during the propagation, which can increase the difficulty of signal processing, and reduce the resolution. Therefore, it is of significant interest to develop a general methodology for crack quantification through the optimal design of the excitation waveform and signal-processing methods. This paper presents a new crack size quantification method based on high-resolution Lamb waves. The linear chirp (L-Chirp) signal and Golay complementary code (GCC) signal are used as Lamb wave excitation signals. After dispersion removal, these excitation waveforms, based on pulse compression, can effectively improve the inspection resolution in plate-like structures. A series of simulations of both healthy plates and plates with different crack sizes are performed by Abaqus CAE, using different excitation waveforms. The first wave package of the S0 mode after pulse compression is chosen to extract the damage features. A multivariate regression model is proposed to correlate the damage features to the crack size. The effectiveness of the proposed crack size quantification method is verified by a comparison with tone burst excitation, and the accuracy of the crack size quantification method is verified by validation experiments.

Self-heating phenomenon of piezoelectric elements excited by a tone-burst electric field

Tone-burst excitation is often used for ultrasonic transducers of specific operation modes or for overcoming transducer overheating problems associated with continuous wave (CW) excitation. In this study, a theoretical model for the self-heating phenomenon of a piezoelectric disc element is established to estimate the temperature rise induced by a tone-burst electric field. An analytical solution for the temperature rise of the piezoelectric element is obtained by using Laplace transform method. Numerical simulations and experimental measurements are performed to investigate the influence of different excitation parameters on the temperature rise. By comparing the experimental results with the simulation results, the temperature-rise difference between tone-burst and CW excitations is quantified, and the validity of the theoretical model is verified. Furthermore, a multiparameter estimation method is proposed for the heat convection coefficient and dielectric properties under high-field operating conditions. These results are useful in both optimization of heat dissipation performance and characterization of high-power ultrasonic transducers.

High-temperature electromechanical loss in piezoelectric langasite and catangasite crystals

Temperature-dependent acoustic loss Q−1 is studied in partially disordered langasite (LGS, La3Ga5SiO14) and ordered catangasite (CTGS, Ca3TaGa3Si2O14) crystals and compared with previously reported CTGS and langatate (LGT, La3Ga5.5Ta0.5O14) data. Two independent techniques, a contactless tone-burst excitation technique and contacting resonant piezoelectric spectroscopy, are used in this study. Contributions to the measured Q−1(T) are determined through fitting to physics-based functions, and the extracted fit parameters, including the activation energies of the processes, are discussed. It is shown that losses in LGS and CTGS are caused by a superposition of several mechanisms, including intrinsic phonon–phonon loss, point-defect relaxations, and conductivity-related relaxations.

Performance of a flexoelectric actuator for lamb wave excitation

A flexoelectric actuator represents a new approach for exciting Lamb waves in plate structures and, thus, can be potentially used for active structural health monitoring systems and microsensors. This paper analytically investigated the performance of a flexoelectric actuator for Lamb wave excitation. The constitutive equation for a thin plate flexoelectric structure was derived using the thermodynamics theory. A significant size effect could be demonstrated by the constitutive equation, which suggests a greatly enhanced curvature excitation performance at a small dimension. The interaction between the ideally bonded flexoelectric actuator with the plate could be simplified into two pairs of pin force and pin moment under the assumption of a weak coupling condition. The strain and the displacement responses to the pin-force and pin-moment pairs were obtained using the integral transform techniques and residue calculus. The pin-moment component mainly yielded an antisymmetric Lamb wave mode, while the pin force was reminiscent of its piezoelectric counterpart. The tuning of either a symmetric or an antisymmetric mode could be achieved by choosing an appropriate excitation frequency. The response under a five-cycle Hanning-window toneburst excitation signal was compared with the finite element analysis results and good agreement between them was found.

The Effect of Piezoelectric Fiber Rosette Configurations on Lamb Wave Direction Detection for Damage Localization

Piezoelectric fiber rosettes respond to the directivity characteristics of Lamb waves, and therefore, are useful in detecting the Lamb wave propagation direction. Considering material damage as a secondary wave source, two piezoelectric fiber rosettes are arranged to measure the scattered wave propagation directions for damage localization. The influences of various rosette configurations, i.e., 45°‐rectangular, 135°‐rectangular, 60°‐delta, and 120°‐delta, on the estimation accuracy of the propagation direction are investigated in this paper. The response of the piezoelectric fiber to the A0 mode Lamb wave under narrowband tone‐burst excitation is theoretically derived. Experimental tests and piezoelectric coupling simulations are performed to obtain the Lamb wave signal of each fiber. The matching pursuit (MP) algorithm is applied to extract the weak damage‐related wave packet by using Hann‐windowed narrowband excitation as an atom. The Lamb wave propagation directions are estimated based on the error function. The accuracies of the directions with 4 types of rosette configurations are compared, and their error sources are discussed. The results show that the accuracy of the 135°‐rectangular configuration is relatively satisfactory, and the errors depend on the size and location of each fiber in the rosette. The proposed damage localization method is validated by experimental tests. The predicted locations are close to the actual damage location. The research results are significant for piezoelectric fiber rosette design and optimization and damage location without wave speed or time‐of‐flight information in complex or irregular structures.

Bayesian in-situ parameter estimation of metallic plates using piezoelectric transducers

Identification of structure parameters is crucial in Structural Health Monitoring (SHM) context for activities such as model validation, damage assessment and signal processing of structure response. In this paper, guided waves generated by piezoelectric transducers are used for in-situ and non-destructive structural parameter estimation based on Bayesian approach. As Bayesian approach needs iterative process, which is computationally expensive, this paper proposes a method in which an analytical model is selected and developed in order to decrease computational time and complexity of modeling. An experimental set-up is implemented to estimate three target elastic and geometrical parameters: Young's modulus, Poisson ratio and thickness of aluminum and steel plates. Experimental and simulated data are combined in a Bayesian framework for parameter identification. A significant accuracy is achieved regarding estimation of target parameters with maximum error of 8, 11 and 17 percent respectively. Moreover, the limitation of analytical model concerning boundary reflections is addressed and managed experimentally. Pulse excitation is selected as it can excite the structure in a wide frequency range contrary to conventional tone burst excitation. The results show that the proposed non-destructive method can be used in service for estimation of material and geometrical properties of structure in industrial applications.

Maxwell stress excitation of wire vibrations at difference and sum frequencies of electric currents in separate circuits.

Oscillating electric currents through a wire under tension can excite transverse vibrational modes of the wire when a perpendicular static magnetic field is present and the frequency of the current is close to the natural frequency of the mode of interest. The excitation of the mode is associated with temporally oscillating Maxwell stresses on the wire, often also known as oscillating Lorentz forces. That excitation process is sometimes demonstrated in educational contexts. The investigation here concerns situations where a temporally oscillating magnetic field generated by oscillating electric currents in a cylindrical coil replaces the imposed perpendicular static magnetic field. The frequencies of the currents in the wire and in the coil are related to the frequency of the oscillating stress. In this experiment, this effect is documented for sum-frequency excitation (with input frequencies in the range of half that of the excited lowest vibrational mode of the wire) and the difference-frequency excitation (with input frequencies an order-of-magnitude larger than the mode frequency). This coupling may be useful when it is desirable to use only high-frequency currents. The experiment uses tone-burst stress excitation and a differential photodiode for detecting transverse low-amplitude wire oscillations. Signal envelopes decayed exponentially after the tone-burst.

Wave propagation analysis of laminated composite shell panels using a frequency domain spectral finite element model

This paper presents a frequency domain spectral finite element model (SFEM) for studying wave propagation in laminated composite shell panels. The SFEM formulation is derived using two different theories: (i) the first order shear deformation theory (FSDT) that takes shear deformation into consideration, and (ii) the classical shell theory (CST) that neglects shear deformation. The spectral approach here is based on the use of fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT). The spectral element uses exact shape functions and a frequency dependent exact dynamic stiffness matrix is obtained relating the nodal displacements to the nodal forces of an element. The formulation is validated by comparing the present results for wavenumber dispersion and natural frequencies with the published results. The present SFEM is then used to perform wavenumber dispersion, phase and group velocities, and wave propagation analyses of laminated composite shell panels. The numerical studies show that the wavenumbers obtained from the SFEM based on the CST are significantly different from those of the FSDT at high frequencies. The CST results for the group velocity and wave propagation response to tone burst excitation show significant deviation from the FSDT results for out-of-plane A0 flexural mode even at relatively low frequencies. The orthotropy ratio and lamination arrangements in a composite shell panel have significant effect on the group velocity as well as the flexural mode wave propagation response.

Spatial waveguide mode separation for acoustic waves in a meta-slab composed of subunits with graded thicknesses

A meta-slab composed of subunits with graded thicknesses is proposed for spatially separating the zeroth- and first-order acoustic waveguide modes according to the generalized Snell's law. The phase velocity for the first-order mode depends on the waveguide thickness, whereas that for the zeroth-order mode does not. This enables the required phase-shift gradients of the meta-slab to be obtained for spatially separating the two waveguide modes. To design the meta-slab, analytic solutions are derived for the transmission coefficients and phase shifts of the incident acoustic waves with the two modes propagating through the subunits. Numerical simulations with transient finite-element analyses are implemented to demonstrate the propagation of the two waveguide modes. Sinusoidal signal and tone-burst excitations are applied in the analyses. The latter case shows that the two waveguide modes can be successfully separated in space by the designed meta-slab.

Lamb wave inspection for composite laminates using a combined method of sparse reconstruction and delay-and-sum

A narrowband tone burst excitation is usually required in most Lamb wave inspection techniques in order to reduce the dispersion effect and maintain mode purity, especially in the case that dispersion compensation is hard to implement, such as the scenarios prior knowledge of accurate dispersion curves is not available. The duration of the excitation is relatively large because of its narrow bandwidth, which degrades the resolution for inspection. Following the emerging sparse representation theory, a combined method of sparse reconstruction and delay-and-sum (DAS) for high resolution Lamb wave inspection is proposed in this paper. The scattering signals are compressed in time domain without losing the information of the arrival time of each echo. Unlike most methods that signal decomposition and reconstruction use the same dictionary, the proposed approach utilizes two different dictionaries: one for signal decomposition and another for feature extraction. The DAS imaging method combined with the feature signals is applied to damage imaging for carbon fiber reinforced plastic (CFRP) laminates. The effectiveness of the proposed approach is validated on a quasi-isotropic laminated CFRP plate. The imaging results show that the proposed approach can achieve a higher localization resolution and lower noise floor without degrading the localization accuracy.

Laboratory study of nonlinear propagation of transient signals in a sandstone bar

Experiments are reported on finite-amplitude, impact propagation in a thin bar of Texas moss sandstone. Wideband, unipolar pulses were generated by excitation with a pendulum hammer at one end of the bar, in contrast to prior work with either tone-burst excitation or resonance methods. The bar was rectangular, 8 cm on each side and 175 cm in length, with a density of 2.0 g/cc. Impacts had a center frequency around 3 kHz, amplitude of 10 to 130 microstrain, and propagated repetitively between reflections at each end. Measurements were made with a laser Doppler vibrometer at multiple locations along the bar, while ultrasonic tone-burst probes were used at a central location, transverse to the axis. The sound speed and effective modulus were reduced in proportion to the impact amplitude as the finite-amplitude impact pulse propagated through the transverse and other measurement sites. The attenuation of the impact signal was also found to follow a power law in the frequency range of 1–6 kHz, in proportion to impact intensity. Although amplitude-dependent attenuation and softening of the elastic modulus are both found in micro-inhomogeneous materials, the present results were enhanced, up to an order of magnitude, compared to those in previously reported experiments.

Transport and Electromechanical Properties of Ca3TaGa3Si2O14 Piezoelectric Crystals at Extreme Temperatures

Transport mechanisms in structurally ordered piezoelectric Ca3TaGa3Si2O14 (CTGS) single crystals are studied in the temperature range of 1000-1300 °C by application of the isotope 18O as a tracer and subsequent analysis of diffusion profiles of this isotope using secondary ion mass spectrometry (SIMS). Determined oxygen self-diffusion coefficients enable calculation of oxygen ion contribution to the total conductivity, which is shown to be small. Since very low contributions of the cations have to be expected, the total conductivity must be dominated by electron transport. Ion and electron conductivities are governed by different mechanisms with activation energies (1.9±0.1) eV and (1.2±0.07) eV, respectively. Further, the electromechanical losses are studied as a function of temperature by means of impedance spectroscopy on samples with electrodes and a contactless tone-burst excitation technique. At temperatures above 650 °C the conductivity-related losses are dominant. Finally, the operation of CTGS resonators is demonstrated at cryogenic temperatures and materials piezoelectric strain constants are determined from 4.2 K to room temperature.

Lamb Wave Directional Sensing with Piezoelectric Fiber Rosette in Structure Health Monitoring

Directional piezoelectric sensors can detect the Lamb wave propagation direction to locate damage in structural health monitoring (SHM). The directivity of the round piezoelectric fiber is exploited with a 0°/45°/90° rosette configuration to acquire flexural Lamb wave signals. The directional response of the piezoelectric fiber under narrowband tone‐burst excitation is theoretically deduced. Experimental tests are conducted to demonstrate the directivity and the frequency response property of the piezoelectric fiber under different excitation central frequencies in comparison with the MFC, rectangular piezoelectric sheet, and circular piezoelectric disc. Continuous wavelet transform (CWT) is applied to extract the maximum response amplitude information of the acquired Lamb wave signal at a central frequency. Experimental test results indicate that the piezoelectric fiber is capable to be used as a Lamb wave directional sensor than other piezoelectric sensors. A numerical estimation method for the Lamb wave propagation direction is proposed by defining an error function between the theoretical and experimental normalized response amplitude. The proposed method is generally applicable for different rosette configurations. Experimental results validate the accuracy of the proposed estimation method. The research results are significant to design or select the piezoelectric sensor to measure Lamb wave signals.

Optoacoustic signal excitation with a tone-burst of short pulses

Individual light pulses with durations in the nanosecond range are most often employed in biomedical optoacoustic imaging. In this excitation regime, ultra-wideband acoustic responses are generated from tissues that cannot be efficiently captured with ultrasound transducers having a limited detection bandwidth. Here, we analyse a narrowband optoacoustic signal excitation mechanism consisting of a tone-burst of multiple equally-delayed pulses. The signal generation efficiency of single-pulse versus tone-burst excitation is compared for normal light exposure levels in the linear optoacoustic signal generation regime as well as when considering non-linearities associated with temperature increase or absorption saturation. The signal-to-noise ratio of the excited signals is also experimentally compared using a highly-absorbing ink phantom.

Local Discontinuous Galerkin Methods for the Khokhlov–Zabolotskaya–Kuznetzov Equation

Khokhlov–Zabolotskaya–Kuznetzov (KZK) equation is a model that describes the propagation of the ultrasound beams in the thermoviscous fluid. It contains a nonlocal diffraction term, an absorption term and a nonlinear term. Accurate numerical methods to simulate the KZK equation are important to its broad applications in medical ultrasound simulations. In this paper, we propose a local discontinuous Galerkin method to solve the KZK equation. We prove the $$L^2$$ stability of our scheme and conduct a series of numerical experiments including the focused circular short tone burst excitation and the propagation of unfocused sound beams, which show that our scheme leads to accurate solutions and performs better than the benchmark solutions in the literature.

Focal areas of increased lipid concentration on the coating of microbubbles during short tone-burst ultrasound insonification.

Acoustic behavior of lipid-coated microbubbles has been widely studied, which has led to several numerical microbubble dynamics models that incorporate lipid coating behavior, such as buckling and rupture. In this study we investigated the relationship between microbubble acoustic and lipid coating behavior on a nanosecond scale by using fluorescently labeled lipids. It is hypothesized that a local increased concentration of lipids, appearing as a focal area of increased fluorescence intensity (hot spot) in the fluorescence image, is related to buckling and folding of the lipid layer thereby highly influencing the microbubble acoustic behavior. To test this hypothesis, the lipid microbubble coating was fluorescently labeled. The vibration of the microbubble (n = 177; 2.3–10.3 μm in diameter) upon insonification at an ultrasound frequency of 0.5 or 1 MHz at 25 or 50 kPa acoustic pressure was recorded with the UPMC Cam, an ultra-high-speed fluorescence camera, operated at ~4–5 million frames per second. During short tone-burst excitation, hot spots on the microbubble coating occurred at relative vibration amplitudes > 0.3 irrespective of frequency and acoustic pressure. Around resonance, the majority of the microbubbles formed hot spots. When the microbubble also deflated acoustically, hot spot formation was likely irreversible. Although compression-only behavior (defined as substantially more microbubble compression than expansion) and subharmonic responses were observed in those microbubbles that formed hot spots, both phenomena were also found in microbubbles that did not form hot spots during insonification. In conclusion, this study reveals hot spot formation of the lipid monolayer in the microbubble’s compression phase. However, our experimental results show that there is no direct relationship between hot spot formation of the lipid coating and microbubble acoustic behaviors such as compression-only and the generation of a subharmonic response. Hence, our hypothesis that hot spots are related to acoustic buckling could not be verified.

Higher order acoustoelastic Lamb wave propagation in stressed plates.

Modeling and experiments are used to investigate Lamb wave propagation in the direction perpendicular to an applied stress. Sensitivity, in terms of changes in velocity, for both symmetrical and anti-symmetrical modes was determined. Codes were developed based on analytical expressions for waves in loaded plates and they were used to give wave dispersion curves. The experimental system used a pair of compression wave transducers on variable angle wedges, with set separation, and variable frequency tone burst excitation, on an aluminum plate 0.16 cm thick with uniaxial applied loads. The loads, which were up to 600 με, were measured using strain gages. Model results and experimental data are in good agreement. It was found that the change in Lamb wave velocity, due to the acoustoelastic effect, for the S1 mode exhibits about ten times more sensitive, in terms of velocity change, than the traditional bulk wave measurements, and those performed using the fundamental Lamb modes. The data presented demonstrate the potential for the use of higher order Lamb modes for online industrial stress measurement in plate, and that the higher sensitivity seen offers potential for improved measurement systems.

Experimental study on slow flexural waves around the defect modes in a phononic crystal beam using fiber Bragg gratings

This work experimentally studies influences of the point defect modes on the group velocity of flexural waves in a phononic crystal Timoshenko beam. Using the transfer matrix method with a supercell technique, the band structures and the group velocities around the defect modes are theoretically obtained. Particularly, to demonstrate the existence of the localized defect modes inside the band gaps, a high-sensitivity fiber Bragg grating sensing system is set up and the displacement transmittance is measured. Slow propagation of flexural waves via defect coupling in the phononic crystal beam is then experimentally demonstrated with Hanning windowed tone burst excitations.

Ultrasonic Imaging of a Crack Using Modified Time Reversal

A majority of the research in Structural Health Monitoring focuses on detection of damage. This paper presents a method of imaging crack damage in an isotropic material using the Time Reversal imaging algorithm. Inputs for the algorithm are obtained via computational simulation of the propagation field of a crack in a medium under tone-burst excitation. The approach is similar to existing techniques such as Diffraction Tomography which makes use of the multi-static data matrix constructed using scatter field measurements from the computational simulation. Results indicate excellent reconstruction quality and accurate estimation of damage size.

Analytical extension of Finite Element solution for computing the nonlinear far field of ultrasonic waves scattered by a closed crack

Nonlinear scattering of ultrasonic waves by closed cracks subject to contact acoustic nonlinearity (CAN) is determined using a 2D Finite Element (FE) coupled with an analytical approach. The FE model, which includes unilateral contact with Coulomb friction to account for contact between crack faces, provides the near-field solution for the interaction between in-plane elastic waves and a crack of different orientations. The numerical solution is then analytically extended in the far-field based on a frequency domain near-to-far field transformation technique, yielding directivity patterns for all linear and nonlinear components of the scattered waves. The proposed method is demonstrated by application to two nonlinear acoustic problems in the case of tone-burst excitations: first, the scattering of higher harmonics resulting from the interaction with a closed crack of various orientations, and second, the scattering of the longitudinal wave resulting from the nonlinear interaction between two shear waves and a closed crack. The analysis of the directivity patterns enables us to identify the characteristics of the nonlinear scattering from a closed crack, which provides essential understanding in order to optimize and apply nonlinear acoustic NDT methods.