Fundamental Guided Wave Modes Research Articles

Propagation of fundamental Lamb modes along the non-principal axes of strain-stiffened soft compressible plates: A numerical investigation.

This paper numerically investigates the propagation of elastic plate waves along the non-principal directions in a prestretched compressible material described by the Gent model of hyperelasticity. We formulate the elastic tensor and the underlying wave equations in the Lagrangian space by employing the theory of nonlinear elasticity together with the linearized incremental equations. An extension of the Semi-Analytical Finite Element (SAFE) method is discussed for computing the dispersion characteristics of the two fundamental guided wave modes. The predictive capabilities of the numerical framework are established using the previously published data for a weakly nonlinear as well as hyperelastic material models. Using the numerical framework, we then bring out the effects of applied prestretch, orientation of the propagation direction, and material parameters on the dispersion characteristics of the fundamental Lamb modes. A limiting case of the neo-Hookean material model is first considered for elucidating such implicit dependencies, which are further highlighted by considering the strain-stiffening effect captured through the Gent material model. Our results indicate the existence of a threshold prestretch for which the Gent-type material can encounter a snap-through instability; leading to the change in the dispersion characteristics of the fundamental symmetric Lamb mode.

Generation of selective single-mode guided waves by d36 type piezoelectric wafer

In general, mixed modes and dispersion of guided wave occur at any excitation frequency, while single modes are needed for effective nondestructive evaluation of structures. In this work, we present an approach to generate a selective single-mode guided wave in plate-like structures by exploiting the unique directionality of the d36 type piezoelectric wafer and the symmetry of fundamental guided wave modes. Specifically, we devise a unified fundamental shear horizontal (SH0) wave/fundamental antisymmetric mode (A0) wave directional transducer pair by attaching the d36 type piezoelectric wafers back to back on the opposite sides of the plate to provide selective, directional single-mode guided waves for actuation and sensing. Originally, the d36-type piezoelectric wafer, poled and cut from the lead magnesium niobate-lead titanate crystal, produces a mixture of the in-plane SH0 (symmetric) mode and out-of-plane A0 (asymmetric) and S0 (symmetric) modes. By applying the in-phase or out-of-phase applied electrical field to the coupled d36-type piezoelectric wafer pair, our devised approach generates selective single modes, SH0 or A0, respectively, to propagate in the structure. We describe the theoretical development of our approach and conduct both numerical simulations and laboratory experiments for validations.

Elastic Properties Measurement Using Guided Acoustic Waves.

Nondestructive evaluation of elastic properties plays a critical role in condition monitoring of thin structures such as sheets, plates or tubes. Recent research has shown that elastic properties of such structures can be determined with remarkable accuracy by utilizing the dispersive nature of guided acoustic waves propagating in them. However, existing techniques largely require complicated and expensive equipment or involve accurate measurement of an additional quantity, rendering them impractical for industrial use. In this work, we present a new approach that requires only a pair of piezoelectric transducers used to measure the group velocities ratio of fundamental guided wave modes. A numerical model based on the spectral collocation method is used to fit the measured data by solving a bound-constrained nonlinear least squares optimization problem. We verify our approach on both simulated and experimental data and achieve accuracies similar to those reported by other authors. The high accuracy and simple measurement setup of our approach makes it eminently suitable for use in industrial environments.

Optimization and experimental validation of stiff porous phononic plates for widest complete bandgap of mixed fundamental guided wave modes

Abstract Phononic crystal plates (PhPs) have promising application in manipulation of guided waves for design of low-loss acoustic devices and built-in acoustic metamaterial lenses in plate structures. The prominent feature of phononic crystals is the existence of frequency bandgaps over which the waves are stopped, or are resonated and guided within appropriate defects. Therefore, maximized bandgaps of PhPs are desirable to enhance their phononic controllability. Porous PhPs produced through perforation of a uniform background plate, in which the porous interfaces act as strong reflectors of wave energy, are relatively easy to produce. However, the research in optimization of porous PhPs and experimental validation of achieved topologies has been very limited and particularly focused on bandgaps of flexural (asymmetric) wave modes. In this paper, porous PhPs are optimized through an efficient multiobjective genetic algorithm for widest complete bandgap of mixed fundamental guided wave modes (symmetric and asymmetric) and maximized stiffness. The Pareto front of optimization is analyzed and variation of bandgap efficiency with respect to stiffness is presented for various optimized topologies. Selected optimized topologies from the stiff and compliant regimes of Pareto front are manufactured by water-jetting an aluminum plate and their promising bandgap efficiency is experimentally observed. An optimized Pareto topology is also chosen and manufactured by laser cutting a Plexiglas (PMMA) plate, and its performance in self-collimation and focusing of guided waves is verified as compared to calculated dispersion properties.

Vibro-acoustic stimulating ultrasonic guided waves in long bone

Ultrasonic guided wave is sensitive to waveguide microstructure and material property, which has great potential applications in long cortical bone evaluation. Due to the multimodal dispersion effect, low-frequency guided wave is usually used to avoid multimode overlapping and simplify the signal processing. However, the traditional low-frequency ultrasound transducer is usually designed on a large-scale (around several millimeters), leading to relatively low-spatial resolution. In response to such a technique limit, an ultrasound-stimulated vibro-acoustic method is introduced to excite low-frequency ultrasonic guided waves. There are two excitation ways of the ultrasound-stimulated vibro-acoustic method, i.e., a single amplitude-modulated (AM) beam and confocal beam excitation. In the case of the single beam excitation, a high-frequency signal is modulated by using a low-frequency amplitude. In addition, low-frequency vibration can also be produced by a confocal transducer, where two beams are close to the center frequency and focus on a small region. In this way, the frequency difference between two beams can be selected to generate the arbitrary low-frequency excitation in a given bandwidth on the focus point. In this paper, we first introduce the theory of ultrasonic guided wave in the plate and the basic principle of ultrasound-stimulated acoustic emission. Second, the three-dimensional finite element method is used to simulate the phenomena of the low-frequency ultrasonic guided waves excited by the ultrasound-stimulated vibro-acoustic method. Two Gaussian-function enveloped tone-burst signals close to the center frequencies of 5 MHz are used to excite 150 kHz low-frequency guided wave in a 3 mm-thick bone plate. An ex-vivo bovine bone plate is involved in the experiments to test the feasibility of the proposed method. The axial transmission ultrasonic guided waves are recorded at eight different propagation distances. The time-frequency representation method is used to analyze the dispersive guided waves. The results indicate that both the two confocal beams and the single AM beam are capable of stimulating low-frequency ultrasonic guided waves in the bone plate. The first two fundamental guided wave modes, i.e., symmetrical S0 and asymmetrical A0 are observed in the bone plate. Similar spectrum can be obtained in the two different excitation ways. In the simulation and experiment, two wave packets can be separated in the distance-time diagram of the received signals. Good agreement can be found between the results of time-frequency representation and the theoretical group dispersion curves. This study can enhance the spatial resolution of measuring ultrasonic guided wave in long bone, and improve the flexibility of excitation with arbitrary frequency in a given bandwidth. The study can be helpful for developing the new clinical techniques of using low-frequency guided waves for long cortical bone assessment.

Optimum design of phononic crystal perforated plate structures for widest bandgap of fundamental guided wave modes and maximized in-plane stiffness

This paper presents a topology optimization of single material phononic crystal plate (PhP) to be produced by perforation of a uniform background plate. The primary objective of this optimization study is to explore widest exclusive bandgaps of fundamental (first order) symmetric or asymmetric guided wave modes as well as widest complete bandgap of mixed wave modes (symmetric and asymmetric). However, in the case of single material porous phononic crystals the bandgap width essentially depends on the resultant structural integration introduced by achieved unitcell topology. Thinner connections of scattering segments (i.e. lower effective stiffness) generally lead to (i) wider bandgap due to enhanced interfacial reflections, and (ii) lower bandgap frequency range due to lower wave speed. In other words higher relative bandgap width (RBW) is produced by topology with lower effective stiffness. Hence in order to study the bandgap efficiency of PhP unitcell with respect to its structural worthiness, the in-plane stiffness is incorporated in optimization algorithm as an opposing objective to be maximized. Thick and relatively thin Polysilicon PhP unitcells with square symmetry are studied. Non-dominated sorting genetic algorithm NSGA-II is employed for this multi-objective optimization problem and modal band analysis of individual topologies is performed through finite element method. Specialized topology initiation, evaluation and filtering are applied to achieve refined feasible topologies without penalizing the randomness of genetic algorithm (GA) and diversity of search space. Selected Pareto topologies are presented and gradient of RBW and elastic properties in between the two Pareto front extremes are investigated. Chosen intermediate Pareto topology, even not extreme topology with widest bandgap, show superior bandgap efficiency compared with the results reported in other works on widest bandgap topology of asymmetric guided waves, available in the literature. Finally, steady state and transient frequency response of finite thin PhP structures of selected Pareto topologies are studied and validity of obtained bandgaps is confirmed.

Three-Dimensional Scattering of an Incident Plane Shear Horizontal Guided Wave by a Partly through-Thickness Hole in a Plate**Supported by the National Natural Science Foundation of China under Grant Nos 11474195, 11274226, 51478258 and 51405287.

We investigate the three-dimensional (3D) scattering problem of an incident plane shear horizontal wave by a partly through-thickness hole in an isotropic plate, in which the Lamb wave modes are also included due to the mode conversions by the scattering obstacle in the 3D problem. An analytical model is presented such that the wave fields are expanded in all of propagating and evanescent SH modes and Lamb modes, and the scattered far-fields of three fundamental guided wave modes are analyzed numerically for different sizes of the holes and frequencies. The numerical results are verified by comparing with those obtained by using the approximate Poisson/Mindlin plate model for small hole radius and low frequency. It is also found that the scattering patterns are different from those of the S0 wave incidence. Our work is useful for quantitative evaluation of the plate-like structure by ultrasonic guided waves.

The anisotropic propagation of ultrasonic guided waves in composite materials and implications for practical applications

Ultrasonic guided wave propagation in anisotropic attenuative materials like CFRP (carbon fibre reinforced polymer) is much more complicated than in isotropic materials. Propagation phenomena need to be understood and quantified before reliable NDE (Non-destructive Evaluation)/SHM (Structural Health Monitoring) inspection systems can be realized. The propagation characteristics: energy velocity, dispersion, mode coupling, energy focusing factor and attenuation are considered in this paper. Concepts of minimum resolvable distance and sensitivity maps are extended to anisotropic attenuative materials in order to provide the means for comparison of different guided wave modes in composite materials. The paper is intended to serve as a framework for evaluating and comparing different modes and choosing the optimum operating conditions (frequency, sensor layout) for possible NDE/SHM applications on composite materials. Fundamental guided wave modes in the low frequency regime for highly anisotropic CFRP plates are investigated experimentally and theoretically and the implications for NDE/SHM are discussed.

Scattering of S0 Lamb Mode from a Blind Hole in a Plate Using Mindlin/Mindlin Plate Theory

An analytical model of Lamb wave scattering from a circular blind hole in isotropic plates is presented using the Mindlin plate theory for describing in-plane and flexural wave modes simultaneously. The model makes use of the wave function expansion technique and the boundary conditions at the hole edge to evaluate the scattered far fields of three fundamental guided wave modes. Comparisons are made to existing approximate models using Poisson/Kirchhoff theory and Poisson/Mindlin theory and a 3D model using the exact 3D equations. The results reveal that the present model is more consistent with the exact 3D model at higher frequencies than existing approximate models.

Wavlet-Based Active Sensing for Health Monitoring of Plate Structures using Baseline Free Ultrasonic Guided Wave Signals

Abstract A wavelet-based active sensing technique for health monitoring of isotropic thin plate-like structures using baseline-free ultrasonic guided Lamb wave signals is presented. In this technique, a built in clock-like piezoelectric (PZT) wafer array of small footprint comprising of a single transmitter and multi-receivers (STMR) is considered. The recorded signals in absence of defects are compared with a theoretical model first, and the velocity and amplitude dispersion of guided waves are studied in an effort to tune an appropriate guided wave mode. A five cycle Hanning pulse is transmitted, and the pulse-echo data recorded at the receivers is processed using two novel algorithms, namely damage index 1 (DI1) and damage index 2 (DI2), based on wavelet transformation to identify defects in the form of cracks and loose rivet holes, which are located both near and far away from the array. In both cases, damage index (DI) maps are generated for identification of defects in a particular coverage area on demand by considering the reflected fundamental guided wave modes. Simulation studies are also carried out to demonstrate the effectiveness of the proposed sensing technique. The DI maps clearly show higher values of DI at defect locations enabling identification of multiple defects. The DI2 is found to produce better angular resolution of the defect location than the DI1.

FRP 보강판 부착 콘크리트에서 유도초음파 모드 거동에 대한 접착층의 영향

In this study, effects of bonding agent, e.g. epoxy, on the behavior of fundamental guided wave modes propagated in FRP plate bonded on a concrete, are investigated. Global matrix model of multilayered FRP-epoxy-concrete system was constructed to obtain the velocity and attenuation dispersion curves of the fundamental A0 and S0 modes. Two variables, thickness and elastic modulus of epoxy layer, were considered in the dispersion analysis. It was found that both the thickness and the elastic modulus of epoxy layer greatly affect the phase velocity and attenuation of S0 mode while those are negligible for A0 mode. Based on the results, it was concluded that S0 mode is more effective than A0 mode for bonding condition assessment for FRP plate bonded concrete.

Low peak-power laser ultrasonics

Techniques for the successful excitation of guided ultrasonic waves using a low peak-power laser ultrasonic source are discussed and compared with more conventional Q-switched laser sources. The paper considers acoustic propagation in thin plates, in which the frequencies used, typically only the fundamental guided wave modes, are considered. Aspects of excitation and detection geometry are considered along with the physical mechanisms of photo-acoustic generation and the practical issues surrounding available source wavelengths and power outputs. Understanding of the effects of these constraints is critical for the successful application of the technique. Continuous wave excitation and fully arbitrary modulation schemes are compared, and a technique to control the bandwidth of Golay code modulation is introduced. It is shown that earlier work by the authors was capable of guided wave detection at peak-power densities of 104 W cm− 2. Later work has focussed on the use of erbium-doped fibre amplifiers combined with Golay code modulation to improve the recovered signal-to-noise ratio. Two key applications of the techniques are considered: material properties measurements (using inversion of dispersion curve data) and acoustic emission system calibration.

Fundamental guided wave attenuations and sensor location estimation in fluid-filled steel pipes

The sound intensities required to sustain a certain interval between two ultrasonic sensors that are installed outside a steep pipe for structural health monitoring are numerically investigated. Two fundamental guided wave modes, longitudinal and flexural, are considered for the calculation of their attenuations via the concept of parametric density and a sink inside steel pipes, and these attenuations are used for the sound-intensity calculations. The results, attenuations, and sound intensities are useful as a guideline when guided-ultrasonic-wave-based inspection is planned for pipeline maintenance and safety, especially for estimation of the axial location between ultrasonic sensors.

Analytical prediction and experimental measurement for mode conversion and scattering of plate waves at non-symmetric circular blind holes in isotropic plates

A model for guided wave scattering from non-symmetric blind holes in isotropic plates using Poisson and Mindlin plate wave theories for in-plane and flexural wave modes, respectively, is presented. It makes use of the wave function expansion technique and coupling conditions at the defect boundary in order to evaluate the scattered far fields of the three fundamental guided wave modes. The results were compared to other analytical models as well as experimental measurements for mode conversion from S0 to A0. Measurements agreed well with predictions confirming the validity of the model, highlighting at the same time the strong frequency dependence of the scattering and mode conversion behaviour.