Fundamental Torsional Mode Research Articles

Guided torsional wave generation of a linear in-plane shear piezoelectric array in metallic pipes

Cylindrical guided waves based techniques are effective and promising tools for damage detection in long pipes. The essential operations are generation and reception of guided waves in the structures utilizing transducers. A novel in-plane shear (d36 type) PMNT wafer is proposed to generate and receive the guided wave, especially the torsional waves, in metallic pipes. In contrast to the traditional wafer, this wafer will directly introduce in-plane shear deformation when electrical field is conveniently applied through its thickness direction. A single square d36 PMNT wafer is bonded on the surface of the pipe positioned collinearly with its axis, when actuated can predominantly generate torsional (T) waves along the axial direction, circumferential shear horizontal (C-SH) waves along circumferential direction, and other complex cylindrical Lamb-like wave modes along other helical directions simultaneously. While a linear array of finite square size d36 PMNT wafers was equally spaced circumferentially, when actuated simultaneously can nearly uniform axisymmetric torsional waves generate in pipes and non-symmetric wave modes can be suppressed greatly if the number of the d36 PMNT wafer is sufficiently large. This paper first presents the working mechanism of the linear d36 PMNT array from finite element analysis (FEA) by examining the constructive and destructive displacement wavefield phenomena in metallic pipes. Furthermore, since the amplitude of the received fundamental torsional wave signal strongly depends on frequency, a series of experiments are conducted to determine the frequency tuning curve for the torsional wave mode. All results indicate the linear d36 PMNT array has potential for efficiently generating uniform torsional wavefield of the fundamental torsional wave mode, which is more effective in monitoring structural health in metallic pipes.

Ultrasonic guided waves in elliptical annular cylinders.

This paper studies the influence of cross-section ovalness or ellipticity on lower order axisymmetric guided wave modes in thin pipes. The second longitudinal mode L(0,2) and the fundamental torsional mode T(0,1) are studied, as these are of interest to current pipe inspection. The semi-analytical finite element (FE) method is mainly used, with three-dimensional FE simulations for visualization and cross-validation of results. The studies reveal that even a small degree of ovalness can affect mode shapes and velocities. The effect is more pronounced on the L(0,2) mode than on T(0,1) and this may be important for practical inspection applications.

Simulations and Experiments for the Detection of Flow-Assisted Corrosion in Pipes

Flow-accelerated corrosion (FAC) is a phenomenon which causes wall thinning of pipes, fittings, vessels, and other components in the metal based piping systems that carry water or water-steam mixture in power plants and refineries. Currently used nondestructive techniques, such as radiographic testing (RT), ultrasonic testing (UT), and pulsed eddy current (PEC) testing in order to determine the remaining wall thickness, are time consuming and not economical. Hence, in this work, the use of the fundamental torsional mode ultrasonic guided wave to detect FAC was investigated using the finite element method (FEM) simulations and that were validated with experiments. The torsional wave was generated by the magnetostriction principle using surface mounted strips made of magnetostrictive Hyperco (FeCo) material that provided the source for the surface tractions required to generate the ultrasonic guided wave. The transient electric field was provided through a solenoid coil wound over the strips and permanent magnets were employed to provide the bias magnetic field. From this work, it was observed that the pulse-echo method is not suitable for the FAC detection because of the insignificant reflections from FAC defect region that could not be effectively detected. The through-transmission method was found to be more suitable for the FAC detection because the amplitude of transmitted signal decreased with increase in radial depth of FAC in both the simulation and experiment.

Array of Fundamental Torsional Mode EMATs and Experiment in Thick-wall Pipe with Small Diameter

Pipe inspection is an important issue from the perspective of power plant thermal equipment safety. It is difficult to inspect pipe with the conventional non-destructive methods, because of a high temperature and a limited accessibility in the region. The fundamental torsional guided wave is very effective for long range crack of pipe inspection, because of its non-dispersive characteristics. In order to generate non-contact T(0,1) mode, array of fundamental torsional mode electromagnetic acoustic transducers(EMATs) is designed and developed. Using the transducer, T(0,1) mode is generated and detected in the thick-wall pipe with small diameter. By optimizing the element connections of array of EMATs, when the elements are connected in parallel, the generated signal energy not only can be improved, but also other modes can be inhibited. Meanwhile, the frequency response characteristic is tested and the artificial defect along the circumferential direction of the sample pipe is detected. The transducer can achieve identification and accurate location of crack in the circumferential direction of the sample pipe. This proposed method provides a certain foundation for generation and detection T(0,1) mode and non-contact detection of cracks in the pipe.

Classifying and removing monopole mode propagating through drill collar

Understanding characteristics of the acoustic wave propagating through drill collars is important for formation evaluation with logging-while-drilling (LWD) sonic tools. Knowing the frequency-slowness information of different types of the wave propagating through the collar, we can minimize the unwanted wave propagating through the collar by processing and robustly identify formation compressional and shear arrivals. Extensional modes of the steel drill collar are generally dispersive and range from 180 μs/m to 400 μs/m depending on the frequency band. A fundamental torsional mode of the drill collar is nondispersive, but its slowness is sensitive to the geometry of the drill collar. Depending on the geometry and shear modulus of the material, the slowness of the torsional mode can be slower than 330 μs/m. For identifying slowness of the formation arrivals, those different slownesses of the wave propagating through the collar need to be identified separately from those of the wave propagating through formations. Examining various types of the acoustic wave propagating through a drill collar, we determined that the waves can be properly muted by processing for the semblance of waveforms acquired with LWD sonic tools.

Torsional mode magnetostrictive patch transducer array employing a modified planar solenoid array coil for pipe inspection

In recent investigations, the application of the transducers used in plates has been extended to pipe inspection with circumferential arrays because of the similar particle displacement patterns of some modes between plate and pipe, such as SH and torsional modes. Motivated by the configuration of magnetostrictive patch transducer (MPT), in which a planar solenoid array (PSA) coil was adopted to generate SH waves in plates, we proposed a MPTs array employing a modified planar solenoid array (MPSA) coil, i.e. MPSA coil-MPTs array, for generating and receiving the torsional mode in pipes. The configuration of the MPSA coil modified from PSA coil is suitable to be arranged on the pipe surface and can generate high-power waves. In the suggested configuration of MPT, because the direction of the actuating dynamic magnetic field produced by the MPSA coil is orthogonal to the direction of the static magnetic field produced by the permanent magnets in the magnetostrictive patch, the shear deformation induced by the magnetostriction in the patch will be delivered to the pipe, thus generating the torsional mode. First, it was experimentally verified that the fundamental torsional mode, T(0,1), could be effectively generated and received in pipes with the developed MPSA coil-MPTs array. Then, we studied the relationship between the frequency response characteristic of the developed MPSA coil-MPTs array and the interval defined by the distance of adjacent solenoids in the MPSA coil. Simultaneously, the circumferential crack defects in pipe were successfully identified. Finally, the performance of the MPSA coil-MPTs array was compared with that of previous meander coil-MPTs array. The comparison results demonstrated that the developed MPSA coil-MPTs array could enhance the power of the torsional mode.

Vortex-Induced Vibrations on Cross Sections in Tandem Arrangement

The progressive increase in the construction of long-span bridges in recent years has led to an increasingly detailed study of the aeroelastic effects observed for structural components such as decks, towers and cables. The greater flexibility due to larger spans and optimized cross sections result in critical wind speeds below the design wind speed and would have therefore a certain probability of occurrence during the service life. Such critical wind speeds should be increased by introducing some modification on the cross section geometry.Cables for suspension and cable-stayed bridges are subject to vibrations caused by galloping or gust effects, though these typically occur at high wind speeds. Flutter instability is driven by a fundamental vertical and torsional mode coupling at very high wind speeds. On the contrary, vortex-induced vibrations (VIV) are associated with a single vibration mode and are characteristic of a lower wind speed range. Vortex shedding causes amplitude-limited oscillations, as VIV is not aeroelastic instability. However, it can pose a danger to the structural integrity of the deck or discomfort to users, which would require the temporary bridge closure. Towers of cable-stayed and suspension bridges can also suffer this type of aeroelastic phenomenon.This paper examines the VIV phenomena on towers and decks in tandem configuration by computational fluid dynamic (CFD) methods and experimental wind tunnel tests. This paper specifically discusses the influence of the gap that separates the two main sections and the presence of obstacles, as bracing elements, that affect the fluid–structure interaction and thus their aerodynamic properties. The choice of a proper geometry in the design stage can avoid such low-wind speed vibrations on sections in tandem arrangement.

Mode Conversion and Total Reflection of Torsional Waves for Pipe Inspection

The group velocity of each higher torsional mode in a pipe depends on the wall thickness and it will convert to a lower mode when the thickness is smaller than a critical value, the so-called cut-off thickness. The fundamental torsional mode, T(0,1), and the first higher mode, T(0,2), are generated in pipes by an electromagnetic acoustic transducer (EMAT) and their mode conversion behaviors are investigated by changing the shape of a defect on the pipe. It is confirmed that the conversion behavior is sensitive to the shape of thickness transition and the total reflection of the T(0,2) mode occurs in a pipe with a tapered defect. On the basis of the mode conversion, defects with a cross-sectional loss larger than 35% are detectable.

비틀림 유도파를 이용한 토양 특성 규명 및 지하매설 배관 결함 검출

A technique is presented that uses a circular waveguide for the measurement of the bulk shear (S-wave) velocities of unconsolidated, saturated media, with particular application to near surface soils. The technique requires the measurement of the attenuation characteristics of the fundamental torsional mode that propagate along an embedded pipe, from which the acoustic properties of the surrounding medium are inferred. From the dispersion curve analysis, the feasibility of using fundamental torsional mode which is non-dispersive and have constant attenuation over all frequency range is discussed. The principles behind the technique are discussed and the results of an experimental laboratory validation are presented. The experimental data are best fitted for the different depths of wetted sand and the shear velocities are evaluated as a function of depths. Also the characteristics of the reflected signal from the defects are examined and the reflection coefficients are calculated for identifying the relation between defect sizes and the magnitude of the reflected signal.

Resonant ultrasound spectroscopy of cubes over the full range of Poisson's ratio

Methods are developed for study of isotropic cubes via resonant ultrasound spectroscopy. To that end, mode structure maps are determined for freely vibrating isotropic cubes via finite element method over the full range of Poisson's ratio ν (-1 to +0.5). The fundamental torsional mode has the lowest frequency provided ν is between about -0.31 and +0.5. Experimental measurements for the mode structures of materials with Poisson's ratio +0.33, +0.3, +0.15, -0.15, and -0.72 are performed using resonant ultrasound spectroscopy and interpreted. Methods are developed to identify pertinent modes. The experimental results match well with the analysis with the exception of some splitting of some modes because of slight material anisotropy. The effects of slight imperfection of specimen shape on the first 10 modes are analyzed for various Poisson's ratios.

Probing the Equation of State of Nuclear Matter via Neutron Star Asteroseismology

We general-relativistically calculate the frequency of fundamental torsional oscillations of neutron star crusts, where we focus on the crystalline properties obtained from macroscopic nuclear models in a way that is dependent on the equation of state of nuclear matter. We find that the calculated frequency is sensitive to the density dependence of the symmetry energy, but almost independent of the incompressibility of symmetric nuclear matter. By identifying the lowest-frequency quasiperiodic oscillation in giant flares observed from soft gamma-ray repeaters as the fundamental torsional mode and allowing for the dependence of the calculated frequency on stellar models, we provide a lower limit of the density derivative of the symmetry energy as L≃50 MeV.

On the scattering of torsional elastic waves from axisymmetric defects in coated pipes

Long range ultrasonic testing is now a well established method for examining in-service degradation in pipelines. In order to protect pipelines from the surrounding environment it is common for viscoelastic coatings to be applied to the outer surface. These coatings are, however, known to impact on the ability of long range ultrasonic techniques to locate degradation, or defects, within a coated pipe. The coating dissipates sound energy travelling along the pipe, attenuating both the incident and reflected signals making responses from defects difficult to detect. This article aims to investigate the influence of a viscoelastic coating on the ability of long range ultrasonic testing to detect a defect in an axisymmetric pipe. The article focuses on understanding the behaviour of the fundamental torsional mode and quantifying the effect of bitumen coatings on reflection coefficients generated by axisymmetric defects. Reflection coefficients are measured experimentally for coated and uncoated pipes and compared to theoretical predictions generated using numerical mode matching and a hybrid finite element technique. Good agreement between prediction and measurement is observed for uncoated pipes, and it is shown that the theoretical methods presented here are fast and efficient making them suitable for studying long pipe runs. However, when studying coated pipes agreement between theory and prediction is observed to be poor for predictions based on those bulk acoustic properties currently reported in the literature for bitumen. Good agreement is observed only after conducting a parametric study to identify more appropriate values for the bulk acoustic properties. Furthermore, the reflection coefficients obtained for the fundamental torsional mode in a coated pipe show that significant sound attenuation is present over relatively short lengths of coating, thus quantifying those problems commonly encountered with the use of long range ultrasonic testing on coated pipes in the field.

The reflection of the fundamental torsional mode from pit clusters in pipes

Localised corrosion is a major problem in the oil and gas industry, and is difficult to detect using conventional inspection methods. This paper studies the reflection coefficient (RC) from pit clusters using the fundamental torsional guided wave. The clusters consist of a random number of pits that have developed randomly in size and depth following certain growth rules. The relationship between maximum pit depth and maximum RC is assessed for a large number clusters. Problematic cases where low maximum RCs are obtained from pit clusters with deep maximum pit depth are investigated in detail. Results show that the majority of such clusters consist of a single small and deep pit, with otherwise shallow attack only; such corrosion morphologies are unlikely to occur in practice. With more realistic pit cluster morphologies, where the pit clusters are part of a larger, wider corrosion attack, fewer cases with deep maximum pit depth result in a low maximum RC. The main findings are validated experimentally.

The effect of complex defect profiles on the reflection of the fundamental torsional mode in pipes

The capacity of guided ultrasonic waves to size real corrosion defects remains challenging due to the complexity of the profiles encountered in practice. In the past many studies on the reflection from defects with relatively simple shapes have been done. The purpose of this work is to analyze the effect of complex defect profiles on the reflection coefficient. A study of the reflection of the fundamental torsional mode T(0, 1) from three dimensional (3D) defects in pipes with different shapes has been carried out. Firstly, flat-bottomed defects with different surface profiles have been analyzed, and then the reflection from 3D defects with varying depth profile has been studied. It is revealed that at a given maximum depth of a finite discontinuity, the peak of the reflection coefficient from a defect is linearly dependent on the circumferential extent of the defect, and is independent of its shape. The influence of the depth profile of a real corrosion defect in the axial and circumferential directions on the reflection coefficient has also been studied. The results from these analyses have been used to propose a practical approach to determine the maximum depth of a complex discontinuity from the reflection coefficient behaviour. This method has been applied to real corrosion patches and validated with experiments.

Resonant ultrasound spectroscopy of cylinders over the full range of Poisson's ratio

Mode structure maps for freely vibrating cylinders over a range of Poisson's ratio, ν, are desirable for the design and interpretation of experiments using resonant ultrasound spectroscopy (RUS). The full range of isotropic ν (-1 to +0.5) is analyzed here using a finite element method to accommodate materials with a negative Poisson's ratio. The fundamental torsional mode has the lowest frequency provided ν is between about -0.24 and +0.5. For any ν, the torsional mode can be identified utilizing the polarization sensitivity of the shear transducers. RUS experimental results for materials with Poisson's ratio +0.3, +0.16, and -0.3 and a previous numerical study for ν = 0.33 are compared with the present analysis. Interpretation of results is easiest if the length∕diameter ratio of the cylinder is close to 1. Slight material anisotropy leads to splitting of the higher modes but not of the fundamental torsion mode.

The scattering of the fundamental torsional mode from axi-symmetric defects with varying depth profile in pipes

Guided ultrasonic waves have been successfully applied to detect defects and corrosion in plates and pipes; however, defect sizing remains challenging due to the complex profiles of the defects encountered in practice. A study of the reflection of the fundamental torsional mode T(0,1) from an axi-symmetric defect with varying depth profile has been carried out via finite element modeling and experimental validation. Defects with gradually varying depth are represented by a series of tapered steps. It is revealed that, for both tapered up- and down-steps, the wave packet is reflected only at the start and end of the steps. The reflections from the start and end of the step have been predicted, and the frequency dependence of the overall reflection from the step has been studied. The study shows that the reflection coefficient varies as a function of the ratio of the average length of the tapered defect to the wavelength due to the interference between the waves reflected from the two ends of the defect. The reflection coefficient maxima decrease as the slope of the taper becomes more gradual, this effect being more pronounced when the ratio of the average defect length to the wavelength increases.

Scattering of the fundamental torsional mode at an axial crack in a pipe

A quantitative study of the interaction of the T(0,1) torsional mode with an axial defect in a pipe is presented. The results are obtained from finite element simulations and experiments. The influence of the crack axial extent, depth, excitation frequency, and pipe circumference on the scattering is examined. It is found that the reflection from a defect consists of a series of the wave pulses with gradually decaying amplitudes. Such behavior is caused by the shear waves diffracting from the crack and then repeatedly interacting with the crack due to circumferential propagation. Time-domain reflection coefficient analysis demonstrates that the trend of the reflection strength for different crack lengths, pipe diameters, and frequencies from a through-thickness crack satisfies a simple normalization. The results show that the reflection coefficient initially increases with the crack length at all frequencies but finally reaches an oscillating regime. Also, at a given frequency and crack length the reflection decreases with the increase in pipe circumference. An additional scattering study of the shear wave SH(0) mode at a part-thickness notch in a plate shows that the reflection coefficient, when plotted against depth of the notch, increases with both frequency and notch depth.

Parametric Instability of a Traveling Plate Partially Supported by a Laterally Moving Elastic Foundation

The parametric excitation of an axially moving plate is examined in an application where a partial foundation moves in the plane of the plate and in a direction orthogonal to the plate’s transport. The stability of the plate’s out-of-plane vibration is of interest in a magnetic tape data storage application where the read/write head is substantially narrower than the tape’s width and is repositioned during track-following maneuvers. In this case, the model’s equation of motion has time-dependent coefficients, and vibration is excited both parametrically and by direct forcing. The parametric instability of out-of-plane vibration is analyzed by using the Floquet theory for finite values of the foundation’s range of motion. For a relatively soft foundation, vibration is excited preferentially at the primary resonance of the plate’s fundamental torsional mode. As the foundation’s stiffness increases, multiple primary and combination resonances occur, and they dominate the plate’s stability; small islands, however, do exist within unstable zones of the frequency-amplitude parameter space for which vibration is marginally stable. The plate’s and foundation’s geometry, the foundation’s stiffness, and the excitation’s amplitude and frequency can be selected in order to reduce undesirable vibration that occurs along the plate’s free edge.

Torsional waveguide sensor system for monitoring the setting and hardening of concrete

A torsional waveguide sensor system that monitors the setting and hardening of early-age cementitious materials during the first twenty-four hours of hydration is presented. The fundamental torsional wave mode is transmitted on the free end of a cylindrical steel rod partially embedded in the concrete and then the reflected signals are received. The method monitors both the reflection from the end of the rod embedded in concrete and the reflection from the location where the waveguide pierces the concrete. The waveguide sensor has the advantage of being able to operate from one side of the specimen, often a necessity for field measurements. The method has previously been shown to be able to monitor the development of the mechanical properties of various mortar mixtures (for example, different water-cement ratios, presence of chemical and mineral admixtures). In this technical note, preliminary results show that the method can be extended to concrete mixtures.

Monitoring the setting times and strength gain of mortar using ultrasonic guided waves

A guided wave approach that characterises the setting and hardening of early age mortar during the first twenty-four hours of hydration is presented. Using a through-transmission system, the method measures the energy leakage of the fundamental torsional wave mode from a cylindrical steel rod to the surrounding mortar. The evolution of the mortar properties are related to the energy leakage or attenuation of the guided wave. The study shows that the technique is useful for monitoring the strength development and the microstructure of varying water-cement ratios (w/c = 0.40, 0.50, and 0.60). In addition, the effects of chemical (accelerant and retardant) and mineral (silica fume and fly ash) admixtures on the guided wave are also presented and discussed. Compressive strength and setting time measurements were performed on the various mortar mixtures. Correlations were developed relating the energy leakage of the guided wave to the compressive strength and the setting times of the mortar.