Sourav Banerjee

Elastic Wave Propagation in Sinusoidally Corrugated Waveguides

The ultrasonic wave propagation in sinusoidally corrugated waveguides is studied in this paper. Periodically corrugated waveguides are gaining popularity in the field of vibration control and for designing structures with desired acoustic band gaps. Currently only numerical method (Boundary Element Method or Finite Element Method) based packages (e.g., PZFlex) are in principle capable of modeling ultrasonic fields in complex structures with rapid change of curvatures at the interfaces and boundaries but no analyses have been reported. However, the packages are very CPU intensive; it requires a huge amount of computation memory and time for its execution. In this paper a new semi-analytical technique called Distributed Point Source Method (DPSM) is used to model the ultrasonic field in sinusoidally corrugated waveguides immersed in water where the interface curvature changes rapidly. DPSM results are compared with analytical solutions. It is found that when a narrow ultrasonic beam hits the corrugation peaks at an angle, the wave propagates in the backward direction in waveguides with high corrugation depth. However, in waveguides with small corrugation the wave propagates in the forward direction. The forward and backward propagation phenomenon is found to be independent of the signal frequency and depends on the degree of corrugation.

An experimental investigation of guided wave propagation in corrugated plates showing stop bands and pass bands

Nonplanar surfaces are often encountered in engineering structures. In aerospace structures, periodically corrugated boundaries are formed by friction-stir-welding. In civil engineering structures, rebars used in reinforced concrete beams and slabs have periodic surface. Periodic structures are also being used to create desired acoustic band gaps. For health monitoring of these structures, a good understanding of the elastic wave propagation through such periodic structures is necessary. Although a number of research papers on the wave propagation in periodic structures are available in the literature, no one experimentally investigated the guided wave propagation through plates with periodic boundaries and compared the experimental results with theoretical predictions as done in this paper. The experimental results clearly show that elastic waves can propagate through the corrugated plate (waveguide) for certain frequencies called “pass bands,” and find it difficult to propagate for some other frequencies called “stop bands.” Stop bands are found to increase with the degree of corrugation. Experimental results are compared with the theoretical predictions, and good matching is observed for plates with small degree of corrugation. Only two parameters—the depth of corrugation and the wavelength of the periodicity—are sufficient for modeling the elastic wave propagation in slightly corrugated plates.

DPSM Modeling for Studying Interaction Between Bounded Ultrasonic Beams and Corrugated Plates with Experimental Verification

Periodically corrugated structures play an important role in the field of vibration control and for designing structures with desired acoustic band gaps. Analytical solutions for corrugated plates are available for well-defined, smooth corrugations, such as sinusoidal corrugations that are not very common in the real world. Often corrugated plates are fabricated by cutting grooves at regular intervals in a flat plate. No analytical solution is available to predict the wave propagation behavior in such a periodically corrugated plate in which the equation of the plate surface changes periodically between a planar flat surface and a nonplanar parabolic groove. This problem is solved here for steady-state case by a newly developed semianalytical technique called distributed point source method (DPSM), and the theoretical predictions are compared with the experimental results generated by reflecting a bounded 2.25 MHz ultrasonic beam by a fabricated corrugated plate. The main difference that is observed in the reflected beam profile from a flat plate and a corrugated plate is that the back- scattering effect is much stronger for the corrugated plate, and the forward reflection is stronger for the flat plate. The energy distribution inside the corrugated plate also shows backward propagation of the ultrasonic energy.

Ultrasonic Field Modeling in Multilayered Fluid Structures Using the Distributed Point Source Method Technique

In the field of nondestructive evaluation (NDE), the newly developed distributed point source method (DPSM) is gradually gaining popularity. DPSM is a semi-analytical technique used to calculate the ultrasonic field (pressure and velocity fields) generated by ultrasonic transducers. This technique is extended in this paper to model the ultrasonic field generated in multilayered nonhomogeneous fluid systems when the ultrasonic transducers are placed on both sides of the layered fluid structure. Two different cases have been analyzed. In the first case, three layers of nonhomogeneous fluids constitute the problem geometry; the higher density fluid is sandwiched between two identical fluid half-spaces. In the second case, four layers of nonhomogeneous fluids have been considered with the fluid density monotonically increasing from the bottom to the top layer. In both cases, analyses have been carried out for two different frequencies of excitation with various orientations of the transducers. As expected, the results show that the ultrasonic field is very sensitive to the fluid properties, the orientation of the fluid layers, and the frequency of excitation. The interaction effect between the transducers is also visible in the computed results. In the pictorial view of the resulting ultrasonic field, the interface between two fluid layers can easily be seen. DOI: 10.1115/1.2164516 Ultrasonic nondestructive evaluation NDE generally has two objectives: to detect defects in structures and to determine the material properties of the structure, without damaging it. Ultrasonic transducers are commonly used to generate ultrasonic waves used in NDE experiments. Transducers are used both as transmitters and receivers. Multilayered fluid systems excited by multiple transducers are modeled in this paper. Multilayered fluid structure is not that uncommon in nature. For example, in the early stage of pregnancy, in the human female body the embryo grows in layered fluid surroundings. The plasma of any cell, suspended in a fluid inside or outside of an animal body, is also an example of a layered fluid system. Human eye lenses also behave almost like layered fluid structures. Elastic properties of biological materials are needed for understanding their interaction with implant materials. Layers of crude oil in sea water, as seen after an oil spill in the ocean, are another example of layered fluid structure. Ultrasonic nondestructive testing can be used to find the acoustical properties and thickness of different fluid layers in a multilayered fluid structure. With these applications in mind, an efficient semi-analytical tool has been developed in this paper to model the ultrasonic field in multilayered fluid structures. The method is based on the DPSM distributed point source method technique originally developed to model ultrasonic or eddy current fields, i.e., pressure and velocity fields or magnetic fields generated by ultrasonic or eddy current transducers. DPSM technique for ultrasonic field modeling was first developed by Placko and Kundu 1. They used this technique to model ultrasonic fields

Pipe Wall Damage Detection in Buried Pipes Using Guided Waves

It is well known that cylindrical guided waves are very efficient for detecting pipe wall defects when pipes are open in the air. In this paper it is investigated how efficient the guided waves are for detecting pipe wall damage when the pipes are embedded in the soil. For this purpose guided waves were propagated through pipes that were buried in the soil by placing transmitters on one end of the embedded pipe and receivers on the other end. Received signals for both defect-free and defective pipes were recorded. Then the received signals were subjected to wavelet transforms. To investigate whether embedding the pipe in the soil makes it more difficult to detect the pipe wall defects, the same set of defective and defect-free pipes were studied before and after burying them in the soil. In both cases the defective pipes could be easily identified. Interestingly, contrary to the intuition, it was observed that under certain conditions defective pipes could be identified more easily in buried conditions. For example, the difference between the strengths of the initial parts of the received signal from defect-free and dented pipes was found to be greater for the buried pipes. Some qualitative justification for easier detection of buried dented pipes is provided.

Prediction of Progressive Damage State at the Hot Spots Using Statistical Estimation

The conventional prediction of fatigue crack growth relies on a priori data set and hence, a calibration procedure is required. However, the occurrence of damage and the prediction of damage growth in real time are very unpredictable. Several factors inherently influence the wave signal and make it difficult for the user to interpret the data through direct comparison. To minimize this error in damage estimation, a statistical approach would be the best available solution. A model which can explicitly represent the a priori data set and can also estimate the output parameter (such as damage quantity) from the current data set is extremely important. Simultaneously, there should be a minimum power consumption for the proposed algorithm. Hence, in this effort a two-step analysis is adopted. First, the signal features are extracted using newly proposed discrete time energy model and then Gaussian mixture model (GMM) is used as a classification modeling technique to estimate and quantify the progressive damage. In this article, the effort is not limited to estimating the damage growth but extended to generate an ‘early alarm system’. The early alarm system is achieved by the damage occurrence identification and damage extent which can be calculated using the Mahalanobis distance. GMM is frequently used in the field of computer science for pattern recognition and classification. This would be the first attempt towards implementing such models for hot spot monitoring problems.

Elastic Wave Field Computation in Multilayered Nonplanar Solid Structures: A Mesh-Free Semianalytical Approach

Multilayered solid structures made of isotropic, transversely isotropic, or general anisotropic materials are frequently used in aerospace, mechanical, and civil structures. Ultrasonic fields developed in such structures by finite size transducers simulating actual experiments in laboratories or in the field have not been rigorously studied. Several attempts to compute the ultrasonic field inside solid media have been made based on approximate paraxial methods like the classical ray tracing and multi-Gaussian beam models. These approximate methods have several limitations. A new semianalytical method is adopted in this article to model elastic wave field in multilayered solid structures with planar or nonplanar interfaces generated by finite size transducers. A general formulation good for both isotropic and anisotropic solids is presented in this article. A variety of conditions have been incorporated in the formulation including irregularities at the interfaces. The method presented here requires frequency domain displacement and stress Greens functions. Due to the presence of different materials in the problem geometry various elastodynamic Greens functions for different materials are used in the formulation. Expressions of displacement and stress Greens functions for isotropic and anisotropic solids as well as for the fluid media are presented. Computed results are verified by checking the stress and displacement continuity conditions across the interface of two different solids of a bimetal plate and investigating if the results for a corrugated plate with very small corrugation match with the flat plate results.

On sequencing the feature extraction techniques for online damage characterization

The current state of the health-monitoring technology lacks a generalized and definitive approach to the identification and localization of mechanical damage in structural materials. In past decades, several signal-processing tools have been used for solving different health-monitoring problems but the commutability of the tools between different problems has been restricted. The fundamental reasons for this shortcoming have never been investigated in detail. A thorough study is presented in this article employing almost all promising feature extraction tools on a representative problem—a plate with rivet holes. The cracks around rivet holes in a joint panel of a steel truss bridge are very difficult to detect. Although well established, Lamb wave–based nondestructive evaluation techniques are revisited and new tools are developed to address this issue. The simulation of scattered ultrasonic wave field is carried out using the finite element method. This ultrasonic wave field is further analyzed to evaluate the integrity of the structure using various feature extraction techniques. The joint time–frequency–energy representation is obtained from ultrasonic signals recorded at various locations on the plate (joint panel) and used to extract damage-sensitive features. Those features were then used to formulate a new damage parameter for better visualization of the crack. The results are shown to demonstrate the comparative effectiveness of these techniques. It is concluded that any particular feature extraction technique cannot detect all possible sizes and orientations of the crack. It is suggested that the statistical occurrence and pattern of the crack must be visualized through few selective feature extraction techniques in a sequence.

Scattering of Ultrasonic Waves by Internal Anomalies in Plates

Real-time nondestructive testing (NDT) and nondestructive evaluation (NDE) of plate-type structures are important for structural health monitoring (SHM) applications. In this work, the wave scattering from horizontally oriented internal cavities or cracks in a plate is studied using the distributed point source method (DPSM). DPSM has gained popularity in the last few years in the field of ultrasonic field modeling. DPSM is a semianalytical technique that can be used to calculate the ultrasonic field (pressure, velocity, and displacement fields in a fluid, or stress and displacement fields in a solid) generated by ultrasonic transducers. So far, the technique has been used to model the ultrasonic field near a fluid-solid interface when a solid half-space is immersed in a fluid. This method has also been used to model the ultrasonic field generated in a homogeneous isotropic solid plate immersed in a fluid. The objective of this study is to present the theoretical modeling of the diffraction and scattering pattern of guided waves in the solid plate when transducers of finite dimension are used to generate guided waves in the defective plate.

Estimation of Intrinsic Damage State in Materials using Non-local Perturbation: Application to Active Health Monitoring

Quantifying damage parameters from macroscale wave signals has gained enormous popularity in recent years in the field of structural health monitoring (SHM). However, suitable parametric variation which manifests such lower scale effect to predict incubation of damage is an intricate subject. Hence, a relatively simpler way of quantifying the damage state is discussed in this article. An effort has been made to preset the dispersive solution of Cristoffel equation using non-local formulation. The solution of non-local Cristoffel equation is presented for isotropic (iron crystal—metal) and anisotropic material (cubic crystal—gallium arsenide—semiconductor). Conventional solution of Cristoffel equation is non-dispersive, but this study shows that the wave modes such as quasi-longitudinal, quasi-shear wave speeds are dispersive when non-local theory is employed. However, velocity directions are not perturbed from the non-local Cristoffel equation. Non-local parameters can be used as a migratory parameter for elastodynamic analysis at the macroscale considering the intrinsic length scale effect. The variations of wave velocities (phase velocities) in frequency domain are also presented under the influence of non-local parameter. This study has two implications in the SHM field. The dispersive nature of waves in a periodic crystal structure can be obtained from a MD study of the undamaged condition. Hence, a suitable value of the non-local parameter can be found and can be used as an input parameter in the derived equation in this article. On the other hand, the experimental study on wave velocity can be used to estimate the suitable non-local parameter as a damage parameter which carries the property of damaged crystals. In this article, the later approach has been adopted to study using COMSOL multiphysics software. Three different types of damages are considered inside the materials mentioned above. The effect on wave velocity is found and from the reverse analysis, non-local parameter is determined.