C. V. Krishnamurthy

Genetic algorithm based reconstruction of the elastic moduli of orthotropic plates using an ultrasonic guided wave single-transmitter-multiple-receiver SHM array

The reconstruction of all nine unknown elastic moduli of orthotropic plate structures has been achieved using a single-transmitter-multiple-receiver (STMR) compact structural health monitoring (SHM) array. This method uses the velocity measurement of the fundamental guided Lamb wave modes (S0 and A0), generated from a central transmitter, and received by a sparse array of receivers that encircle the transmitter. The measured velocities are then used in an inversion algorithm based on genetic algorithms. A prototype compact STMR array was developed and used in the measurement. Simulated data were used to demonstrate the feasibility of the technique. Experiments were conducted on 3.15 mm graphite–epoxy composite plate using a PZT based STMR array as well as laser vibrometer based displacement measurement. Experimental Lamb wave velocity data were used to validate the present technique. This technique finds application in the areas of material characterization and SHM of anisotropic plate-like structures used in aerospace and automobile components made using fiber reinforced composites.

Patch Element Model for the Evaluation of Displacement Fields Within an Elastic Solid from a Non‐Contact Immersion Transducer: Application to the 2004 Ultrasonic Benchmark Problem

The ultrasonic benchmark problem requires models to predict, given a reference pulse waveform, the pulse echo response of cylindrical voids of various radii located in an elastic solid for various incidence angles of a transducer immersed in water. We present a conceptually simple yet reliable numerical technique to determine these internal fields in any region of interest within the elastic solid for the specified angles made by the transducer in water. The technique, equivalent to evaluating the Rayleigh‐Sommerfeld integral but through a computationally less demanding procedure, regards the transducer as made of elemental rectangular/square patches and uses the well‐known expression for the radiation pattern of an elemental patch to obtain the total transducer radiation field. A ray‐based method is adopted to propagate the elementary radiation field across a fluid‐solid interface. The FBH is treated in terms of explicit patch element reflectors, its response is evaluated and validated with measurements....

The 2004 Ultrasonic Benchmark Problem — SDH Response Under Oblique Incidence: Measurements and Patch Element Model Calculations

The 2004 ultrasonic benchmark problem requires models to predict, given a reference pulse waveform, the pulse echo response of cylindrical voids of various radii located in an elastic solid for various incidence angles of a transducer immersed in water. We present the results of calculations based on the patch element model, recently developed at CNDE, to determine the response of an SDH in aluminum for specific oblique incidence angles. Patch element model calculations for a scan across the SDH, involving a range of oblique incidence angles, are also presented. Measured pulse‐echo scans involving the SDH response under oblique incidence conditions are reported. In addition, through transmission measurements involving a pinducer as a receiver and an immersion planar probe as a transmitter under oblique incidence conditions are also reported in a defect‐free Aluminum block. These pinducer‐based measurements on a defect‐free block are utilised to characterize the fields at the chosen depth. Comparisons are ...

Structural Health Monitoring of Composite Structures Using Guided Lamb Waves

Structural Health Monitoring (SHM) of aircrafts is of great relevance in the present age aircraft industry. The present study demonstrates three techniques that have the potential for the SHM of multi-layered composite structures. The first technique is based on multi-transmitter-multireceiver (MTMR) technique with tomographic methods used for data reconstruction. In the MTMR, the possibility of SHM using algebraic reconstruction techniques (ART) for tomographic imaging with Lamb wave data measured in realistic materials is examined. Defects (through holes and low velocity impact delaminations) were synthetic and have been chosen to simulate impact damage in composite plates. The second technique is a single-transmitter-multi-receiver (STMR) technique that is more compact and uses reconstruction techniques that are analogous to synthetic aperture techniques. The reconstruction algorithm uses summation of the phase shifted signals to image the location of defects, portions of the plate edges, and any reflectors from inherent structural features of the component. The third technique involves a linear array of sensors across a stiffener for the detection of disbanded regions.

SHM OF ORTHOTROPIC PLATES THROUGH AN ULTRASONIC GUIDED WAVE STMR ARRAY PATCH

The Single Transmitter Multiple Receiver (STMR) array based Structural health monitoring (SHM) technique has been introduced for evaluation of isotropic and anisotropic plate like structures. SHM is carried out by utilizing a phased addition reconstruction algorithm for imaging damage in large plate‐like structures. A flexible Printed Circuit Board (PCB) based patch was developed for SHM of aluminum and composite plates. Additionally, an elastic moduli reconstruction algorithm is described here, using the PCB array patch, which can be applied in at least two cases; (a) for SHM applications, the leave‐in‐place compact array can provide a means for the in‐situ measurement of changes in the elastic moduli during the life time monitoring of structures, thereby providing velocity data for the phased addition reconstruction algorithm, and (b) for materials characterization, where the compact array can be developed as a portable sensor for the measurement of elastic moduli of in‐service and as‐fabricated structu...

Material Symmetries from Ultrasonic Velocity Measurements: A Genetic Algorithm Based Blind Inversion Method

The determination of material symmetries and principle plane orientations of anisotropic plates, whose planes of symmetries are not known apriori, were calculated using a Genetic Algorithm (GA) based blind inversion method. The ultrasonic phase velocity profiles were used as input data to the inversion. The assumption of a general anisotropy was imposed during the start of each blind inversion. The multi‐parameter solution space of the Genetic Algorithm was exploited to identify the “statistically significant” solution sets of elastic moduli in the geometric coordinate system of the plate, by thresholding the coefficients‐of‐variation (Cv). Using these “statistically significant” elastic moduli, the unknown material symmetry and the principle planes (angles between the geometrical coordinates and the material symmetry coordinates) were evaluated using the method proposed by Cowin and Mehrabadi. This procedure was verified using simulated ultrasonic velocity data sets on material with orthotropic symmetry....

The 2006 Ultrasonic Benchmark Problem — FDTD Simulations in 2D

The 2006 ultrasonic benchmark problem involves pulse‐echo angle beam scanning of a notch located on an inclined planar back surface. The response from a side‐drilled hole is to be used as a reference. The models are to simulate (a) the peak‐to‐peak B‐scan P‐ and SV‐ responses of the slots normalized by the appropriate SDH response and (b) the maximum peak‐to‐peak corner response of the slots (either mode‐converted or not). At CNDE, several simulation tools are being developed to assess/predict UT response for various geometries. The Finite‐Difference‐Time‐Difference (FDTD) scheme is one such simulation tool that has been under development in 1D, 2D and 3D. The FDTD is an explicit time domain tool that can simulate pulse propagation characteristics in acoustic/elastic media. The computational domain is limited by implementing Perfectly Matched Layers (PMLs) at the domain boundaries. We present the results of calculations based on 2D FDTD to determine the response of rectangular shaped surface‐breaking defe...