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At least 19 records

Distributed Optical Fiber Sensor Systems: Application to Natural Gas Pipeline Monitoring

Distributed fiber optic sensing is a cutting-edge technology that has found extensive applications in the monitoring of pipelines. Considering the low backscattering level of standard single-mode fiber as fiber under test, a Rayleigh enhanced optical fiber embedded within the tight-buffered cable is demonstrated in field testing. We analyzed the increased backscattering fiber cable's vibration performance to the conventional single-mode telecom fiber using a custom-built Φ-OTDR interrogator system. Thereafter, using a 4-inch steel pipeline with a flow rate of 5, 10, 15, and 20 ft/s and a fixed pressure level of 1000 psi, we field-tested the sensor system for monitoring natural gas pipeline acoustic vibrations. We also field tested Brillouin optical time domain analysis (BOTDA) system for pipeline hoop strain monitoring under various pressure conditions. The pilot-scale testing results presented in this study suggested that pipeline operators can accurately perform flow monitoring, leak detection, and pressure monitoring for pipeline integrity monitoring.

Lalam, Nageswara↗

Use of Machine Learning for Signature Development in a Multi-Sensor Environment for Safeguard Applications of Solvent Extraction Processes

Idaho National Laboratory is constructing the Special Nuclear Material test bed (Beartooth) for research and development pertaining to nuclear fuel processing operations using centrifugal contactors. Beartooth will enable give researchers the opportunity to study the dissolution, separation, and conversion of special nuclear materials (e.g., plutonium, enriched uranium, and thorium). As a lead-in to Beartooth, this project constructed a test bed to study the process and equipment behavior with real time series data collection using a variety of non-traditional sensors, in order to identify process failures and label them as either accidental or purposeful, thus enhancing nuclear nonproliferation stewardship. The measurement sources in this test bed include vibration, acoustic, current, flow, colorimetric, and thermal data. These measurements vary in terms of magnitude, frequency, and location. This information will be combined and used within data-driven machine-learning methods to detect operation condition changes that are either intentional (i.e., changes in operating set points) or malicious (i.e., flow diversion) in nature. This presentation covers the data processing and signature development activities necessary for utilizing this heterogeneous dataset to classify process anomalies.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Status Update on the Development of Transducers and Bonding Techniques for Enabling Acoustic Measurements of Damage in Microreactor Components

This report provides an overview of potential sensors and sensor-bonding techniques to enable the online acoustic interrogation of microreactor components and enhance structural health monitoring capabilities. The report focuses primarily on optical fiber–based acoustic sensors and describes initial experimental progress toward the deployment of these sensors for microreactor applications. The general approach is to monitor the resonant frequencies of microreactor components and search for evidence of structural defects that could indicate imminent failure. If properly identified, then the components could be repaired during the next reactor outage to prevent costly unplanned shutdowns. The ability to monitor the structural health of components could also reduce the need for time-consuming visual inspections and reduce staffing to improve microreactor economic viability. Increased sensor density is also one of the first steps to moving toward eventual semiautonomous operation. The expected microreactor conditions in which acoustic sensors must survive are characterized, including temperatures, neutron fluences, thermomechanical strains, and vibrational frequencies. Optical fiber–based acoustic sensors are identified as an attractive candidate for acoustic monitoring because of their high accuracy, immunity to electromagnetic interference, and resiliency in high-temperature, high-radiation environments. Optical fiber–based intrinsic sensors, such as type-II fiber-Bragg gratings and Fabry-Pérot Cavities (FPCs), are particularly attractive for a microreactor environment because of their high temperature stability, and FPCs also enable higher frequency interrogation with a lower sensitivity to radiation-induced drift. This report describes multiple interrogation systems, but the best interrogation system for a given situation will depend on the specific microreactor application, including the desired acoustic vibrational amplitudes, modes, and resonant frequencies. Initial experiments included fabricating three FPCs, tack-welding these FPCs to stainless-steel pipes or rods and performing room-temperature acoustic sensing tests to capture the vibrational frequency content. Peaks were identified in the measured frequency spectra and compared with the theoretical fundamental frequencies obtained from Euler-Bernoulli beam theory. Two of the three FPCs measured vibrational frequencies that generally matched those obtained from theory. Future work will include similar testing on pipes or other microreactor components with intentional flaws to evaluate the ability to determine changes in resonant frequencies. Finally, these tests will be repeated at high temperatures, potentially with an applied thermomechanical stress, to include environmental conditions similar to those for a microreactor application.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Multichannel deconvolution of vibrational signals: A state-space inverse filtering approach

Deconvolution of noisy measurements, especially when they are multichannel, has always been a challenging problem. The processing techniques developed range from simple Fourier methods to more sophisticated model-based parametric methodologies based on the underlying acoustics of the problem at hand. Methods relying on multichannel mean-squared error processors (Wiener filters) have evolved over long periods from the seminal efforts in seismic processing. However, when more is known about the acoustics, then model-based state-space techniques incorporating the underlying process physics can improve the processing significantly. The problems of interest are the vibrational response of tightly coupled acoustic test objects excited by an out-of-the-ordinary transient, potentially impairing their operational performance. Further, employing a multiple input/multiple output structural model of the test objects under investigation enables the development of an inverse filter by applying subspace identification techniques during initial calibration measurements. Feasibility applications based on a mass transport experiment and test object calibration test demonstrate the ability of the processor to extract the excitations successfully.

42 ENGINEERING↗

Pipeline Monitoring Using Highly Sensitive Vibration Sensor Based on Fiber Ring Cavity Laser

A vibration fiber sensor based on a fiber ring cavity laser and an interferometer based single-mode-multimode-single-mode (SMS) fiber structure is proposed and experimentally demonstrated. The SMS fiber sensor is positioned within the laser cavity, where the ring laser lasing wavelength can be swept to an optimized wavelength using a simple fiber loop design. To obtain a better signal-to-noise ratio, the ring laser lasing wavelength is tuned to the maximum gain region biasing point of the SMS transmission spectrum. A wide range of vibration frequencies from 10 Hz to 400 kHz are experimentally demonstrated. In addition, the proposed highly sensitive vibration sensor system was deployed in a field-test scenario for pipeline acoustic emission monitoring. An SMS fiber sensor is mounted on an 18” diameter pipeline, and vibrations were induced at different locations using a piezoelectric transducer. The proposed method was shown to be capable of real-time pipeline vibration monitoring.

47 OTHER INSTRUMENTATION↗

In-Sodium Testing of a Prototype Thermoacoustic Power Sensor for Sodium-Cooled Fast Reactors

The ultimate goal of this project is to develop and demonstrate a thermoacoustic power sensor (TAPS) for Sodium-Cooled Fast Reactors (SFRs), with potential application also envisioned to other nuclear technologies such as Lead-Cooled Fast Reactors (LFRs), Molten Salt Reactors (MSRs), in addition to Light Water Reactors (LWRs). The project was led by Westinghouse Electric Company, LLC (Westinghouse) and carried out in collaboration with Argonne National Laboratory (ANL) and the University of Pittsburgh. A TAPS is a passive (self-powered), non-invasive (wireless) sensor envisioned for measuring key parameters, such as local temperature and neutron flux, in a nuclear reactor core. The sensor generates pressure waves (i.e., sound waves) with a frequency and amplitude dependent upon nuclear operating conditions (coolant temperature or power changes). The acoustic waves are able to travel through the core and associated structures, and reach to the sensor network placed outside and/or inside of the reactor vessel. These sensors require a very small amount of power which, during loss of power events, can be provided, for example, by harvesting gamma radiation energy, thus resulting in a monitoring system that can function both during normal operation and during loss of power events. Westinghouse and the University of Pittsburgh designed and fabricated TAPS prototypes for Argonne National Laboratory (ANL) to carry out in-sodium testing to evaluate the effects of sodium on the TAPS and the performance of the TAPS technique in sodium. Argonne received a TAPS prototype from Westinghouse, and the prototype was modified such that it can be installed into a test vessel and function in sodium at elevated temperature without potentially leaking. A water mockup test apparatus was constructed to validate proper working of the prototype. An instrumentation and control (I&C) system, running on the National Instruments (NI) LabView platform, was developed to: 1) operate both the water mockup test and the in-sodium test facility; and 2) process and analyze the received acoustic signals from an array of accelerometers and the Argonne sodium-submersible high-temperature acoustic sensor. The prototype was successfully tested in a water bath at different temperatures. Water mockup tests demonstrated that the TAPS prototype is working properly and its resonance frequency changes linearly with the coolant (water) temperature. A TAPS test apparatus was constructed and integrated with the upgraded Under-Sodium Viewing (USV) sodium test facility. The integrated USV-TAPS sodium test facility has been operational. The TAPS prototype and a high-temperature sodium-submersible acoustic sensor (SSAS) developed by Argonne were both installed inside the TAPS test vessel. Being operated within argon cover gas under ambient conditions, the TAPS prototype demonstrated that it was functioning properly with a resonance frequency at 1407.2 Hz, which was successfully detected by the accelerometers mounted on the external wall of the vessel and the high-temperature SSAS installed inside the vessel. After successfully transferring sodium into the vessel, in-sodium tests of the prototype were conducted. Tests of the TAPS prototype demonstrated that the resonance frequency of the TAPS changes linearly with respect to the temperature difference between the interior of the TAPS and bulk sodium. The early tests showed that the TAPS prototype could not establish a continuous and consistent resonance in sodium. The resonance diminished before the prototype reached its operating temperature. A signal postprocessor was added to the DAQ module latterly to isolate interferences, enhance signal conditioning, improve peak detection, and generate resonance frequency versus temperature plots. After testing in molten sodium and immersion at higher temperature for several weeks, the TAPS prototype was able to establish a continuous resonance. Performance evaluation of the TAPS prototype was then conducted in sodium. The tests included the investigation of 1) the effects of the temperature difference between the TAPS and bulk sodium, 2) the effects of sodium flowrate; and 3) the performance of the different sensor-receiver systems positioned inside or outside the vessel. Results of a test demonstrated that, with limited sodium circulation, a continuous and consistent resonance of the TAPS prototype was established occasionally. The tests also demonstrated that, because of the nature of detection principles and mounting methods, the high temperature SSAS is more affected by acoustic noise, while accelerometers are more affected by vibrations, in the test environment. It is unknown why the TAPS prototype only occasionally established a continuous and consistent resonance when the TAPS temperature reached its operating temperature in molten sodium, and why it ultimately failed to resonate at all. A failure modes assessment was conducted and a few potential causes of failure were identified. Different post in-sodium tests were conducted to obtain additional information potentially relevant to the cause of the failure. Nondestructive evaluation techniques are suggested to examine the internal integrity as well as the gas mixture of the prototype. If they prove inconclusive, the prototype should be cut open to conduct a thorough inspection of its internal integrity and determine the state of the gas mixture.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Pilot-Scale Validation of Distributed Optical Fiber Sensors for Underground Pipeline Monitoring

Monitoring parameters such as hoop strain, pressure, and acoustic vibrations is key to detecting potential leaks, intrusions, or structural issues. Distributed optical fiber sensor (DOFS) systems provide a compelling solution for continuous, real-time monitoring over long distances. This paper details the development and pilot-scale implementation of DOFS systems for underground pipeline monitoring, evolving from a proof-of-concept stage. Multiple custom-designed DOFS interrogator units—such as optical frequency-domain reflectometry (OFDR), Brillouin optical time-domain analysis (BOTDA), and multimodal interferometer-based fiber acoustic sensor systems were tested to measure the key parameters, such as hoop strain, pipe pressure, surrounding soil temperature, and acoustic vibrations. The underground product pipeline’s outer diameter is 30 inches, the wall thickness is 1.28 inches, and 3 feet deep from the surface. The fiber deployment strategies and sensing data acquisition methods for these systems are discussed. The results demonstrate the effectiveness of DOFS in detecting hoop strain, temperature changes, and acoustic vibrations, showcasing their potential for real-time monitoring and enhancing pipeline safety. These findings from pilot-scale testing offer valuable insights into advancing pipeline monitoring technologies and improving the reliability of underground pipeline systems.

fiber optic sensors↗

Development Plan for Acoustic Emission and Vibration Sensors

This document discusses the need for high temperature, radiation tolerant sensors for monitoring vibration and acoustic emissions in advanced reactors and irradiation experiments. Testing of several commercial sensors using infrastructure available at Idaho National Laboratory was performed to benchmark currently available sensors as well as the test facilities. Finally, a strategy for developing sensors for more extreme environments is presented.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

TEAMER – Harvesting Subsea Water Motion to Provide Clean Electrical Power (Abstract)

Power generation from vortex induced vibration (VIV) is an emerging field with new technologies that are just beginning to be field tested. In this TEAMER project, WITT Energy will be field testing the power production of its pendulum system in two different configurations to evaluate its performance. The amount of power produced by a VIV instrument depend on the frequency at which it vibrates. The vibrational frequency is controlled by the device shape and its interaction with the flow velocity. Computer models are used to predict vibration frequencies as a function of flow velocity but they may be inaccurate due to complicated bathymetry and bottom roughness that is not captures by the models. This project will test the WITT VIV device in the Sequim Bay channel over a range of tidal velocities. Two tests will be completed with different pipe lengths that are expected to vary the vibrational frequency and therefore the power produced. PNNL will use an acoustic doppler current profiler (ADCP) to monitor the flow conditions during the tests. These tests will help WITT Energy evaluate how closely field operations follow computer model predictions and how best to configure their device for electricity production.

16 TIDAL AND WAVE POWER↗

Non-destructive structural characterization of graphite components using mechanical resonance and deep learning

As compared to conventional nuclear reactors, microreactors have the potential to significantly reduce construction timelines and capital costs, decreasing the barriers for advanced nuclear reactor technologies. However, the lower power output of these microreactors (typically < 20 MWe) creates challenging economics if operation and maintenance costs cannot be sufficiently reduced. The compact size of these designs presents an opportunity for comprehensive in-situ structural health monitoring to provide real-time feedback in order to reduce operational costs associated with maintenance and downtime. Many microreactor concepts use graphite for both in-core neutron moderation and as a structural material, which has typically required some form of periodic and laborious inspection. This report provides a description and assessment of recent work with graphite to couple acoustic-based experimental measurements and characterization with machine learning models to mature structural health monitoring capabilities and generate benefits for the nuclear microreactor industry. With resilient embedded sensors in development in other programs funded by the US Department of Energy’s Office of Nuclear Energy and elsewhere, the work described herein builds upon previously funded efforts to mature non-destructive testing technology that relates measured vibrational signatures to structural changes, using a combination of new experimental measurements and machine learning processing. Building on past successful demonstrations of predictive workflows to identify structural changes in a hexagonal stainless steel test article with excellent acoustic propagation, we first performed baseline characterization on graphite samples with canonical geometries to ensure compatibility and confidence in the applied techniques for a material with distinctly different mechanical properties. In contrast to efforts in previous years, we worked exclusively with unidirectional vibration data that is more comparable to those expected from the existing embedded sensor technologies which are suitable for deployment in a reactor setting. Established acoustic and modern machine-learning-based characterization approaches were applied to the resulting datasets from these simple geometries. Both approaches were found to be highly capable of detecting even small geometric irregularities amongst nominally identical samples. As such, we then moved to testing these approaches for detection of artificial local stress perturbations introduced into a more complex geometry: a hexagonal block with drilled holes. A main outcome of this work is that a generalizable ML workflow can be used to detect and predict the characteristics of small artificial anomalies in a graphite component with a relevant geometry. While this work was performed using surficial vibration data, we expect the approach to be flexible and viable for other monitoring scenarios, such as those with different arrangements or types of sensor arrays. As compared to previously funded efforts, an existing ML workflow based on neural networks was enhanced through the addition of recently developed Fourier neural operators. As applied to previously collected and new vibration datasets, prediction accuracies of anomaly characterizations were greatly improved with minimal added computational cost. As trained on small durations of vibration data (tens of seconds) collected over a realistic number of locations, the model was able to reliably determine the presence of a subtle stress anomaly and begin to provide location estimates. Such an approach is likely to be viable for more relevant reactor damage scenarios for graphite components, such as progressive crack growth or creep.

36 MATERIALS SCIENCE↗

Determination of acoustic nonlinearity parameters using thermal modulation of ultrasonic waves

This study presents a test method and its theoretical framework to determine the acoustic nonlinearity parameters (α, β, δ) of material using thermal modulation of ultrasonic waves. Temperature change-induced thermal strain excites the nonlinear response of the material and modulates the ultrasonic wave propagating in it. Experimental results showed a strong correlation between the relative wave velocity change and the temperature change. With a quadratic polynomial model, the acoustic nonlinearity parameters were obtained from the polynomial coefficients by curve fitting the experimental data. Their effects on thermal-induced velocity change were discussed. The parameters α, β, and δ govern the hysteretic gap, average slope, and curvature of the correlation curve, respectively. The proposed theory was validated on aluminum, steel, intact and damaged concrete samples. The obtained nonlinear parameters show reasonable agreement with values reported in the literature. Compared to other nonlinear acoustic methods using vibration or acoustic excitation, the thermal modulation method generates more uniform, slow changing, and larger strain field in the test sample. Employing the thermal effect as the driving force for nonlinearity instead of an undesired influencing factor, this method can measure the absolute values of α, β, and δ with good accuracy using a simple ultrasonic test setup.

Physics↗

Development and experimental evaluation of an acoustic flow meter prototype for measuring air flow

Here, this study outlines the development and testing of a flow meter prototype specifically designed for use in nuclear reactor environments. The meter uses flow-induced vibration to measure flow rates and is designed for remote monitoring in harsh environments where radiation can damage electronics. The device generates a vibration signal produced by a feedback system when fluid flows out of an orifice and interacts with a downstream wedge. The frequency of the vibration signal corresponds directly to flow rate and velocity. The study investigates geometric parameters intrinsic to the prototype, such as orifice height, width, edge distance, and chamber length. Different configurations were also tested, including a bypass loop with variable cross-sections around the device. The investigation results reveal the impact of these geometric parameters on the vibration signal output, providing valuable insights for future design improvements and enhancing the effectiveness of flow metering systems used in nuclear reactor applications.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Bayesian-based response expansion and uncertainty quantification using sparse measurement sets

Systems subjected to dynamic loads often require monitoring of their vibrational response, but limitations on the total number and placement of the measurement sensors can hinder the data-collection process. Here, we present an indirect approach to estimate a system’s full-field dynamic response, including all uninstrumented locations, using response measurements from sensors sparsely located on the system. This approach relies on Bayesian inference that utilizes a system model to estimate the full-field response and quantify the uncertainty in these estimates. By casting the estimation problem in the frequency domain, this approach utilizes the modal frequency response functions as a natural, frequency-dependent weighting scheme for the system mode shapes to perform the expansion. This frequency-dependent weighting scheme enables an accurate expansion, even with highly correlated mode shapes that may arise from spatial aliasing due to the limited number of sensors, provided these correlated modes do not have natural frequencies that are closely spaced. Furthermore, the inherent regularization mechanism that arises in this Bayesian-based procedure enables the utilization of the full set of system mode shapes for the expansion, rather than any reduced subset. This approach can produce estimates when considering a single realization of the measured responses, and with some modification, it can also produce estimates for power spectral density matrices measured from many realizations of the responses from statistically stationary random processes. A simply supported beam provides an initial numerical validation, and a cylindrical test article excited by acoustic loads in a reverberation chamber provides experimental validation.

42 ENGINEERING↗

IDENTIFICATION OF POTENTIAL SUPERCONDUCTOR QUENCH PRECURSORS USING FREQUENCY DOMAIN FEATURE ANALYSIS

Superconducting magnets are important pieces of technology in the world of particle accelerators, allowing researchers to study atomic and subatomic phenomena, among other things. In some instances, superconductors can lose this non-resistive property in a phenomenon known as quenching, which can cause damage to the magnets. This potential danger prompts the introduction of systems to predict when a quench is imminent; one such implementation is through the use of acoustic sensors that detect vibrations within the magnet. Within these acoustic sensor signals, significantly above-noise disturbances (referred to as ”events”) can be identified. Our research applies the statistical framework of a permutation test to features calculated from the power spectral density (PSD) to distinguish between events far from the quench at the end of the signal to events at the start of the signal. We found that dividing the PSD into frequency bands produced a feature capable of distinguishing between events early in the signal and late in the signal leading up the quench, providing a promising starting place for future quench prediction systems.

Roehrig, Benjamin [Northern Illinois U.]↗

Data Challenges in Multi-Sensor Data Science System for Monitoring a Solvent Extraction Process

Idaho National Laboratory (INL) is maintaining and gaining knowledge into the nuclear fuel cycle by building a test bed to allow researchers the opportunity to study nuclear fuel processing operations. This includes studying solvent extraction processes that use centrifugal contactors. As part of INL’s mission, the goal of this project is to develop a system that utilizes non-traditional measurement sources such as vibration, acoustics, current, light, flow, and temperature in conjunction with data-based, machine learning techniques that will allow for signal discovery. This multisensory data can support the development of safeguards by design, provide operator process awareness, and discover process anomalies. This poster will highlight some of the data collection and analytics challenges for the multi-sensor system as well as the mitigation strategies to build a robust system. Additionally, some preliminary data from the first testing campaign will be shown to help illustrate the data needs of the system.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Nonlinear Impact-Echo Test for Quantitative Evaluation of ASR Damage in Concrete

Nonlinear acoustic methods demonstrate high sensitivity for concrete damage evaluation. Among these methods, nonlinear resonance acoustic methods have been widely used in laboratory tests on small scale test samples. In this study, a nonlinear impact-echo (IE) method for concrete damage evaluation was introduced, in which the IE frequency shift was measured at different impact force levels. The nonlinear IE test and the nonlinear impact resonance acoustic spectroscopy (NIRAS) test share similarities in the experimental setup and analysis method. However, the nonlinear IE test excites a local thickness resonance mode of a member instead of the global resonance vibration. Therefore, the analyzed mode is unaffected by member boundary conditions and is applicable to large concrete structural members. To identify the fundamental IE frequencies, multiple impacts were applied along the members. Once the fundamental IE frequencies were determined, the effectiveness of the nonlinear IE method was evaluated by testing seven concrete beam specimens with varying levels of alkali-silica reaction (ASR) damage. In conclusion, the nonlinear IE test demonstrates high sensitivity to concrete damage and allows for quantitative assessment of the damage state of concrete without a baseline measurement.

36 MATERIALS SCIENCE↗

Development of a Multi-Sensor Data Science System Used for Signature Development on Solvent Extraction Processes in support of safeguards- an overview

A new nuclear fuel cycle test bed is being built at Idaho National Laboratory to support the purification of special nuclear material recovered from used fuel. The test bed provides an opportunity to research process flow and the application of computational tools in solvent extraction processes. A deeper understanding of process and equipment behavior coupled with real time data collection can indicate whether a process failure is accidental or purposeful. The goal of this project is to develop a system that utilizes non-traditional measurement sources such as vibration, acoustics, current, light, flow, and temperature in conjunction with data-based, machine learning techniques that will allow for signal discovery. This multi-sensor data can support the development of safeguards by design and security by design measures for such a facility. Additionally, it can aid in early detection and identification of removed materials indicating diversion, which is essential for initiating material recovery and actor identification. This overview encompasses the current research and testing of sensors to develop a spectrum of process signatures. To be followed by planned experiments aimed to characterize said signatures and study potential feature extraction techniques to identify a fault in the system (i.e. flow diversion).

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Development, Testing, and Validation of Fabry-Pérot Cavity Acoustic Sensors for Microreactor Applications

Nuclear microreactors are a unique reactor design which may allow for the nuclear energy industry to tap into unconventional markets, and their modularity presents some advantages over larger, conventional reactor designs. For nuclear microreactors to be economically viable, on-line structural health monitoring may be necessary to reduce operation and maintenance costs with lower power production. Optical fiber sensors, and specifically optical Fabry-Pérot cavities (FPCs), may present the opportunity to monitor vibrational frequencies of microreactor components during operation, enabling identification of the location and severity of potential damage. In this work, FPCs were designed and fabricated with materials which may be able to survive in the extremely harsh environment of nuclear microreactors. The FPCs were bonded to metal test specimens to monitor their vibrational frequencies, along with a reference piezoelectric accelerometer. Euler-Bernoulli theory was used to calculate the fundamental modes and mode-shapes to compare with experimentally measured frequency spectra. The peak frequencies detected with the FPC and piezoelectric accelerometer, and theoretical modes, all agreed well for the first four fundamental modes (within 5%). Furthermore, when the FPC and accelerometer were co-located on the test specimen, their peak frequencies all agreed within 1%.

Birri, Tony↗