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At least 19 records

Full Rod Length Gamma Spectroscopy Measurements of LWR Used Fuel Rods

Twenty-five high-burnup pressurized water reactor used fuel rods were scanned in the Irradiated Fuels Examination Laboratory at Oak Ridge National Laboratory with a high-resolution gamma spectrometer. A planar high-purity germanium detector was used across an energy range from 60 keV to 3 MeV. Gamma spectra of individual fuel rods were collected in 4.5 mm steps along the entire length of each rod. Additional spectra were collected on select rods in rotational increments of 30 degrees to provide data on the distribution of fission products along the rod perimeter.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND

Ultrasonic Nondestructive Evaluation of Pultruded Rod Stitched Efficient Unitized Structure (PRSEUS) During Large-Scale Load Testing and Rod Push-Out Testing

The Pultruded Rod Stitched Efficient Unitized Structure (PRSEUS) is a structural concept developed by the Boeing Company to address the complex structural design aspects associated with a pressurized hybrid wing body (HWB) aircraft configuration. The HWB has long been a focus of NASA's environmentally responsible aviation (ERA) project, following a building block approach to structures development, culminating with the testing of a nearly full-scale multi-bay box (MBB), representing a segment of the pressurized, non-circular fuselage portion of the HWB. PRSEUS is an integral structural concept wherein skins, frames, stringers and tear straps made of variable number of layers of dry warp-knit carbon-fiber stacks are stitched together, then resin-infused and cured in an out-of-autoclave process. The PRSEUS concept has the potential for reducing the weight and cost and increasing the structural efficiency of transport aircraft structures. A key feature of PRSEUS is the damage-arresting nature of the stitches, which enables the use of fail-safe design principles. During the load testing of the MBB, ultrasonic nondestructive evaluation (NDE) was used to monitor several sites of intentional barely-visible impact damage (BVID) as well as to survey the areas surrounding the failure cracks after final loading to catastrophic failure. The damage-arresting ability of PRSEUS was confirmed by the results of NDE. In parallel with the large-scale structural testing of the MBB, mechanical tests were conducted of the PRSEUS rod-to-overwrap bonds, as measured by pushing the rod axially from a short length of stringer.

Johnston, Patrick H.

Gold Quantum Rods: Modulation of Singlet and Triplet Exciton Populations by the Rod Length

Abstract Gold quantum rods (QRs) of Au60, Au78, Au96, and Au114 (protected by thiolate ligands) exhibit exclusive fluorescence, which is different from the shorter Au42 QR with dual emission (fluorescence + phosphorescence). Herein, we report the excitation wavelength-dependent near-infrared-II photoluminescence (PL) and exciton dynamics of this series of QRs. Interestingly, the fluorescence quantum yield (QY) of the QRs is much higher (2–10×) when the lowest singlet excited state (S1) is excited compared to the excitation of high-lying states (Sn). A metastable intermediate singlet state (denoted S′) is identified by transient absorption spectroscopy when Sn is excited, and this S′ state leads to fast “skybridge” intersystem crossing (ISC), which contributes primarily (>60%) to the total triplet population. With increasing aspect ratio (AR) of QRs (from 6.3 to 18.7), nonradiative processes accelerate, leading to fast decay of the S1 state (hence, less QY) and of the T1 state (barely phosphorescent). A detailed energy flow mechanism is determined for the QRs after photoexcitation, which offers a design principle for manipulation of exciton dynamics toward potential utilization of higher excited states in applications.

77 NANOSCIENCE AND NANOTECHNOLOGY

Tantalum Experiments in Fully-Reflected Water-Moderated Triangular-Pitched U(6.90)O 2 Fuel Rod Lattices (1.02 cm Pitch)

The United States (US) Department of Energy (DOE) Nuclear Energy Research Initiative funded the design and construction of the Seven Percent Critical Experiment (7uPCX) at Sandia National Laboratories (SNL). The start-up of the experiment facility and the execution of the experiments described here were funded by the DOE Nuclear Criticality Safety Program. The 7uPCX is designed to investigate critical systems with fuel for light water reactors in the enrichment range above 5 % 235 U. The 7uPCX assembly is a water moderated and — reflected array of aluminum-clad U(6.90 %)O 2 fuel rods. Other critical experiments performed in the 7uPCX assembly are documented in LEU-COMP-THERM-078, LEU-COMP-THERM-080, LEU-COMP-THERM 096, LEU- COMP-THERM-097, LEU-COMP-THERM-101, LEU-COMP-THERM-102, and LEU-COMP-THERM-111. Applied interests in neutron-absorbing elements at epithermal and intermediate neutron energy ranges at DOE’s Hanford Site and Savannah River Site were identified through DOE Office of Environmental Management (EM) workshops and needs surveys performed in conjunction with the National Nuclear Security Administration/Nuclear Criticality Safety Program. In response, a team lead by Oak Ridge National Laboratory (ORNL) performed a study evaluating the use of 7uPCX for testing the epithermal cross sections of materials at SNL. This marked the inception of the set of experiments described here. The purpose of these experiments was to measure the effects of tantalum in nearly-critical systems. The tantalum was introduced into the fuel arrays as experiment rods within a central test region. The central test region was designed to target the epithermal neutron energy range by providing a dry cylindrical cavity constructed of aluminum and lined with 0.04 in (0.1016 cm) thick cadmium sheet. The central test region has an outer diameter of 3.75 in (9.525 cm) length of 31 in (78.74 cm) and can hold 85 tantalum rods nominally 0.25 in (0.635 cm) outside diameter and 31.25 in (79.375 cm) long. The critical experiments were done using a set of triangular-pitched grid plates fabricated for these experiments. The grid plate set accommodated a fuel array of a total of 2016 fuel rod positions on a pitch of 0.4 in (1.016 cm) in a series of 21 hexagonal rings positioned around the central test region. The fuel used in these experiments was fabricated using unirradiated 6.90 % enriched UO 2 fuel pellets from fuel elements designed to be used in the internal nuclear superheater section of the Pathfinder boiling water reactor operated in South Dakota by the Northern States Power Company in the 1960s. The fuel elements were obtained from The Pennsylvania State University where they had been stored for many years. The fuel pellets in those fuel elements were removed from the original Incoloy cladding and reclad in 3003 aluminum tubes and end caps for use in the experiments reported here. The eight cases in this experiment series were performed in 2024 in the Sandia Critical Experiments (SCX) at the Sandia Pulsed Reactor Facility by varying the number of fuel rods in the critical assembly. The personnel involved in conducting these experiments included David Ames, Elijah Lutz, Beth Hanson, Patrick Ward, Jason Soares, and Augie Chapa from SNL, as well as Mathieu Dupont and B.J. Marshall from ORNL. Case 1 had no tantalum experiment rods. Case 2 had seven tantalum rods in the center of the central test region. Case 3 had 18 tantalum rods in the third hexagonal ring of the central test region. Case 4 had 19 tantalum rods in the center of the central test region. Case 5 had 30 tantalum rods in the outer most positions of the central test region. Case 6 had 37 tantalum rods in the center of the central test region. Case 7 had 61 tantalum rods in the center of the central test region. Case 8 had 85 tantalum rods filling all positions in the central test region. All eight critical experiments are judged to be acceptable as benchmark experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

NON-DESTRUCTIVE POST IRRADIATION EXAMINATION OF FIRST CYCLE ACCIDENT TOLERANT AND ADVANCED ZIRCONIUM ALLOY HIGH BURNUP FUEL RODS

Post irradiation examination (PIE) of accident tolerant fuel concepts and high burnup uranium dioxide advanced zirconium alloy clad fuel contribute to near term nuclear industry goals of enhancing light water reactor safety and economics. Westinghouse is developing chromium coated zirconium alloy cladding as an accident tolerant fuel option for current pressurized water reactors. Examination of high burnup fuel further augments the technical foundation for extending the peak rod average burnup limits beyond the current regulatory limit of 62 MWd/kgU. Seven fuel rods were received at the Oak Ridge National Laboratory Irradiated Fuel Examination Facility. This includes three chromium coated zirconium alloy fuel rods and four high burnup advanced zirconium alloy fuel rods. Six of the seven rods were fueled with standard uranium dioxide while one of the chromium coated rods contained Westinghouse’s ADOPT fuel. The overall hot-cell PIE plan and some PIE results have been presented previously. This paper focuses on the additional non-destructive examination and fission gas release. Highlights from visual examination of these rods are presented. The chromium coating showed little to no visual change following irradiation. Observations of the axial burnup trends in the fuel rods are derived from full rod axial gamma-ray scans with additional observations related to local fission product migration. The axial dimensional changes of the seven rods are evaluated. As expected, creep down had not yet occurred in the chromium coated rods, and the maximum diameter strain in the high burnup advanced zirconium alloy cladding was less than 0.5%. Finally, the steady state fission gas release for these rods was measured ranging from 4.1% to 17.6% which matched expectation from literature. These fuel rods now await further destructive examination.

Harp, Jason

Design and fabrication of a four-rod radio frequency quadrupole with a variable aperture

Radiofrequency quadrupole (RFQ) linear accelerators with variable aperture cell parameters offer an effective means of accelerating high-intensity ion beams exceeding 100 mA and have been implemented in various RFQ designs. However, in a four-rod RFQ, the use of dielectric perturbation methods to measure the voltage distribution behind the rod electrodes is not applicable when implementing variable aperture geometries, because changes in the rod shape influence the electric field at the location of the perturbation element. Therefore, it was necessary to design the rod profile for each cell such that the electric field distribution behind the rods remains unaffected by changes in the aperture. In this study, we present a method to adjust the voltage distribution by modifying the geometry of the rod electrodes according to each cell's aperture parameters. This design approach enables the integration of variable aperture cells into a four-rod RFQ linac, significantly enhancing the achievable beam current. To ensure uniform capacitance and maintain a constant rod-electrode voltage despite variations in the average aperture radius, we developed a systematic method for shaping the rod electrodes. This method was refined using two-dimensional (2D) and three-dimensional (3D) electromagnetic field simulations to optimize the electrode cross-sectional profiles. The fabricated rod electrodes were then installed in a four-rod RFQ, and the electric field distribution was measured using the perturbation method and tuned by adjusting the base plates. As a result, the measured variation of ±1.1 % confirms that this design methodology can produce a sufficiently uniform voltage distribution for high-current beam acceleration. These results demonstrate the practical feasibility of a variable-aperture four-rod RFQ linac.

43 PARTICLE ACCELERATORS

Structural Integrity Testing Method for PRSEUS Rod-Wrap Stringer Design

NASA Langley Research Center and The Boeing Company are developing an innovative composite structural concept, called PRSEUS, for the flat center section of a future environmentally friendly hybrid wing body (HWB) aircraft. The PRSEUS (Pultruded Rod Stitched Efficient Unitized Structure) concept uses dry textile preforms for the skins, frames, and stiffener webs. The highly loaded stiffeners are made from precured unidirectional carbon/epoxy rods and dry fiber preforms. The rods are wrapped with the dry fiber preforms and a resin infusion process is used to form the rod-wrap stiffeners. The structural integrity of the rod-wrap interface is critical for maintaining the panel s high strength and bending rigidity. No standard testing method exists for testing the strength of the rod-wrap bondline. Recently, Boeing proposed a rod push-out testing method and conducted some preliminary tests using this method. This paper details an analytical study of the rod-wrap bondline. The rod-wrap interface is modeled as a cohesive zone for studying the initiation and growth of interfacial debonding during push-out testing. Based on the correlations of analysis results and Boeing s test data, the adequacy of the rod-wrap testing method is evaluated, and potential approaches for improvement of the test method are proposed.

Wang, John T.

Noise reduction in a Mach 5 wind tunnel with a rectangular rod-wall sound shield

A rod wall sound shield was tested over a range of Reynolds numbers of 0.5 x 10 to the 7th power to 8.0 x 10 to the 7th power per meter. The model consisted of a rectangular array of longitudinal rods with boundary-layer suction through gaps between the rods. Suitable measurement techniques were used to determine properties of the flow and acoustic disturbance in the shield and transition in the rod boundary layers. Measurements indicated that for a Reynolds number of 1.5 x 10 to the 9th power the noise in the shielded region was significantly reduced, but only when the flow is mostly laminar on the rods. Actual nozzle input noise measured on the nozzle centerline before reflection at the shield walls was attenuated only slightly even when the rod boundary layer were laminar. At a lower Reynolds number, nozzle input noise at noise levels in the shield were still too high for application to a quiet tunnel. At Reynolds numbers above 2.0 x 10 the the 7th power per meter, measured noise levels were generally higher than nozzle input levels, probably due to transition in the rod boundary layers. The small attenuation of nozzle input noise at intermediate Reynolds numbers for laminar rod layers at the acoustic origins is apparently due to high frequencies of noise.

Creel, T. R., Jr.

Lightning discharge protection rod

A system for protecting an in-air vehicle from damage due to a lighning strike is disclosed. It is an extremely simple device consisting of a sacrificial graphite composite rod, approximately the diameter of a pencil with a length of about five inches. The sacrificial rod is constructed with the graphite fibers running axially within the rod in a manner that best provides a path of conduction axially from the trailing edge of an aircraft to the trailing end of the rod. The sacrificial rod is inserted into an attachment hole machined into trailing edges of aircraft flight surfaces, such as a vertical fin cap and attached with adhesive in a manner not prohibiting the conduction path between the rod and the aircraft. The trailing end of the rod may be tapered for aerodynamic and esthetic requirements. This rod is sacrificial but has the capability to sustain several lightning strikes and still provide protection.

Bryan, Charles F., Jr.

Comparing the Performance of Hyperbolic and Circular Rod Quadrupole Mass Spectrometers with Applied Higher Order Auxiliary Excitation

This work applies higher order auxiliary excitation techniques to two types of quadrupole mass spectrometers (QMSs): commercial systems and spaceborne instruments. The operational settings of a circular rod geometry commercial system and an engineering test-bed for a hyperbolic rod geometry spaceborne instrument were matched, with the relative performance of each sensor characterized with and without applied excitation using isotopic measurements of Kr+. Each instrument was operated at the limit of the test electronics to determine the effect of auxiliary excitation on extending instrument capabilities. For the circular rod sensor, with applied excitation, a doubling of the mass resolution at 1% of peak transmission resulted from the elimination of the low-mass side peak tail typical of such rod geometries. The mass peak stability and ion rejection efficiency were also increased by factors of 2 and 10, respectively, with voltage scan lines passing through the center of stability islands formed from auxiliary excitation. Auxiliary excitation also resulted in factors of 6 and 2 in peak stability and ion rejection efficiency, respectively, for the hyperbolic rod sensor. These results not only have significant implications for the use of circular rod quadrupoles with applied excitation as a suitable replacement for traditional hyperbolic rod sensors, but also for extending the capabilities of existing hyperbolic rod QMSs for the next generation of spaceborne instruments and low-mass commercial systems.

Gershman, D. J.

Truss beam having convex-curved rods, shear web panels, and self-aligning adapters

A truss beam comprised of a plurality of joined convex-curved rods with self-aligning adapters (SAA) adhesively attached at each end of the truss beam is disclosed. Shear web panels are attached to adjacent pairs of rods, providing buckling resistance for the truss beam. The rods are disposed adjacent to each other, centered around a common longitudinal axis, and oriented so that adjacent rod ends converge to at least one virtual convergence point on the common longitudinal axis, with the rods' curvature designed to increase prevent buckling for the truss beam. Each SAA has longitudinal bores that provide self-aligning of the rods in the SAA, the self-aligning feature enabling creation of strong adhesive bonds between each SAA and the rods. In certain embodiments of the present invention, pultruded unidirectional carbon fiber rods are coupled with carbon fiber shear web panels and metal SAA(s), resulting in a lightweight, low-cost but strong truss beam that is highly resistant to buckling.

Fernandez, Ian M.

Comparing the Performance of Hyperbolic and Circular Rod Quadrupole Mass Spectrometers with Applied Higher Order Auxiliary Excitation

This work applies higher order auxiliary excitation techniques to two types of quadrupole mass spectrometers (QMSs): commercial systems and spaceborne instruments. The operational settings of a circular rod geometry commercial system and an engineering test-bed for a hyperbolic rod geometry spaceborne instrument were matched, with the relative performance of each sensor characterized with and without applied excitation using isotopic measurements of Kr+. Each instrument was operated at the limit of the test electronics to determine the effect of auxiliary excitation on extending instrument capabilities. For the circular rod sensor, with applied excitation, a doubling of the mass resolution at 1% of peak transmission resulted from the elimination of the low-mass side peak tail typical of such rod geometries. The mass peak stability and ion rejection efficiency were also increased by factors of 2 and 10, respectively, with voltage scan lines passing through the center of stability islands formed from auxiliary excitation. Auxiliary excitation also resulted in factors of 6 and 2 in peak stability and ion rejection efficiency, respectively, for the hyperbolic rod sensor. These results not only have significant implications for the use of circular rod quadrupoles with applied excitation as a suitable replacement for traditional hyperbolic rod sensors, but also for extending the capabilities of existing hyperbolic rod QMSs for the next generation of spaceborne instruments and low-mass commercial systems.

auxiliary excitation

Sister Rod Destructive Examinations (FY23) Appendix B: Segmentation, Defueling, Metallographic Data and Total Cladding Hydrogen

As a part of the DOE-NE High Burnup Spent Fuel Data Project, Oak Ridge National Laboratory (ORNL) is performing destructive examinations (DEs) of high burnup (HBU) (>45 GWd/MTU) spent nuclear fuel (SNF) rods from the North Anna Nuclear Power Station operated by Dominion Energy. The SNF rods, called sister rods or sibling rods are all HBU and include four different kinds of fuel rod cladding: standard Zircaloy-4 (Zirc-4), low-tin (LT) Zirc-4, ZIRLO ® , and M5 ® . The DEs are being conducted to obtain a baseline of the HBU rod’s condition before dry storage and are focused on understanding overall SNF rod strength and durability. Both composite fuel and defueled cladding will be tested to derive material properties. Although the data generated can be used for multiple purposes, one primary goal for obtaining the post-irradiation examination data and associated measured mechanical properties is to support SNF dry storage licensing and relicensing activities by (1) addressing identified knowledge gaps and (2) enhancing the technical basis for post-storage transportation, handling, and subsequent disposition of the SNF. This report documents the status of the ORNL Phase 1 DE activities related to: Rough segmentation (RS), Defueling (DEF), DE.02 optical microscopy (MET), and DE.03, cladding total hydrogen measurements. It is a cumulative update to the FY22 status report.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Microgravity Flammability of PMMA Rods in Concurrent Flow

Microgravity experiments burning cast PMMA cylindrical rods in axial flow have been conducted aboard the International Space Station in the Microgravity Science Glovebox (MSG) facility using the Burning and Suppression of Solids (BASS) flow duct, as part of the BASS-II experiment. Twenty-four concurrent-flow tests were performed, focusing on finding flammability limits as a function of oxygen and flow speed. The oxygen was varied by using gaseous nitrogen to vitiate the working volume of the MSG. The speed of the flow parallel to the rod was varied using a fan at the entrance to the duct. Both blowoff and quenching limits were obtained at several oxygen concentrations. Each experiment ignited the rod at the initially hemispherical stagnation tip of the rod, and allowed the flame to develop and heat the rod at a sufficient flow to sustain burning. For blowoff limit tests, the astronaut quickly turned up the flow to obtain extinction. Complementary 5.18-second Zero Gravity Facility drop tests were conducted to compare blowoff limits in short and long duration microgravity. For quenching tests, the flow was incrementally turned down and the flame allowed to stabilize at the new flow condition for at least the solid-phase response time before changing it again. Quenching was observed when the flow became sufficiently weak that the flame could no longer provide adequate heat flux to compensate for the heat losses (conduction into the rod and radiation). A surface energy balance is presented that shows the surface radiative loss exceeds the conductive loss into the rod near the limit. The flammability boundary is shown to represent a critical Damkohler number, expressed in terms of the reaction rate divided by the stretch rate. For the blowoff branch, the boundary exhibits a linear dependence on oxygen concentration and stretch rate, indicating that the temperature at blowoff must be fairly constant. For the quenching branch, the dominance of the exponential nature of the Arrhenius kinetics reaction rate indicates that the temperature is critical.

flammability

Effect of feed-rod tilting on friction surfacing of steel

During the friction surfacing process, the forge-axial force, rotation rate, and traverse speed of the consumable feed-rod play crucial roles in determining the deposition rate and layer morphology. Although some researchers have studied the enhancement of deposition by introducing a backward tilt relative to the traverse direction, there has been limited investigation into the effects of other tilt orientations. Therefore, this study aims to provide a more comprehensive understanding of feed-rod tilting in friction surfacing. In this investigation, the consumable feed-rod undergoes tilting in four distinct directions: forward, backward, advancing side, and retreating side, each tested at two different tilt angles (1.5° and 3.0°). The results reveal that the feed-rod tilting can influence the deposition dynamics by altering the location and area of the rubbing interface situated between the feed-rod and the substrate. Moreover, the feed-rod tilting can significantly enhance the bond width, deposition rate, and deposition efficiency. The enhancement in deposition efficiency signifies a successful reduction in flash formation. Furthermore, a distinct layered microstructure is evident within each deposition layer, regardless of tilt conditions, indicating the unique deposition process inherent to friction surfacing. Finally, the innovative approach proposed in this study not only offers a straightforward and feasible means to improve deposition rate and efficiency but also expands the potential for constructing more intricate geometries or authentic surfaces.

36 MATERIALS SCIENCE

Combustion of solid carbon rods in zero and normal gravity

In order to investigate the mechanism of carbon combustion and to assess the importance of gravitational induced convection on the process, zero and normal gravity experiments were conducted in which spectroscopic carbon rods were resistance ignitied and burned in dry oxygen environments. In the zero-gravity drop tower tests, a blue flame surrounded the rod, showing that a gas phase reaction in which carbon monoxide was oxidized to carbon dioxide was taking place. The ratio of flame diameter to rod diameter was obtained as a function of time. It was found that this ratio was inversely proportional to both the oxygen pressure and the rod diameter. In the normal gravity tests, direct mass spectrometric sampling was used to measure gas phase concentrations. The gas sampling probe was positioned near the circumference of a horizontally mounted 0.615 cm diameter carbon rod, either at the top or at angles of 45 deg to 90 deg from the top, and yielded concentration profiles of CO2, CO, and O2 as a function of distance from the surface. The mechanism controlling the combustion process was found to change from chemical process control at the 90 deg and 45 deg probe positions to mass transfer control at the 0 deg probe position at the top of the rod. Under the experimental conditions used, carbon combustion was characterized by two surface reactions, 2C + O2 yields 2CO and CO2 + C yields 2CO, and a gas phase reaction, 2CO + O2 yields 2CO2.

Spuckler, C. M.

Evaluation of ceramic packed-rod regenerator matrices

An extensive evaluation of a modified cryocooler with various regenerator matrices is reported. The matrices examined are 0.015 in. diam. Pb spheres and 0.008, 0.015, and 0.030 in. diam. rods of a 0.2% SnCl2 doped ceramic labelled LS-8A. Specific heat and thermal conductivity data on these rod materials are also reported. The chronic pulverization/dusting problem common to Pb spheres was investigated. During a 1000 hr life test with 0.0008 in. diam. rods there was no degradation of the refrigerator performance, and a subsequent examination of the rods themselves revealed no evidence of breakage or pulverization. The load temperature characteristics for the rod packed regenerators were inferior to that for the Pb spheres, the effect being to shift the Pb spheres load curve up in temperature. This temperature shift was 5.0, 7.4, and 11.6K for the 0.0008, 0.015, and 0.030 in. diam. rods, respectively.

Lawless, W. N.

Vibrational Power Flow Analysis of Rods and Beams

A new method to model vibrational power flow and predict the resulting energy density levels in uniform rods and beams is investigated. This method models the flow of vibrational power in a manner analogous to the flow of thermal power in a heat conduction problem. The classical displacement solutions for harmonically excited, hysteretically damped rods and beams are used to derive expressions for the vibrational power flow and energy density in the rod and beam. Under certain conditions, the power flow in these two structural elements will be shown to be proportional to the energy density gradient. Using the relationship between power flow and energy density, an energy balance on differential control volumes in the rod and beam leads to a Poisson's equation which models the energy density distribution in the rod and beam. Coupling the energy density and power flow solutions for rods and beams is also discussed. It is shown that the resonant behavior of finite structures complicates the coupling of solutions, especially when the excitations are single frequency inputs. Two coupling formulations are discussed, the first based on the receptance method, and the second on the travelling wave approach used in Statistical Energy Analysis. The receptance method is the more computationally intensive but is capable of analyzing single frequency excitation cases. The traveling wave approach gives a good approximation of the frequency average of energy density and power flow in coupled systems, and thus, is an efficient technique for use with broadband frequency excitation.

Wohlever, James Christopher