High Modal Density Research Articles

Chasing the high-resolution mapping of rotational and strain FRFs as receptance processing from different full-field optical measuring technologies

Thanks to the recent advances in digital vision systems, a question might arise about where the full-field optical and contactless methods can bring modern design procedures. An answer lies on the methodologically detailed comparison of the results, processed from different full-field optical techniques, in exploring consistent and high-resolution maps of rotational and strain FRFs that is done through this paper.Great exertions were first put in thoroughly testing a thin aluminium plate, in its real dynamics as a lightweight structure with broad frequency band dynamics and high modal density, in a unique comparative set-up, to obtain Receptance FRF maps of displacements-over-force by means of 3 different full-field optical techniques (SLDV, DIC, ESPI). There resulted superior quality Receptance maps in a broad and dense frequency domain, with high-resolution and continuity-wise consistent mapping at each frequency line.This paper exploits the here detailed robust numerical differentiation and signal processing in order to calculate the Impedance-based models of rotational and strain FRFs. Especially for DIC and for ESPI, both rarely used on many frequency lines, the fully populated FRFs for rotations and strains are a clear novelty, with rotational Coherence functions as added quality assessment features.The systematic comparison of the results obtained in the same location of the sample, by means of spatial and frequency domain metrics, is possible because of the proposed pointwise procedure, permitting the first numerical matching assessment of the 3 optical technologies on these awaited experiment-based quantities, as the full-field rotational and strain FRFs.

Amplification and modulation effect of elliptical surface polaritons on a thermal diode

With the development of surface polaritons of two-dimensional metasurfaces with high mode density, considerable attention has been paid to their application in optimising the performance of the thermal diode; however, presently, the main focus is on isotropic metasurfaces. In this study, we investigated the amplification and modulation effect of elliptical surface polaritons on a near-field radiative thermal diode. Introducing black phosphorus (BP) in forward and reverse terminals of the thermal diode (comprising VO2 and Si) demonstrated prominent amplification of rectification performance (of ∼3.59 times) in the modified thermal diode than in the one without BP. Selecting different electron densities of BP and different doping densities of Si revealed the influence of the hybridisation effect of elliptical polaritons on thermal rectification and near-field radiative heat transfer. Finally, based on the in-plane intrinsic anisotropic lattice of BP, the modified thermal diode facilitated highly flexible manipulation of rectification performance through mechanical rotating, which to the best of our knowledge, has never been discussed in the field of near-field radiative diodes. Our findings provides significant insights to intensify asymmetric energy transfer and explore the radiative heat transfer mechanism of a coupled system comprising an anisotropic metasurface and an out-plane anisotropic material.

Development of a hybrid SmEdA/SEA model for predicting the power exchanged between low and high modal density subsystems

Statistical modal Energy distribution Analysis (SmEdA) was developed from classical Statistical Energy Analysis (SEA). It allows computing power flow between coupled subsystems from the deterministic modes of uncoupled subsystems without assuming the SEA modal energy equipartition. SmEdA is well adapted in mid-frequency when the subsystems have not a very high modal density. However, for some systems e.g. the plate-cavity system, one subsystem can exhibit a low modal density while the other one a high one. The goal of the paper is then to propose an extension of SmEdA formulation that allows describing one subsystem by its deterministic modes, and the other one as a diffuse field statistically supposing modal energy equipartition. The uncertain subsystem is then characterized by sets of natural frequencies and mode shapes constructed based on Gaussian Orthogonal Ensemble matrix and the cross-spectrum density of a diffuse field, respectively. This formulation permits not only the computation of mean noise response but also the variance generated by the uncertainties and furthermore without bringing in much computation. It is demonstrated that the obtained analytical results from the proposed hybrid SmEdA/SEA are consistent with numerical results computed by FEM with an appropriate degree of uncertainty.

Model updating for a large multi-span quasi-periodic viaduct based on free wave characteristics

Quasi-periodic structures, as found in multi-span bridges, multi-bay and multi-storey buildings, are often characterized by a high modal density, even at low frequencies. This clustering of modes poses challenges in operational modal analysis, as well as in finite element model updating, where a pairing of experimental and numerically predicted modes is required. To overcome these difficulties, an alternative method for model updating based on the so-called free wave characteristics has recently been proposed. In this work, this method is applied to calibrate a finite element model of the K032 viaduct of the A11 highway in Bruges, Belgium. Vibration measurements are conducted to experimentally determine the free wave characteristics of the viaduct. In the model updating, the discrepancy between the calculated and identified free wave characteristics is minimized. The results are validated by comparing measured frequency response functions with those obtained from the updated finite element model.

Determining material properties of components with complex shapes using Resonant Ultrasound Spectroscopy

In this paper, Resonance Ultrasound Spectroscopy (RUS) is used to invert the elastic properties of components with complex shapes from a limited selection of mode matched frequencies. RUS is based on the unique relationship between the vibrational resonance response (resonance frequencies and mode shapes) of a component and its set of material properties, geometry, and boundary conditions. The study is conducted on 3 nominally identical components that have geometric imperfections due to the manufacturing process. The study reveals that an accurate characterization of the shape is critical to the success of the RUS process. The RUS process presented in this paper also relies on matching measured and computed vibrational mode shapes, in addition to the resonance frequencies. This strategy enables using high-order modes with complex modal information, in a frequency range with high modal density where modal identification based on the resonance frequencies alone would be challenging. This approach contrasts with the traditional approach of matching a number of resonance frequencies in sequential order. With the proposed approach, the elastic constants for the three components are similar, consistent with values found in the literature, and lead to small error of the RUS inversion, despite variations in the shapes and the resulting changes in the resonance response of the components.

Structural analysis and health monitoring of twentieth-century cultural heritage: the Flaminio Stadium in Rome

This work deals with structural analysis and health monitoring (SHM) of a valuable structure of the twentiethcentury cultural heritage: the Flaminio Stadium in Rome. The Flaminio is one of the iconic reinforced concrete sport facilities designed and built by Pier Luigi Nervi for the 1960 Olympic Games of Rome. In view of the foreseen SHM activity, the structural analysis of the Flaminio Stadium is firstly reported by presenting either preliminary analyses, aimed at studying the stadium response under different modeling hypotheses, and a three-dimensional Finite Element (FE) model of the entire structure. It turns out that the main grandstand canopy plays a pivotal role in the Flaminio's structural response to seismic excitation; in addition, its state of conservation raises some concern. Therefore, the structural modeling and dynamic characterization of the canopy is deepened in the paper. Its unusual features, such as geometry, material characteristics and dynamic interplay with the hosting main reinforced concrete frames are thoroughly assessed. To validate the FE results, characterized by a high modal density, and investigate the response of the structure, dynamic tests carried out under operating conditions are presented. The output-only collected data are used to calibrate the initial FE model. The predicted static and dynamic responses of the canopy are eventually exploited to guide the design of a tailored monitoring system. The relevant data management is framed in a heritage building information modeling (HBIM) context. This study draws a viable process for a proactive structural conservation strategy of twentieth-century heritage buildings and infrastructures.

Enhancement and active mediation of near-field radiative heat transfer through multiple nonreciprocal graphene surface plasmons

Metasurfaces, the two-dimensional counterparts of three-dimensional metamaterials, have recently attracted much attention due to their interesting properties, such as negative refraction, hyperbolic dispersion, and the ability to manipulate the evanescent spectrum. In this work, we propose a theoretical model for near-field radiative heat transfer between two multilayered systems consisting of anisotropic metasurfaces. The choice of metasurface is graphene, with an adjustable drift current, since this provides an ideal platform to support a high density of modes around the plasmon frequency. In this configuration, multiple nonreciprocal surface plasmon polaritons are excited, providing a strong way for near-field energy transport. The resulting heat transfer, assisted by the graphene's multilayered structure and with a high drift-current velocity, is more than 36 times stronger than that of a graphene monolayer structure without a drift current for the same vacuum gap. By adjusting the vacuum gap and the thickness of a dielectric spacer, this enhanced effect can be modulated over a large range, and can even turn into a suppression. Our findings provide a powerful way to enhance and regulate energy transport, and in turn, open up a way to enrich the moir\'e physics inherent to the anisotropic optical properties of a metasurface.

Coupling a Superconducting Qubit to a Left-Handed Metamaterial Resonator

Metamaterial resonant structures made from arrays of superconducting lumped circuit elements can exhibit microwave mode spectra with left-handed dispersion, resulting in a high density of modes in the same frequency range where superconducting qubits are typically operated, as well as a bandgap at lower frequencies that extends down to dc. Using this novel regime for multi-mode circuit quantum electrodynamics, we have performed a series of measurements of such a superconducting metamaterial resonator coupled to a flux-tunable transmon qubit. Through microwave measurements of the metamaterial, we have observed the coupling of the qubit to each of the modes that it passes through. Using a separate readout resonator, we have probed the qubit dispersively and characterized the qubit energy relaxation as a function of frequency, which is strongly affected by the Purcell effect in the presence of the dense mode spectrum. Additionally, we have investigated the ac Stark shift of the qubit as the photon number in the various metamaterial modes is varied. The ability to tailor the dense mode spectrum through the choice of circuit parameters and manipulate the photonic state of the metamaterial through interactions with qubits makes this a promising platform for analog quantum simulation and quantum memories.

Dominant substructural vibration modes for fully-loaded spent nuclear fuel canisters

This paper investigates the dynamic characteristics of a multilevel structure for the transportation and storage of spent nuclear fuel (SNF) from commercial power plants. The nuclear fuel is stored in slender rods that are grouped together into fuel assemblies (FA). In a sealed cylindrical container called “canister”, the FA are inserted into a honeycomb basket. The objective of this paper is to develop a computational model that accurately represents the structural dynamics of the canister as seen from its external surface, such that this computational model can be used in the context of structural integrity assessment of the internal components (FA and fuel rods) based on external vibration measurements. The numerous components lead to a large finite element model, and correspondingly, vibration modes and eigenfrequencies. Nevertheless, the localized connections between components enable an efficient domain decomposition with few interface coordinates. Craig–Bampton (CB) substructuring is thus used to perform the modal analysis. However, the high modal density yields a large-scale CB eigenvalue problem that necessitates a sparse solver. A block factorization by Schur complement that exploits the sparsity of the CB matrices allows an efficient calculation of the numerous eigenpairs. Many local vibration modes contribute little to the dynamics of the SNF canister. The main contribution of this paper is the development of an efficient methodology for determining the importance of each of the substructural modes of the CB model. The removal of the least dominant substructural modes allows for reducing the CB model. Using a 75% filtering, a significant speed-up is obtained, without noticeable loss of accuracy.

Optimization of continuous sensor placement for modal analysis: Application to an optical backscatter reflectometry strain sensor

The methods for experimental modal analysis are consolidated, as are the sensors used to perform this analysis. The characteristics of the most commonly used sensors are to be “discrete” and “independent”, that is, each sensor can measure the magnitude of interest in a single point and can be placed independently from the others on the structure. This kind of layout is widely used, for example, with accelerometers, but it presents a strong complexity if the structure is extended or characterized by high modal density in the frequency range of interest, or if the number of modes to be identified is high. Often the “discrete” sensors also have nonnegligible masses compared to the mass of the structure to be analyzed, thus introducing the well-known “mass effect”. Recently, new dynamic sensors have become available based on optical fibers such as the well-known Fiber Bragg grating sensors or the more recent Optical Backscatter Reflectometry (OBR) sensors. Both are sensors of the “continuous” type, or rather, they are a succession of sensors connected in series inside a single optical fiber. The purpose of this paper is to explore the use of OBR for modal analysis and introduce an original algorithm that allows the OBR sensor to be arranged in an optimized manner, to identify up to a certain number of modes in the most effective way and to respect the constraints imposed by the optical fiber itself, such as fiber length or maximum sensor curvature. The results are illustrated by means of the experimental results obtained on a structure characterized by a simple geometry.

Improved Craig–Bampton stochastic method for spacecraft vibroacoustic analysis

This paper addresses the susceptibility of finite element models to uncertainty in frequency ranges with relatively high modal density, particularly in the context of vibroacoustic analysis. The principal idea is based on a stochastic finite element method (FEM) technique called Craig–Bampton stochastic method (CBSM). It is a parametric Monte Carlo simulation (MCS) approach that can be performed at a fraction of the otherwise potentially impractical computational cost, due to the use of reduced rather than full system matrices. An enhanced formulation of the CBSM, significantly improving its efficiency by exploiting the block structure of the condensed model’s stiffness and mass matrices is derived. The improved method is adapted for use with distributed loads, such as diffuse sound field excitation. Its practical implementation is illustrated through a simple theoretical example followed by a high-complexity spacecraft structure case. In both cases solutions are compared to those for a classic MCS of the non-condensed models. Through an extensive parametric survey, recommendations are given on the ideal perturbation levels and underlying statistical distributions for the improved CBSM’s random variables. The proposed technique shows a very strong agreement with the benchmark MCS results. Computational time reductions of over 1 and 3 orders of magnitude against the original CBSM and the MCS, respectively, are demonstrated.

Noise Analysis for Large Silencers of Ships and Off-shore Plants using Energy Flow Analysis

In the study, energy flow analysis is performed to predict the performance of silencers. To date, deterministic approaches such as finite element method have been widely used for silencer analysis. However, they have limitations in analyzing large structures and mid-high frequency ranges due to unreasonable computational costs and errors. However, silencers used for ships and off-shore plants are much larger than those used in other engineering fields. Hence, energy governing equation, which is significantly efficient for systems with high modal density, is solved for silencers in ships and off-shore plants. The silencer is divided into two different acoustic media, air and absorption materials. The discontinuity of energy density at interfaces is solved via hypersingular integrals for the 3-D modified Helmholtz equation to analyze multi-domain problems with the energy flow boundary element method. The method is verified by comparing the measurements and analysis results for ship silencers over mid–high frequency ranges. The comparisons confirm good agreement between the measurement and analysis results. We confirm that the applied analysis method is useful for large silencers in mid-high frequency ranges. With the proven procedures, energy flow analysis can be performed for various types of silencer used in ships and off-shore plants in the first stage of the design.

Highly Efficient Optical Add-Drop Filter With an Angle-Polished Fiber Coupler

Microbubble whispering-gallery resonators have shown great promise in fiber-optic communications because of their low confinement loss and hollow cores, which allow for facile stress-based tunability. Usually, the transmission spectrum of taper-coupled microbubbles contains closely spaced modes due to the relatively large radii and oblate geometry of microbubbles. In this letter, we develop an optical add-drop filter using a microbubble coupled to fiber taper and angle-polished fiber waveguides. Because of the extra degree of freedom in the angle of its polish surface, the angle-polished fiber can be used for the discriminatory excitation of certain radial-order modes in the optical microcavity, reducing the high modal density and enhancing add-drop selectivity. Our robust and tunable add-drop filter demonstrated a drop efficiency of 85.9% and quality factor of 2 x 10^7, corresponding to a linewidth of 9.68 MHz. As a proof of concept, the drop frequency was tuned using internal aerostatic pressure at a rate of 7.3 +/- 0.2 GHz/bar with no diminishing effects on the add-drop filter performance.

Prediction of insertion loss of lagging in rectangular duct using statistical energy analysis

In this article, statistical energy analysis (SEA) is used to predict insertion loss from a lagged rectangular HVAC duct. For a lagged duct, all duct walls are treated from outside with acoustic material. Although deterministic methods like the finite element method (FEM), boundary element method (BEM), and wave based methods can predict the breakout noise, these methods have limitations in handling systems with high modal density due to higher computational cost. In this study, a rectangular duct is divided into six subsystems, which are four duct walls (each wall considered as a subsystem), internal air cavity and external airspace. Power flow analysis is performed on all subsystems to calculate transverse transmission loss of an unlined duct and insertion loss for a lagged duct. Predicted transverse transmission loss values are validated with ASHRAE data and Insertion loss values with literature. The results obtained are in good agreement.

Road Noise Reduction of a Sport Utility Vehicle via Panel Shape and Damper Optimization on the Floor Using Genetic Algorithm

Road noise is always a major concern in automotive industries. The contribution of the floor of a automotive vehicle to road noise is large because of its large area and close location to chassis in terms of structure-borne noise. Therefore, the panel shape and damper of the floor should be carefully designed, which are effective on medium frequency region of the road noise. Because there are so many design options on the floor panels that experience high modal density and short wavelength at medium frequencies, traditional mode-decoupling approaches are no longer efficient. This study shows that a proposed optimization process based on a finite element model and a genetic algorithm is successful to reduce road noise at medium frequencies. Some background theories about the genetic algorithm and acoustic radiation efficiency in the frame of vibro-acoustics are explained to understand the optimization process. Vehicle performance evaluation and experimental study are given to validate this study. Finally, this verified process is applied to a sport utility vehicle (SUV) under development, whose road noise reduction is shown to be successful.

A hybrid Finite Element-Statistical Energy Analysis method for impulsive and transient loading

The hybrid approach coupling Statistical Energy Analysis (SEA) and the finite element method has become a prominent technique for analysing structures under steady-state loads in the ‘mid-frequency’ range where some components behave in a deterministic manner with low modal density and others in a statistical manner with high modal density and statistical overlap. In this paper, the method is extended from its current steady-state capability to provide calculation of structural responses under impulsive and time-varying loads. Similar to the steady-state method, a system is split into deterministic components that are modelled using the finite element approach and statistical components that are modelled as SEA subsystems.An evolutionary spectrum approach based on the Priestley description of random processes is applied to model the response of both the SEA and deterministic components which are coupled by considering a power balance between the SEA subsystems. The diffuse field reciprocity relationship that relates the reverberant forces generated by a subsystem to the energy within it is explored under transient conditions where it is found that it can be important to account for the build-up of a reverberant field following an impulse. Results from the method are compared against finite element simulations for a system of plates coupled by a beam and it is found to generate predictions with the accuracy expected of an SEA-based method, although deterministic oscillations of the deterministic system at early times are not accounted for.

Substructuring for Contact Parameters Identification in Bladed-disks

Single stage bladed-disks are fundamental bricks of the rotating parts of a turbomachine. Although made of nominally identical sectors, the presence of imperfections or misalignment produces a large amplification of the forced response. Furthermore, due to their high modal density, friction dampers must be designed to mitigate resonance stresses, since a perfect detuning of the resonances from the excitation forces is impossible. Blade-root joints in these structures can provide the much-desired damping but the contact between the disk slot platform and blade-root lobes is characterized by uncertainty due to the actual locking position and machining tolerances.The cases of two simple beams and a bladed-disk test rig of an array of blades with dovetail root joints are studied to identify contact parameters. A dynamic Lagrange multiplier frequency based sub-structuring (LM-FBS) method is applied in a hybrid manner (experimental and numerical frequency response functions) to identify a parameter associated to each contact by mounting only one blade at a time. A sensitivity analysis is performed that will provide the basis for future work on non-linear frequency response prediction.

Temperature gradient effect on dynamic properties of a polymeric circular cylindrical shell

In this paper, an experimental study on the dynamic of cylindrical shells made of Polyethylene terephthalate (PET) is presented; a thermic gradient has been applied on a specimen of the present work to obtain a functionally gradient material (FGM) equivalent properties: the PET shell had been exposed at a thermal temperature gradient in the range of its glass transition temperature of 79 °C. A complex setup has been specifically designed and built to characterise, with dynamic tests, the structural properties of the specimen on temperature change from −10 °C up to about 90 °C and under thermic gradient with different forcing load. Predicting the mechanical properties of shells, panels and plates is one of the main concerns of structural engineers; since shell elements present complicated stability behaviours, rich linear vibration spectra (high modal density), high sensitivity to perturbations and strong interactions with surrounding elements. The linear and dynamic behaviour have been investigated. The shell behaviour is also investigated by means of a finite element model, in order to enhance the comprehension of experimental results.

Competing optical instruments for the estimation of Full Field FRFs

Thanks to the progress of optical measurement systems, known to use non-contact transducers (with their own peculiarities, application domains and drawbacks), nowadays addressing complex testing problems, especially direct dynamic measurements and modal analyses on lightweight structural components, is becoming even more common than in the recent past. Furthermore, obtaining vibration patterns with optical gears, in broad frequency bands with high spatial resolution, is easier than before, for the advantage of many advanced applications in vibration engineering, testing and product development.The characteristics and uniqueness of three different measurement technologies, based on distinguished physics and processing grounds, are here compared on a shared test rig with multiple excitations. SLDV, Hi-Speed DIC and Dynamic ESPI are here challenged in a complex and unique matching test for the estimation of FRFs with high spatial resolution, exploiting, as benchmark of the methodologies, a vibrating lightweight rectangular plate. The plate was selected for its exhibiting a broad band dynamics with high modal density and potentially repeated and closely spaced roots in the common frequency domain, where the techniques can find an operative intersection. The comparison of estimated FRFs and related Coherences, here as quality features of the measurements, is detailed with specific notes on acquisition and processing techniques, in order to draw extended conclusions on the full field measurement approaches, specific gears and the multiple excitation sources. The peculiar pointwise procedure, here proposed in details as the minimal paradigm to make a meaningful comparison, is addressed by means of discrete geometry transforms to put all the three technologies on an effective and consistent trial at each physical location of the real surface.The obtained results are a significant step forward in understanding the cross comparison of what these optical technologies, which belong to different domains and developing paths, can offer nowadays to further extend the experimental characterisation of vibrating components.

Dominant vibration modes for broadband frequency analysis of multiscale structures with numerous local vibration modes

SummaryIn this paper, an extension of modal analysis in linear computational structural dynamics is presented to deal with complex structures characterized by the presence of numerous local vibration modes and for which the high modal density leads to high‐dimension reduced‐order models. These local modes consist of isolated vibrations that are dissociated from the global vibrations of the structure skeleton and that turn out to often be of negligible contribution to the global dynamics. Therefore, an automatic mode sorting procedure is proposed to extract the dominant modes that represent the global dynamics of the skeleton. Next, an alternative filtering methodology based on a modified eigenvalue problem is presented, which allows to build, a priori, a small‐dimension reduced‐order basis of dominant global modes. The two methods are compared to classic modal analysis using three applications, namely, a heterogeneous plate, a simplified nuclear fuel assembly, and a detailed boiling water reactor fuel assembly.