System Eigenmodes Research Articles

Output-only modal identification with recursive dynamic mode decomposition for time-varying systems

The time-varying modal identification is a prominent analytical means but challenging task to grasp the dynamic characteristics of time-varying systems, which is important guarantee for real-time control and on-line health monitoring of many engineering structures. In this paper, a data-driven approach for time-varying modal identification without requiring parametric modeling about underlying system is presented. Firstly, the fundamental theory for Dynamic Mode Decomposition (DMD) is reviewed combining the Koopman operator. Subsequently, the DMD incorporated into operational modal identification is examined from the perspective of linear system, and the inner connection between modal parameters of vibration system and eigenvalues and eigenmodes of DMD is established. On the basis of that, a weighted recursive strategy integrated with DMD is employed to investigate the capability of time-varying modal identification, and the main identification procedures are elaborated. Finally, the effectiveness and practicability of the proposed method in extracting modal properties of time-varying systems are investigated by a numerical and experiment example. The results demonstrate that, compared to other methods, the proposed approach has high computational efficiency while ensuring the identification accuracy, exhibiting a good engineering application prospect.

Application of metal rubber for semi-active vibration control of mechanical transmission systems

This study proposes a novel semi-active vibration control technique for mechanical transmission systems. The backbone of current research technology is the adaptive stiffness and damping properties of metal rubber (MR) which plays the role of tuning to the vibrational system eigenmodes. The adaptive properties of MR material were proved by a previous study, but the present research investigates the effect of this feature on the structural response and designs an MR-based semi-active vibration controller for industrial application. For this purpose, the semi-active control strategy is created based on an optimal tuning using experimental harmonic test results. The control strategy is applied in practice using a linear actuator controlled by a double pole double throw (DPDT) relay, and National Instruments hardware and software for reading data and writing the control task. The isolator attachment position is defined through the analysis of eigenmode shapes that are predetermined by numerical simulation. A maximum isolation rate of 55.17% is measured near the vibration isolator position. It is observed that the isolation position has a prominent effect on structure vibration behavior where the elastic wave has been reduced in amplitude by passing the isolator position. The effectiveness of the MR-based semi-active control approach is eminent and its application for vibration isolation of commercial mechanical transmission systems could be studied in the future.

Network Topology Invariant Stability Certificates for DC Microgrids With Arbitrary Load Dynamics

DC microgrids are prone to small-signal instabilities due to the presence of tightly regulated loads. This paper develops a decentralized stability certificate which is capable of certifying the small-signal stability of an islanded DC network containing such loads. Utilizing a novel homotopy approach, the proposed standards ensure that no system eigenmodes are able to cross into the unstable right half plane for a continuous range of controller gain levels. The resulting “standards” can be applied to variety of grid components which meet the specified, but non-unique, criteria. These standards thus take a step towards offering <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">plug-and-play</i> operability of DC microgrids. The proposed theorems are explicitly illustrated and numerically validated on multiple DC microgrid test-cases containing both buck and boost converter dynamics.

Semianalytical approach to calculating the dynamic modes of magnetic vortices with Dzyaloshinskii-Moriya interactions

Here we introduce a Landau-Lifshitz based diagonalization (LLD) method, and use this approach to calculate the effects of the interfacial Dzyaloshinskii Moriya interactions (DMI) on the radial-type spin wave modes of magnetic vortices in circular disks. The LLD method is a semi-analytical approach that involves the diagonalization of the magnetostatic kernel, exchange, and DMI contributions to extract the system eigenfrequencies and eigenmodes. The magnetic vortex state provides a convenient model system in which to investigate the effects of the DMI on the dynamics of a magnetic structures with confined geometries. Our calculations show that the DMI leads to shifts of the mode frequencies that are similar in magnitude to what is observed for spin waves of a comparable wavelength in extended films. However, unlike what is found in thin films, only the down-shifted modes are observed in the disks, and these corresponds to modes that propagate either radially outward or inward, depending on the vortex circulation. The semi-analytical calculations agree well with full micromagnetic simulations. This technique also applies to other systems with cylindrical symmetry, for example, magnetic skyrmions.

Identification of fractional-order models for condition monitoring of solid-oxide fuel cell systems

With rising market deployment the condition monitoring of solid oxide fuel cell systems is gaining particular importance. The conventional approaches mainly use electrochemical impedance spectroscopy based on the repeated sinusoidal perturbation over a range of frequencies. One of the notable weaknesses of the approach is excessively long perturbation time needed to properly evaluate the impedance curve. In this paper, we propose a time-efficient approach in which, a short, persistently exciting and small-amplitude perturbation is used to excite all the relevant system eigenmodes. A model structure from a class of linear fractional order models is selected to describe the perturbed dynamics and to account for anomalous diffusion processes in the cells. Then, the model parameters are estimated directly from measured input and output records. The paper presents a computationally efficient parameter estimation procedure in which the numerical issues of differentiation of noisy signals are alleviated by using modulating functions. In practice, that means a combination of filtering and application of conventional least squares. The approach is applied on a case of health assessment of solid oxide fuel cells.

Whip velocity of backward whirl with slip in multiple-degree-of-freedom rotor-stator system

A mathematic model of flexible rotor for the backward rolling with slipping on compliant stator and an exception concept for the contact forces are suggested. Dynamic characteristics for the rotor whirling are determined by the matrix methods. The whirl velocity can be calculated accurately, not only in case of a clear rolling when it is determined by the rotary velocity and a ratio of rotor radius at the contact place to radial clearance, but also in case of the backward slipping. It is shown for the second or whip case, the whip velocity is defined by some eigenfrequency of the supported rotor by the stator as well as by coefficients of the structural and contact friction. And in fact, the friction sets the whip frequency, and the i-th eigenmode of contactless system sets the whip amplitude (rotor deflections outside the contact place).

Symmetry-protected localized states at defects in non-Hermitian systems

Understanding how local potentials affect system eigenmodes is crucial for experimental studies of nontrivial bulk topology. Recent studies have discovered many exotic and highly non-trivial topological states in non-Hermitian systems. As such, it would be interesting to see how non-Hermitian systems respond to local perturbations. In this work, we consider chiral and particle-hole -symmetric non-Hermitian systems on a bipartite lattice, including SSH model and photonic graphene, and find that a disordered local potential could induce bound states evolving from the bulk. When the local potential on a single site becomes infinite, which renders a lattice vacancy, chiral-symmetry-protected zero-energy mode and particle-hole symmetry-protected bound states with purely imaginary eigenvalues emerge near the vacancy. These modes are robust against any symmetry-preserved perturbations. Our work generalizes the symmetry-protected localized states to non-Hermitian systems.

Efficient method for calculating Raman spectra of solids with impurities and alloys and its application to two-dimensional transition metal dichalcogenides

Raman spectroscopy is a widely used, powerful, and nondestructive tool for studying the vibrational properties of bulk and low-dimensional materials. Raman spectra can be simulated using first-principles methods, but due to the high computational cost calculations are usually limited only to fairly small unit cells, which makes it difficult to carry out simulations for alloys and defects. Here, we develop an efficient method for simulating Raman spectra of alloys, benchmark it against full density-functional theory calculations, and apply it to several alloys of two-dimensional transition metal dichalcogenides. In this method, the Raman tensor for the supercell mode is constructed by summing up the Raman tensors of the pristine system weighted by the projections of the supercell vibrational modes to those of the pristine system. This approach is not limited to 2D materials and should be applicable to any crystalline solids with defects and impurities. To efficiently evaluate vibrational modes of very large supercells, we adopt mass approximation, although it is limited to chemically and structurally similar atomic substitutions. To benchmark our method, we first apply it to Mo$_x$W$_{(1-x)}$S$_2$ monolayer in the H-phase, where several experimental reports are available for comparison. Second, we consider Mo$_x$W$_{(1-x)}$Te$_2$ in the T'-phase, which has been proposed to be 2D topological insulator, but where experimental results for the monolayer alloy are still missing. We show that the projection scheme also provides a powerful tool for analyzing the origin of the alloy Raman-active modes in terms of the parent system eigenmodes. Finally, we examine the trends in characteristic Raman signatures for dilute concentrations of impurities in MoS$_2$.

Second harmonic generation from strongly coupled localized and propagating phonon-polariton modes

We experimentally investigate second harmonic generation from strongly coupled localized and propagative phonon polariton modes in arrays of silicon carbide nanopillars. Our results clearly demonstrate the hybrid nature of the system's eigenmodes and distinct manifestation of strong coupling in the linear and nonlinear response. While in linear reflectivity the intensity of the two strongly-coupled branches is essentially symmetric and well explained by their respective localized or propagative components, the second harmonic signal presents a strong asymmetry. Analyzing it in detail, we reveal the importance of interference effects between the nonlinear polarization terms originating in the bulk and in the phonon polariton modes, respectively.

Simultaneous Evolution of Gyre and Atlantic Meridional Overturning Circulation Anomalies as an Eigenmode of the North Atlantic System

The authors identify an interdecadal oscillatory mode of the North Atlantic atmosphere–ocean system in a general circulation model (GFDL CM2.1) via a linear inverse model (LIM). The oscillation mechanism is mostly embedded in the subpolar gyre: anomalous advection generates density anomalies in the eastern subpolar gyre, which propagate along the mean gyre circulation and reach the subpolar gyre center around 10 years later, when associated anomalous advection of the opposite sign starts the other half cycle. As density anomalies reach the Labrador Sea deep convection region, Atlantic meridional overturning circulation (AMOC) anomalies are also induced. Both the gyre and AMOC anomalies then propagate equatorward slowly, following the advection of density anomalies. The oscillation is further demonstrated to be more likely an ocean-only mode while excited by the atmospheric forcing; in particular, it can be approximated as a linearly driven damped oscillator that is partly excited by the North Atlantic Oscillation (NAO). The slowly evolving interdecadal oscillation significantly improves and prolongs the LIM’s prediction skill of sea surface temperature (SST) evolution.

Flat Plate Honeycomb Seals Friction Factor Analysis

Among the various types of seals used in gas turbine secondary air system to guarantee sufficient confinement of the main gas path, honeycomb seals perform well in terms of enhanced stability and reduced leakage flow. Due to the large amount of honeycomb cells typically employed in real seals, it is generally convenient to treat the sealing effect of the honeycomb pack as an increased distributed friction factor on the plain top surface. That is why, this analysis is focused on a simple configuration composed by a honeycomb facing a flat plate. In order to evaluate the sealing performance of such honeycomb packs, an experimental campaign was carried out on a stationary test rig where the effects of shaft rotation are neglected. The test rig was designed to analyze different honeycomb geometries so that a large experimental database could be created to correlate the influence of each investigated parameter. Honeycomb seals were varied in terms of hexagonal cell dimension and depth in a range that represents well actual honeycomb packs employed in industrial compressors. For each geometry, seven different clearances were tested. This work reports the findings of such experimental campaign whose results were analyzed in order to guide actual seals design and effective estimates of shaft loads. Static pressure measurements reveal that the effects of investigated geometrical parameters on friction factor correlate well with a corrected Mach number based on the cell depth. The presence of acoustic effects in the seals was further investigated by means of hot wire anemometry. Acoustic forcing due to flow cavity interaction was found to be characterized by a constant Strouhal number based on cell geometry. Numerical simulations helped in the identification of system eigenmodes and eigenfrequencies providing an explanation to the friction factor enhancement triggered at a certain flow speed. Finally, the generated dataset was tested comparing the predicted leakage flow with experimental data of actual seals (with high pressure and high rotational speed) showing a very good agreement.

Unconventional collective normal-mode coupling in quantum-dot-based bimodal microlasers

We analyze the occurrence of normal-mode coupling (NMC) in bimodal lasers attributed to the collective interaction of the cavity field with a mesoscopic number of quantum dots (QDs). In contrast to the conventional NMC, here we observe locking of the frequencies and splitting of the linewidths of the system's eigenmodes in the coherent coupling regime. The theoretical analysis of the incoherent regime is supported by experimental observations where the emission spectrum of one of the orthogonally polarized modes of a bimodal QD micropillar laser demonstrates a distinct two-peak structure.

Optimal limits of cavity optomechanical cooling in the strong-coupling regime

Laser cooling of mesoscopic mechanical resonators is of great interest for both fundamental studies and practical applications. We provide a general framework to describe the cavity-assisted backaction cooling in the strong coupling regime. By studying the cooling dynamics, we find that the temporal evolution of mean phonon number oscillates as a function of the optomechanical coupling strength depending on frequency mixing. The further analytical result reveals that the optimal cooling limit is obtained when the system eigenmodes satisfy the frequency matching condition. The reduced instantaneous-state cooling limits with dynamic dissipative cooling approach are also presented. Our study provides a guideline for optimizing the backaction cooling of mesoscopic mechanical resonators in the strong coupling regime.

Ultrafast optical bleaching of intersubband cavity polaritons

We report on the transition from the strong to the weak light-matter coupling regime between an intersubband excitation and a photonic crystal resonance in a nanostructured semiconductor membrane. Such a transition is induced by varying the intensity of an ultrafast light pulse, which is employed for pumping and probing the system eigenmodes. The phenomenon is interpreted in terms of the saturation of the intersubband transition due to the large number of photoexcited electrons in the quantum well, as confirmed by a thorough analysis performed both in frequency and time domain.

Thermalization in systems with bipartite eigenmode entanglement

It is analytically shown that the asymptotic correlations following a quantum quench in exactly solvable models can sometimes look essentially thermal provided the initial coupling between the system eigenmodes induces a large gap. We study this phenomenon using simple models, which also illustrate the relationship between the entanglement spectrum of the initial state and the generalized Gibbs ensemble describing the long-time correlations after the quench. We also show that the effective temperature characterizing the correlations is not related to the energy fluctuations after the quench, and therefore does not have thermodynamic meaning. The latter observation implies a breakdown of the fluctuation–dissipation theorem.

Optimal spatial sampling scheme for parameter estimation of nonlinear distributed parameter systems

In this paper a methodology for the estimation of parameters of distributed parameter systems based on optimal spatial measurements is discussed. The concept of the covariance matrix for sampling design is exploited and D-optimality criteria concerning relevant metrics are linked with the computation of optimal measurement locations. These are obtained at the points where sensitivity functions reach their extrema values and coincide with the locations where system eigenmodes obtained by proper orthogonal decomposition (POD) are maximised or minimised as has been shown in a recent work (Alaña & Theodoropoulos, 2011). A tubular reactor with recycle is used as illustrative example to demonstrate the sampling methodology, including cases where the system behaviour is unstable exhibiting sustained oscillations. The estimates with the highest deviation from the nominal parameter values are the ones with the lowest (absolute) sensitivity coefficients. Using a POD-based reduced model can significantly reduce computational costs and in addition improve the estimation procedure by using measurements at the locations where the POD modes extrema occur. The results are strongly influenced by experimental noise, and filtering techniques are needed to mitigate the related uncertainties.

Fundamental limits for noncontact transfers between two bodies

We investigate energy and momentum non-contact exchanges between two arbitrary flat media separated by a gap. This problem is revisited as a transmission problem of individual system eigenmodes weighted by a transmission probability obtained either from fluctuational electrodynamics or quantum field theory. An upper limit for energy and momentum flux is derived using a general variational approach. The corresponding optimal reflectivity coefficients are given both for identical and different media in interaction.

Fluid-Structure Interaction Effects Modeling for the Modal Analysis of a Steam Generator Tube Bundle

Seismic analysis of steam generator is of paramount importance in the safety assessment of nuclear installations. These analyses require, in particular, the calculation of frequency, mode shape, and effective modal mass of the system eigenmodes. As fluid-structure interaction effects can significantly affect the dynamic behavior of immersed structures, the numerical modeling of the steam generator has to take into account FSI. A complete modeling of heat exchangers (including pressure vessel, tubes, and fluid) is not accessible to the engineer for industrial design studies. In the past decades, homogenization methods have been studied and developed in order to model tubes and fluid through an equivalent continuous media, thus avoiding the tedious task to mesh all structure and fluid subdomains within the tube bundle. Few of these methods have nonetheless been implemented in industrial finite element codes. In a previous paper (Sigrist, et al., 2007, “Fluid-Structure Interaction Effects Modeling for the Modal Analysis of a Nuclear Pressure Vessel,” J. Pressure Vessel Technol., 123, pp. 1–6), a homogenization method has been applied to an industrial case for the modal analysis of a nuclear rector with internal structures and coupling effects modeling. The present paper aims at investigating the extension of the proposed method for the dynamic analysis of tube bundles with fluid-structure interaction modeling. The homogenization method is compared with the classical coupled method in terms of eigenfrequencies, eigenmodes, and effective modal masses.

CFD-based application of the Nyquist criterion to thermo-acoustic instabilities

A novel approach for the analysis of self-excited instabilities in thermo-acoustic systems is proposed. Combining computational fluid dynamics with low-order acoustic modeling, the open-loop transfer function of the system under investigation is computed. The system eigenmodes and the linear stability characteristics are then deduced from a Nyquist plot. The method is suitable for systems where – due to geometrical complexities or non-compact regions of heat release – a low-order formulation is not appropriate or not available. Explicit knowledge of the frequency response or the transfer matrix of the heat source is not required. Further advantages of the new approach are discussed in the paper. To establish proof of concept, the method is validated against a simple model of a Rijke tube. Over the frequency range considered, frequencies and growth rates of stable as well as unstable eigenmodes are predicted accurately. The new method, combining flow simulation, low-order acoustic modeling and control theory, makes possible a comprehensive analysis of acoustic stability behavior of complex thermo-acoustic systems at comparatively modest computational cost.

Flow induced aeroacoustic oscillations in a tube with a region of abrupt cross‐sectional area increase

The phenomenon of aeroacoustic oscillations induced by flow through a circular tube with an annular cavity region formed by an abrupt area increase is studied. At the beginning of the area increase, the flow separates and produces a shear layer that subsequently impinges on the downstream end of this region. The shear layer is a medium for propagation of convective vorticity waves. In the surrounding cavity, axial acoustic wave propagation can occur. The central flow region is governed by the convective wave equation, and the simple wave equation applies in the cavity. Coupled axial modes are identifiable as being primarily convective or primarily acoustic. The oscillation mechanism involves the interaction of upstream acoustic modes and downstream convective modes, coupled together by boundary conditions, and driven by mass addition and removal at the rear of the annular cavity caused by shear layer impingement on downstream edge. The oscillation process is analyzed using a cross‐sectional averaging method for quasi one‐dimensional waves to determine system wavenumbers and eigenmodes. Oscillation frequencies are determined by the condition of maximum energy extraction from the mean flow, arising from unstable convective waves, and by a compatible shear layer phase condition. A comparison with simple experiments is presented.