Limited Number Of Modes Research Articles

Topology optimization design of multi-modal resonators for metamaterial panels with maximized broadband vibroacoustic attenuation

Resonant metamaterial panels can achieve exceptional vibroacoustic attenuation by subwavelength local resonators attached to a host structure. While single-mode resonators provide improvements only in a narrow band, recent advancements propose multi-modal resonators for broadband attenuation. However, existing designs utilize only a limited number of modes, and effective methodologies are lacking to systematically design resonator layouts that achieve an appropriate amount of resonances across the target frequency range, with an adequate participating mass. In this study, we tackle this challenge by developing a dedicated topology optimization method for multi-modal resonator design in metamaterial panels. The method leverages effective thin plate modelling, i.e. a homogenized metamaterial representation through an effective mass density, which provides accurate and very efficient vibroacoustic predictions. The optimization objective is to maximize the broadband diffuse field sound transmission loss (STL) of the metamaterial panel while constraining mass. The optimization problem is solved by gradient-based mathematical programming, for which the necessary (adjoint) sensitivities of objective and constraints are derived. The efficacy of the proposed topology optimization approach is demonstrated by targeting the suppression of coincidence dips in orthotropic host plates. For narrowband coincidence dips, the optimized resonator exhibits maximized mass participation in one single mode of interest. For broadband coincidence dips, the method effectively generates multi-modal resonators with up to 6 resonances distributed across the target frequency range. It is finally demonstrated that the topology-optimized designs surpass the performance of simpler, parametrically optimized multi-modal resonator layouts, as well as of conventional treatments by a damping layer of rubber.

Variational three-field reduced order modeling for nearly incompressible materials

This study presents an innovative approach for developing a reduced-order model (ROM) tailored specifically for nearly incompressible materials at large deformations. The formulation relies on a three-field variational approach to capture the behavior of these materials. To construct the ROM, the full-scale model is initially solved using the finite element method (FEM), with snapshots of the displacement field being recorded and organized into a snapshot matrix. Subsequently, proper orthogonal decomposition is employed to extract dominant modes, forming a reduced basis for the ROM. Furthermore, we efficiently address the pressure and volumetric deformation fields by employing the k-means algorithm for clustering. A well-known three-field variational principle allows us to incorporate the clustered field variables into the ROM. To assess the performance of our proposed ROM, we conduct a comprehensive comparison of the ROM with and without clustering with the FEM solution. The results highlight the superiority of the ROM with pressure clustering, particularly when considering a limited number of modes, typically fewer than 10 displacement modes. Our findings are validated through two standard examples: one involving a block under compression and another featuring Cook’s membrane. In both cases, we achieve substantial improvements based on the three-field mixed approach. These compelling results underscore the effectiveness of our ROM approach, which accurately captures nearly incompressible material behavior while significantly reducing computational expenses.

Resonance of “subhemispherical” water balloons: Shape analysis and frequency prediction

Water balloons and water drops are different objects, yet the work by Chang [“On the similarities between the resonance behaviors of water balloons and water drops,” Phys. Fluids 32, 124113 (2020)] reveals the similarities between their resonance behaviors. Chang's work focuses on the balloons with pinning angles beyond 90° (superhemispherical balloons), and the results are based on a limited number of modes. In this study, the resonance of balloons with pinning angles below 90° (subhemispherical balloons) is examined. The setup is similar to that for Chang's work, except each balloon is enlarged to possess a larger inertia, and a correlation-based method is adopted to visualize the balloon's oscillation. With these improvements, this study successfully discovers more than 37 modes, many of them have not been reported in the literature. For these modes, a catalogue is constructed to demonstrate their one-to-one correspondence to the modes of drops. Additionally, a scaling scheme is proposed to assimilate the resonance frequencies of subhemispherical balloons and drops. With these, this study provides a simple framework for predicting a subhemispherical water balloon's resonance with a theory for the resonance of sessile drops on a flat plate.

High-Efficiency Orbital Angular Momentum Beams Multiplexing System With Compact Shaper and Transformation Optics

In recent years, mode-division multiplexing (MDM) has been intensively proposed to cope with the information capacity crisis. However, how to multiplex a large number of OAM modes efficiently with low insertion loss and broad bandwidth is still a crucial issue. To solve this problem, we design a multiplexing system in which we make two functional blocks including a compactable shaper and a pair of free-form refractive optical elements. In one block, a self-designed compactable shaper is used to turn the Gaussian beam output from a single mode fiber into the elongated beams with tilted plane wave so that it can meet the phase requirement for the subsequently transformation. In the other block, a pair of free-form refractive optical elements is reversely used to multiplex multi modes based on coordinate transformations. Based on these structures, OAM multiple modes multiplexing experiment has been successfully performed in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C+L</i> band and the insertion losses of all modes are less than 1.6 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dB</i> . Furthermore, in the limited number of modes, the energy insertion loss does not increase with the increase of the number of OAM modes. The scheme offers a great potential for the integration in the next platform of MDM.

Influence of doping on stimulated Brillouin scattering slow light in few-mode fibers

• A few mode fiber based on SDM is used to realize slow light. • There are a limited number of modes with small inter-mode interference. • The tunable slow light of different modes can be achieved via SBS. • The results provide reference for designing optical buffers or slow light devices. In this paper, characteristics of tunable slow light of different modes based on intramodal stimulated Brillouin scattering in a few-mode fiber are calculated by the full-vector finite element method. In addition, the influences of doping concentration (GeO 2 doped) on the effective refractive index, effective mode area, Brillouin frequency shift, Brillouin threshold, time delay and pulse broadening factor of each mode in the few-mode fiber are also simulated. The simulation results indicate that the effective mode area, Brillouin frequency shift and Brillouin threshold of each mode decrease with the increase of doping concentration, but time delay exhibits an opposite behavior. Time delay of LP 01 mode is greater than that of LP 11 mode for a given doping concentration. When the doping concentration increases from 1.2% to 2.4%, time delay of LP 01 ( LP 11 ) mode increases from 291 ns (64 ns) to 384 ns (187 ns) at a given input pump power of 0.5 W and the effective fiber length of 2 km, meanwhile the corresponding broadening factor varies from 1.17 (1.04) to 1.22 (1.11).

Quantum algorithm for simulating molecular vibrational excitations.

The excitation of vibrational modes in molecules affects the outcome of chemical reactions, for example by providing molecules with sufficient energy to overcome activation barriers. In this work, we introduce a quantum algorithm for simulating molecular vibrational excitations during vibronic transitions. We discuss how a special-purpose quantum computer can be programmed with molecular data to optimize a vibronic process such that desired modes get excited during the transition. We investigate the effect of such excitations on selective bond dissociation in pyrrole and butane during photochemical and mechanochemical vibronic transitions. The results are discussed with respect to experimental observations and classical simulations. We also introduce quantum-inspired classical algorithms for simulating molecular vibrational excitations in special cases where only a limited number of modes are of interest.

Real-Time Aerodynamics Hybrid Simulation: A Novel Wind-Tunnel Model for Flexible Bridges

Despite rapid development in computational fluid dynamics, semiempirical analyses based on parameters identified from spring-mounted sectional models are still widely used to examine wind-induced effects on bridges. In addition, wind tunnel results from full-bridge aeroelastic models, viewed as the most comprehensive representations, are typically a final check for wind design of long-span cable-supported bridges. There are several well-known limitations associated with conventional wind tunnel testing of both sectional and full-bridge models. For example, structural nonlinearities and large deformations are difficult to simulate in sectional models, and only a limited number of modes can be accurately simulated in full-bridge aeroelastic models. To advance aeroelastic modeling of flexible bridges in the wind tunnel, a slightly different version of the real-time hybrid simulation (RTHS) techniques, frequently used in various branches of engineering, is developed here. Specifically, the skeleton of the sectional or full-bridge model, characterizing the dynamic properties (e.g., mass, damping, and stiffness of the structure), is numerically simulated using computational structural dynamics, while its skin, characterizing the aerodynamic and aeroelastic properties, is physically modeled in the wind tunnel. Aerodynamic inputs (gusts) are applied directly on the skin in the wind tunnel, while aeroelastic inputs (motions) are represented by the simulation outputs of the bridge skeleton. On the other hand, the dynamic inputs to the bridge skeleton are acquired from the measured forces (and moments) on the bridge skin. The interactions between the skeleton and skin of the bridge are accomplished through a system consisting of sensors, a network of electromagnetic actuators, and controllers. The time history of the wind-induced bridge responses can be obtained at the end of the proposed real-time aerodynamics hybrid simulation (RTAHS). The feasibility of the RTAHS methodology is demonstrated by a numerical example involving both linear and nonlinear wind-induced forces on the bridge deck.

Proper Orthogonal Decomposition of Self-Induced Instabilities in Decelerated Swirling Flows and Their Mitigation Through Axial Water Injection

The swirling flow exiting the runner of a hydraulic turbine is further decelerated in the discharge cone of the draft tube to convert the excess of dynamic pressure into static pressure. When the turbine is operated far from the best efficiency regime, particularly at part load, the decelerated swirling flow develops a self-induced instability with a precessing helical vortex and the associated severe pressure fluctuations. This phenomenon is investigated numerically in this paper, for a swirl apparatus configuration. The unsteady three-dimensional (3D) flow field is analyzed using a proper orthogonal decomposition (POD), and within this framework we examine the effectiveness of an axial jet injection for mitigating the flow instability. It is shown that a limited number of modes can be used to reconstruct the flow field. Moreover, POD enables to reveal influence of the jet injection on the individual modes of the flow and illustrates continuous suppression of the modes from higher-order modes to lower-order modes as the jet discharge increases. Application of POD offers new view for the future control effort aimed on vortex rope mitigation because spatiotemporal description of the flow is provided. Thereby, POD enables better focus of the jets or other flow control devices.

The potential of asteroseismology for probing the core chemical stratification in white dwarf stars

Context. The details of the C/O core structure in white dwarf stars has mostly remained inaccessible to the technique of asteroseismology, despite several attempts carried out in the past. Aims. We aim to re-assess the potential of asteroseismology for probing the chemical stratification in white dwarf cores, in light of new highly efficient tools recently developed for that purpose. Methods. Using the forward modeling approach and a new parameterization for the core chemical stratification in ZZ Ceti stars, we tested several situations typical of the usually limited constraints available, such as small numbers of observed independent modes, to carry out asteroseismology of these stars. Results. We find that, even with a limited number of modes, the core chemical stratification (in particular, the location of the steep chemical transitions expected in the oxygen profile) can be determined quite precisely due to the significant sensitivity of some confined modes to partial reflexion (trapping) effects. These effects are similar to the well known trapping induced by the shallower chemical transitions at the edge of the core and at the bottom of the H-rich envelope. We also find that success to unravel the core structure depends on the information content of the available seismic data. In some cases, it may not be possible to isolate a unique, well-defined seismic solution and the problem remains degenerate. Conclusions. Our results establish that constraining the core chemical stratification in white dwarf stars based solely on asteroseismology is possible, an opportunity that we have begun to exploit.

Determining the core stratification in white dwarfs with asteroseismology

Using the forward modeling approach and a new parameterization for the core chemical stratification in ZZ Ceti stars, we test several situations typical of the usually limited constraints available, such as small numbers of observed independent modes, to carry out asteroseismology of these stars. We find that, even with a limited number of modes, the core chemical stratification (in particular, the location of the steep chemical transitions expected in the oxygen profile) can be determined quite precisely due to the significant sensitivity of some confined modes to partial reflexion (trapping) effects. These effects are similar to the well known trapping induced by the shallower chemical transitions at the edge of the core and at the bottom of the H-rich envelope. We also find that success to unravel the core structure depends on the information content of the available seismic data. In some cases, it may not be possible to isolate a unique, well-defined seismic solution and the problem remains degenerate. Our results establish that constraining the core chemical stratification in white dwarf stars based solely on asteroseismology is possible, an opportunity that we have started to exploit.

What portion of the soft tissue artefact requires compensation when estimating joint kinematics?

When joint kinematics is analyzed using noninvasive stereophotogrammetry, movements of the skin markers relative to the underlying bone are regarded as artefacts (soft tissue artefact (STA)). Recent literature suggests that an appropriate estimation of joint kinematics may be obtained by compensating for only a portion of the STA, but no evidence for this case has been reported, and which portion of the STA should be selected remains an issue. The aim of this study was to fill this gap. A modal approach was used to represent the STA. This resulted in a series of additive components (modes) and in the possibility to select a subset of them. The following STA definitions were used: individual skin marker displacement (MD), marker-cluster geometrical transformation (GT), and skin envelope shape variation (SV). An STA approximation for each of the three definitions was obtained by ordering modes on the basis of their contribution to the total STA energy and truncating the relevant series at 90% of it. A fourth approximation was obtained when the GT definition was used, by selecting the modes that represented the marker-cluster rigid transformation (i.e., three translation and three rotation modes). The different STA approximations were compared using data obtained during the stance phase of running of three volunteers carrying both pin and skin markers. The STA was measured and knee joint kinematics estimated using four skin marker datasets compensated for the above-mentioned STA approximations. Accuracy was assessed by comparing results to the reference kinematics obtained using pin markers. The different approximations resulted in different numbers of modes. For joint angles, the compensation efficiency across the STA approximations based on an energy threshold was almost equivalent. The median root mean square errors (RMSEs) were below 1 deg for flexion/extension and 2 deg for both abduction/adduction and internal/external rotation. For the joint displacements, the compensation efficiency depended on the STA approximation. Median RMSEs for anterior/posterior displacement ranged from 1 to 4 mm using either MD, GT, or SV truncated series. The RMSEs were virtually null when the STA was approximated using only the GT rigid modes. This result, together with the limited number of modes used by this approximation (i.e., three translations and three rotations of the marker-cluster), makes the STA rigid component and a good candidate for designing an STA model to be incorporated in an enhanced bone pose estimator.

A numerical and experimental study on viscoelastic damping of a 3D structure

Structural vibrations often cause problems in high precision instruments, which may be solved by introducing passive damping. In this paper, different ways of introducing passive damping via viscoelastic materials (VEM) are discussed. Discrete damping elements and constrained layer (CL) configurations are selected and used to efficiently damp an open aluminum box. For the constrained layer configurations, a distinction is made between full and partial coverage of the structure. The steady-state dynamics of the box are simulated using a finite element (FE) model, which includes frequency dependent VEM properties. This model is used to find a design that possesses high damping while taking into account design constraints. The simulation results are experimentally validated using both modal parameters and frequency response functions (FRFs). For the computation of model based FRFs, a new method based on Interpolated Modal Parameter Superposition (IMPS) is proposed. Model based results and experimental results show good resemblance, even without updating the model with deviations in the realized structure. The local dampers add most damping to a limited number of modes. Partially covering the box with CL dampers is found to be more effective than full coverage of the structure with the same mass addition.

A submicron plasmonic dichroic splitter

Spectral imaging and sensing techniques, new solar cell designs and wavelength-division multiplexing in optical communication rely on structures that collect and sort photons by wavelength. The strong push for chip-scale integration of such optical components has necessitated ultracompact, planar structures, and fomented great interest in identifying the smallest possible devices. Consequently, novel micro-ring, photonic crystal and plasmonic solutions have emerged. Meanwhile, the optical coupling of subwavelength plasmonic structures supporting a very limited number of modes has also enabled new functionalities, including Fano resonances and structural electromagnetically-induced transparency. Here we show how two similarly sized subwavelength metal grooves can form an ultracompact submicron plasmonic dichroic splitter. Each groove supports just two electromagnetic modes of opposite symmetry that allows independent control of how a groove collects free-space photons and directs surface plasmon polaritons. These results show how the symmetry of electromagnetic modes can be exploited to build compact optical components.

On the treatment of finite element structures in stochastic linear dynamics using a mode-based meta-model

Abstract This contribution presents a meta-model of the structural modes, which can be used for efficient dynamic analysis of finite element structures in the presence of uncertainties in the loading and structural parameters. The main goal consists in cutting down the computational time required for the repeated number of analyses in order to assess the impact of the uncertainties. The meta-model allows for an efficient evaluation of the structural modes which are represented as a linear combination of the modes of a reference solution. The calibration of the meta-model is based on the modes of about 30–50 samples of the structure obtained with Monte Carlo simulation. The mode-based meta-model can always be advantageously employed when a limited number of modes are required for analysis, such as, e.g. for mode superposition analysis. The numerical examples show the utilization of the meta-model for various applications such as uncertainty analysis, reliability assessment and design optimization.

A hybrid modal analysis for enclosed sound fields

A hybrid modal expansion that combines the free field Green's function and a modal expansion will be presented in this paper based on a review and an extension of the existing modal analysis theories for the sound field in enclosures. The enclosed sound field will be separated into the direct field and reverberant field, which have been treated together in the traditional modal analysis. Studies on a point source in rectangular enclosures show that the hybrid modal expansion converges notably faster than the traditional modal expansions, especially in the region near the source, and introduces much smaller errors with a limited number of modes. The hybrid modal expansion can be easily applied to complex sound sources if the free field responses of the sources are known. Damped boundaries are also considered in this paper, and a set of modified modal functions is introduced, which is shown to be suitable for many damped boundary conditions.

Oscillations in the primordial bispectrum: Mode expansion

We consider the presence of oscillations in the primordial bispectrum, inspired by three different cosmological models; features in the primordial potential, resonant type non-Gaussianities and deviation from the standard Bunch Davies vacuum. In order to put constraints on their bispectra, a logical first step is to put these into factorized form which can be achieved via the recently proposed method of polynomial basis expansion on the tetrahedral domain. We investigate the viability of such an expansion for the oscillatory bispectra and find that one needs an increasing number of orthonormal mode functions to achieve significant correlation between the expansion and the original spectrum as a function of their frequency. To reduce the number of modes required, we propose a basis consisting of Fourier functions orthonormalized on the tetrahedral domain. We show that the use of Fourier mode functions instead of polynomial mode functions can lead to the necessary factorizability with the use of only 1/5 of the total number of modes required to reconstruct the bispectra with polynomial mode functions. Moreover, from an observational perspective, the expansion has unique signatures depending on the orientation of the oscillation due to a resonance effect between the mode functions and the original spectrum. This effect opens the possibility to extract informa- tion about both the frequency of the bispectrum as well as its shape while considering only a limited number of modes. The resonance effect is independent of the phase of the reconstructed bispectrum suggesting Fourier mode extraction could be an efficient way to detect oscillatory bispectra in the data.

Sensitivity and optimal forcing response in separated boundary layer flows

The optimal asymptotic response to time harmonic forcing of a convectively unstable two-dimensional separated boundary layer on a flat plate is numerically revisited from a global point of view. By expanding the flow disturbance variables and the forcing term as a summation of temporal modes, the linear convective instability mechanism associated with the response leading to the maximum gain in energy is theoretically investigated. Such a response is driven by a pseudoresonance of temporal modes due to the non-normality of the underlying linearized evolution operator. In particular, the considered expansion on a limited number of modes is found able to accurately simulate the linear instability mechanism, as suggested by a comparison between the global linear stability analysis and a linearized direct numerical simulation. Furthermore, the dependence of such a mechanism on the Reynolds number and the adverse pressure gradient is investigated, outlining a physical description of the destabilization of the flow induced by the rolling up of the shear layer. Therefore, the convective character of the problem suggests that the considered flat plate separated flows may act as a selective noise amplifier. In order to verify such a possibility, the responses of the flow to the optimal forcing and to a small level of noise are compared, and their connection to the onset of self-excited vortices observed in literature is investigated. For that purpose, a nonlinear direct numerical simulation is performed, which is initialized by a random noise superposed to the base flow at the inflow boundary points. The band of excited frequencies as well as the associated peak match with the ones computed by the asymptotic global analysis. Finally, the connection between the onset of unsteadiness and the optimal response is further supported by a comparison between the optimal circular frequency and a typical Strouhal number predicted by numerical simulations of previous authors in similar cases.

On the propagation of uncertainty in inflow turbulence to wind turbine loads

When stochastic simulation of inflow turbulence random fields is employed in the analysis or design of wind turbines in normal operating states, it is common to use well-established standard spectral models represented in terms of parameters that are usually treated as fixed or deterministic values. Studies have suggested, though, that many of these spectral parameters can exhibit some degree of variability. It is not unreasonable to expect, then, that derived flow fields based on simulation with such spectral models can be in turn highly variable for different realizations. Turbine load and performance variability would also be expected to result if response simulations are carried out with these variable flow fields. The aim here is to assess the extent of variability in derived inflow turbulence fields that arises from the noted variability in spectral model parameters. Simulation of these parameters as random variables forms the basis of this study. A commercial-sized 1.5 MW concept wind turbine is considered in the numerical studies. Variability in turbulence power spectra at field points on the rotor plane and in turbulence coherence functions for separations on the order of a rotor diameter and smaller is studied. Using time domain simulations, variability in various wind turbine response measures is also studied where the focus is on statistics such as response root-mean-square and 10-min extreme estimates. It is seen that while variability in inflow turbulence spectra can be great, the variability in turbine loads is generally considerably lower. One exception is for turbine yaw loads whose larger variability arises due to sensitivity to a coherence decay parameter that is itself highly variable. Finally, because reduced-order representations of turbulence random fields using empirical orthogonal decomposition techniques allow useful physical insights into spatial patterns of flow, variability in the energy distribution and the shapes of such empirical eigenmodes is studied and a simplified model is proposed that retains key variability sources in a limited number of modes and that accurately preserves overall inflow turbulence field uncertainty.

Reference-based combined deterministic–stochastic subspace identification for experimental and operational modal analysis

The modal analysis of mechanical or civil engineering structures consists of three steps: data collection, system identification and modal parameter estimation. The system identification step plays a crucial role in the quality of the modal parameters, that are derived from the identified system model, as well as in the number of modal parameters that can be determined. This explains the increasing interest in sophisticated system identification methods for both experimental and operational modal analysis. In purely operational or output-only modal analysis, absolute scaling of the obtained mode shapes is not possible and the frequency content of the ambient forces could be narrow banded so that only a limited number of modes are obtained. This drives the demand for system identification methods that take both artificial and ambient excitation into account so that the amplitude of the artificial excitation can be small compared to that of the ambient excitation. An accurate, robust and efficient system identification method that meets this requirements is combined deterministic–stochastic subspace identification. It can be used both for experimental modal analysis and for operational modal analysis with deterministic inputs. In this paper, the method is generalized to a reference-based version which is faster and, if the chosen reference outputs have the highest SNR values, more accurate than the classical algorithm. The algorithm is validated with experimental data from the Z24 bridge that overpassing the A1 highway between Bern and Zurich in Switzerland, that have been proposed as a benchmark for the assessment of system identification methods for the modal analysis of large structures. With the presented algorithm, the most complete set of modes reported so far is obtained.

Recirculating beam-breakup thresholds for polarized higher-order modes with optical coupling

Here we will derive the general theory of the beam-breakup (BBU) instability in recirculating linear accelerators with coupled beam optics and with polarized higher-order dipole modes. The bunches do not have to be at the same radio-frequency phase during each recirculation turn. This is important for the description of energy recovery linacs (ERLs) where beam currents become very large and coupled optics are used on purpose to increase the threshold current. This theory can be used for the analysis of phase errors of recirculated bunches, and of errors in the optical coupling arrangement. It is shown how the threshold current for a given linac can be computed and a remarkable agreement with tracking data is demonstrated. General formulas are then analyzed for several analytically solvable problems: (a) Why can different higher order modes (HOM) in one cavity couple and why can they then not be considered individually, even when their frequencies are separated by much more than the resonance widths of the HOMs? For the Cornell ERL as an example, it is noted that optimum advantage is taken of coupled optics when the cavities are designed with an x-y HOM frequency splitting of above 50 MHz. The simulated threshold current is then far above the design current of this accelerator. To justify that the simulation can represent an actual accelerator, we simulate cavities with 1 to 8 modes and show that using a limited number of modes is reasonable. (b) How does the x-y coupling in the particle optics determine when modes can be considered separately? (c) How much of an increase in threshold current can be obtained by coupled optics and why does the threshold current for polarized modes diminish roughly with the square root of the HOMs’ quality factors. Because of this square root scaling, polarized modes with coupled optics increase the threshold current more effectively for cavities that have rather large HOM quality factors, e.g. those without very elaborate HOM absorbers. (d) How does multiple-turn recirculation interfere with the threshold improvements obtained with a coupled optics? Furthermore, the orbit deviations produced by cavity misalignments are also generalized to coupled optics. It is shown that the BBU instability always occurs before the orbit excursion becomes very large.