Modal Expansion Research Articles

Fatigue Analysis of a Jacket-Supported Offshore Wind Turbine at Block Island Wind Farm.

Offshore wind-turbine (OWT) support structures are subjected to cyclic dynamic loads with variations in loadings from wind and waves as well as the rotation of blades throughout their lifetime. The magnitude and extent of the cyclic loading can create a fatigue limit state controlling the design of support structures. In this paper, the remaining fatigue life of the support structure for a GE Haliade 6 MW fixed-bottom jacket offshore wind turbine within the Block Island Wind Farm (BIWF) is assessed. The fatigue damage to the tower and the jacket support structure using stress time histories at instrumented and non-instrumented locations are processed. Two validated finite-element models are utilized for assessing the stress cycles. The modal expansion method and a simplified approach using static calculations of the responses are employed to estimate the stress at the non-instrumented locations-known as virtual sensors. It is found that the hotspots at the base of the tower have longer service lives than the jacket. The fatigue damage to the jacket leg joints is less than 20% and 40% of its fatigue capacity during the 25-year design lifetime of the BIWF OWT, using the modal expansion method and the simplified static approach, respectively.

Design of optical telescopes for laser field wavefront reconstruction in gravitational-wave detectors

Pick-off beams in Interferometric Gravitational Wave Detectors are often used to derive information on the field circulating in the interferometer. In order to retrieve the wavefront of the field at some chosen location, an optical system has to be deployed so to image the desired field characteristics to an optical bench and ultimately to suitable sensors. In this paper, we detail the requirements in terms of Gouy Phase and ABCD matrix for such an optical system to provide the correct information. We show also that by designing the optical system with adequate Gouy Phase evolution, the same kind of transformation holds true not only for the fundamental Gaussian mode, but also for both even and odd Higher Order Modes (HOMs) of the main interferometer beam. This is important because these HOMs are excited by the aberrations of the optical elements in the interferometer, and carry the information one is interested to. Simulations with two tools (Finesse and Zemax OpticsStudio®) are provided to confirm the analytical results obtained using Gaussian modes expansion of a generic field.

Theory and design consideration of a THz superradiant waveguide FEL

We present theoretical analysis and design considerations of a THz superradiant FEL. We derive analytical expressions for the spectral parameter of THz radiation, emitted superradiantly in a rectangular waveguide using a Longitudinal Section Magnetic mode expansion. The results compare well with numerical simulations using UCLA GPTFEL code. GPT simulations of the accelerator e-beam transport show that the chirp provided by a hybrid photocathode RF gun, can produce tight bunching at the undulator site below σ = 100fs. This enables intense superradiant emission up to 3THz, limited by the beam bunching factor. Phase-space analysis of the beam transport indicates that keeping the beam bunching parameter small enough for higher THz frequency operation is limited by the energy spread of the beam in the gun.

Ultra-high Q resonances based on zero group-velocity modes accompanied by bound states in the continuum in 2D photonic crystal slabs

Optical resonators made of 2D photonic crystal (PhC) slabs provide efficient ways to manipulate light at the nanoscale through small group-velocity modes with low radiation losses. The resonant modes in periodic photonic lattices are predominantly limited by nonleaky guided modes at the boundary of the Brillouin zone below the light cone. Here, we propose a mechanism for ultra-high Q resonators based on the bound states in the continuum (BICs) above the light cone that have zero-group velocity (ZGV) at an arbitrary Bloch wavevector. By means of the mode expansion method, the construction and evolution of avoided crossings and Friedrich-Wintgen BICs are theoretically investigated at the same time. By tuning geometric parameters of the PhC slab, the coalescence of eigenfrequencies for a pair of BIC and ZGV modes is achieved, indicating that the waveguide modes are confined longitudinally by small group-velocity propagation and transversely by BICs. Using this mechanism, we engineer ultra-high Q nanoscale resonators that can significantly suppress the radiative losses, despite the operating frequencies above the light cone and the momenta at the generic k point. Our work suggests that the designed devices possess potential applications in low-threshold lasers and enhanced nonlinear effects.

Coherent structures in elastic turbulent planar jets

At low Reynolds numbers, the flow of a Newtonian planar jet remains laminar, thus easy to characterize. In contrast, the presence of elasticity (e.g., attained dissolving polymers in a Newtonian solvent) enables a highly-complex turbulent-like behavior termed elastic turbulence. In this work, we run data-driven modal decomposition algorithms on high-fidelity data collected from the simulation of an elastic turbulent planar jet. The large-scale motions are expressed as a finite expansion of modes that condense the dominant dynamics. The modes associated with lower frequencies weight the most on the reconstruction of the original data, thus they are further decomposed in space to investigate their implications on the sustainment of the elastic turbulent state. Our findings suggest that slower dynamics are crucial for the sustainment of elastic turbulence, which is connected to the interaction of spanwise-coherent structures, steady in space, with spanwise-periodic traveling waves, causing the breakdown of the structures close to the inlet.

A δ-free approach to quantization of transmission lines connected to lumped circuits

The quantization of systems composed of transmission lines connected to lumped circuits poses significant challenges, arising from the interaction between continuous and discrete degrees of freedom. A widely adopted strategy, based on the pioneering work of Yurke and Denker, entails representing the lumped circuit contributions using Lagrangian densities that incorporate Dirac δ-functions. However, this approach introduces complications, as highlighted in the recent literature, including divergent momentum densities, necessitating the use of regularization techniques. In this work, we introduce a δ-free Lagrangian formulation for a transmission line capacitively coupled to a lumped circuit without the need for a discretization of the transmission line or mode expansions. This is achieved by explicitly enforcing boundary conditions at the line ends in the principle of least action. In this framework, the quantization and the derivation of the Heisenberg equations of the network are straightforward. We obtain a reduced model for the lumped circuit in the quantum Langevin form, which is valid for any coupling strength between the line and the lumped circuit. We apply our approach to an analytically solvable network consisting of a semi-infinite transmission line capacitively coupled to an LC circuit and study the behavior of the network as the coupling strength varies.

Quantum correlation and squeezing in pulses propagating in dispersion oscillating fibers

We consider the squeezing and correlation of quantum fluctuations in pulse pairs arising due to soliton fission in dispersion oscillating fibers. The dispersion oscillation acts as a time-domain pulse splitter. After the split, the pulses interact via their tails and acquire nonzero correlations. We analyze the correlation pattern using Karhunen–Loève mode expansion. The regime of high intrapulse and interpulse correlations can be described using single Karhunen–Loève mode. The regime with partial pulse-to-pulse correlation requires to take into account at least two Karhunen–Loève modes. We found that the soliton fission in dispersion oscillating fibers allows to generate squeezed states with highly correlated fluctuations in the output pulses.

Alcohol policy changes during the first three-months of the COVID-19 pandemic: Development and application of a classification scheme

BackgroundPolicy changes in response to the COVID-19 pandemic have impacted on alcohol control. This study describes the development and application of a classification scheme to map alcohol policy changes during the first three-months of the COVID-19 pandemic in five countries and/or subnational jurisdictions. MethodA pre-registered systematic review of policy decisions from March to May 2020, in Australia/New South Wales, Canada/Ontario, Chile, Italy and the United Kingdom. One author extracted the data for each jurisdiction using a country-specific search strategy of government documents. We coded policy changes using an adapted WHO classification scheme, whether the policy was expected to tighten or loosen alcohol control, have mainly immediate or delayed impact on consumption and harm and impact the general population versus specific populations. We present descriptive statistics of policy change. ResultsWe developed a classification scheme with four levels. Existing policy options were insufficient to capture policy changes in alcohol availability, thus we added seventeen new sub-categories. We found 114 alcohol control policies introduced across the five jurisdictions, covering five (out of ten) WHO action areas. The majority aimed to change alcohol availability, by regulating the operation of alcohol outlets. All countries introduced closures to on-premise alcohol outlets and, except Chile, allowed off-sales via take away or home delivery. We also observed several pricing policies introducing subsidies to support the alcohol industry. Seventy-four percent of policy changes were expected to tighten alcohol control and 12.3 % to weaken control. Weakening policy changes were mostly related to retail mode switching or expansion (allowing take away or home delivery). ConclusionAlcohol control policies during the first three months of the COVID-19 pandemic were targeted primarily at alcohol availability and about one tenth might weaken alcohol control. Temporary changes to alcohol retail during the COVID-19 pandemic, if made permanent, could significantly expand alcohol availability.

A reconstruction method for structural stress distribution of wind turbine tower using optimised mathematical model

Wind turbine towers experience complex dynamic loads during actual operation, and these loads are difficult to accurately predict in advance, which may lead to inaccurate structural strength assessment during the structural design phase, thereby posing safety risks to the wind turbine tower. Therefore, a reconstruction method for structural stress distribution of wind turbine tower was developed based on modal expansion and linear superposition theory to estimate the full-field stress distribution of a tower, which can be used for online monitoring of structural strength. The dynamic stress distribution of the tower is assumed to be the superposition of several structural modal stress distributions, in the reconstruction method for structural stress distribution developed in this study. The modes with the greatest contribution to the wind turbine structural response were selected based on the modal effective mass, and used for the base functions of an initial mathematical model for the reconstruction of structural stress distribution of the tower, in which many candidate strain gauge locations and directions were considered. Then, the initial mathematical model was expressed as a linear system of equations. Two numerical examples were used to verify the accuracy and stability of the initial mathematical model for the reconstruction of structural stress distribution of the tower, and the reconstruction results indicate that the initial mathematical model combined with the Moore–Penrose inverse algorithm can provide stable and accurate reconstruction results. However, the initial mathematical model uses too many sensors, which is not conducive to engineering applications. Therefore, D-optimal and C-optimal design methods were used to reduce the dimensions of the initial mathematical model, optimise the system of equations, and determine the location, direction and number of strain gauges. Finally, the numerical examples of stress distribution reconstruction show that dimensionality reduction of the mathematical model leads to higher accuracy, in which the C-optimal design algorithm providing a more robust reconstruction outcome.

Version 2 — RPExpand: Software for Riesz projection expansion of resonance phenomena

The software RPExpand, implemented in MATLAB®, provides modal expansions of physical observables in resonant systems, based on contour integrals. Version 2.0 improves the workflow and adds new features. In addition to the poles corresponding to eigenmodes of the systems, zeros of various quantities can be computed. Their derivatives are evaluated if the required information is supplied at the integration points. Furthermore, expansions based on quasinormal modes are supported.

A Weakly Nonlinear System for Waves and Sheared Currents over Variable Bathymetry

The wave–current–seabed interaction problem is studied by using a coupled-mode system developed for modeling wave scattering by non-homogeneous, sheared currents in variable bathymetry regions. The model is based on a modal series expansion of wave velocity based on vertical eigenfunctions, dependent on local depth and flow parameters, including propagating and evanescent modes. The latter representation is able to accurately satisfy the wave flow continuity condition and the no-entrance boundary condition on the sloping parts of the seabed. A new derivation of a simplified nonlinear system is introduced using decomposition to a mean flow and a perturbative wave field. To force the system to consider incoming waves at the inlet, boundary knowledge of periodic, travelling nonlinear water waves over a flat bottom is required. For this purpose, specific solutions are derived using the semi-analytical method based on the stream function formulation, for cases of water waves propagating above linearly and exponentially sheared currents. Results obtained by the application of the CMS concerning the propagation of waves and currents—in particular, examples characterized by depth inhomogeneities—are presented and discussed, illustrating the applicability and performance of the method.

Local discontinuous Galerkin method coupled with the implicit‐explicit Runge–Kutta method for the time‐dependent micropolar fluid equations

AbstractIn this article, the spatial local discontinuous Galerkin (LDG) approximation coupled with the temporal implicit‐explicit Runge–Kutta (RK) evolution for the micropolar fluid equations are adopted to construct the discretization method. To avoid the incompressibility constraint, the artificial compressibility strategy method is used to convert the micropolar fluid equations into the Cauchy–Kovalevskaja type equations. Then the LDG method based on the modal expansion and the implicit‐explicit RK method are properly combined to construct the expected third‐order method. Theoretically, the unconditionally stable of the fully discrete method are derived in multidimensions for triangular meshs. And the numerical experiments are given to verify the theoretical and effectiveness of the presented methods.

Boundary layer transition of hypersonic flow over a delta wing

Cross-flow transition over a delta wing is systematically studied in a Mach 6.5 hypersonic wind tunnel, employing the Rayleigh scattering flow visualisation, high-speed schlieren and fast-response pressure sensors. Direct numerical simulations and analysis based on linear stability theory under the same flow conditions are applied to analyse the transition mechanism. Three unstable modes are identified: the travelling cross-flow instabilities, the second mode and the low-frequency waves. It is shown that the travelling cross-flow vortices first appear in the cross-flow region near the leading edge of the model. These vortices can modulate the mean profile of the flow, which benefits the growth of second mode. A phase-locked interaction mechanism transfers energy from the cross-flow instabilities to the high-frequency second mode, leading to amplification at the expense of the cross-flow instability. As the second mode grows to a critical amplitude, it triggers a $z$ -type secondary instability within a similar frequency range, which introduces secondary finger-like structures connecting to the cross-flow vortex. It is further found that the generation of these finger-like structures is related to the expansion and compression of the second mode. These finger vortices further evolve along the streamwise direction into low-frequency waves and corresponding hairpin-like structures that finally trigger turbulence. An interaction mechanism likely exists between the secondary instability and the low-frequency waves, since their phase speeds are approaching each other. These observations of the interaction mechanism are consistent with those of previous studies on hypersonic boundary layers (Zhang et al., Phys. Fluids, vol. 32 (7), 2020, 071702; Li et al., Phys. Fluids, vol. 32 (5), 2020, 051701).

Induced effects of a rigid boundary on a pulsating spherical source

This work develops a comprehensive analytical formalism to study the boundary-induced effects on a pulsating spherical radiating source near a rigid planar boundary in an inviscid fluid. Using the modal multipole expansion method, the image method and the translational addition theorem for spherical wave functions, exact closed-form expressions are derived for the dimensionless axial acoustic radiation force function as well as the radiation, amplification and extinction energy efficiency factors. The source-boundary distance and the dimensionless size parameter are especially addressed in the numerical simulations for spherical sources with different vibration modes. It is shown that the axial radiation force is positive or negative, depending on the choice of parameters. Moreover, cases when the extinction acoustic power completely vanishes are predicted theoretically for dipole and quadrupole vibrations, which can be used to achieve acoustic invisibility in acoustic cloaking devices and acoustic stealth technologies. Combination of more than one vibration modes is also investigated to better simulate the acoustic manipulation in practical applications. This work can help us understand the underlying mechanism in manipulating the active spherical radiating sources in a bounded field.

Forced resonance of a buckled beam flexibly restrained at the inner point

Restraints along slender structures, such as pipes conveying fluid and beams, play important roles in enhancing their bending stiffness. The current work investigates the influence of the midpoint restraint on the buckled axial force and dynamic characteristics for the first time. A continuous model is introduced by treating the midpoint restraint force as a concentrated force using Dirac function. The influence of the midpoint restraint is discussed based on modal expansion, and a partitioned model is proposed for validation. The conclusion is that the continuous model has good accuracy. Based on this model, it finds out two stable buckled states changing with the midpoint stiffness. The first stable buckled state occurs under weak midpoint restraint and has a cambered shape. The zero- and double frequency components occur in symmetric modal shapes and the response is softened along the whole beam. However, in the second stable buckled state, it turns into a whole sine function shape. The zero- and double frequency components just occur in the second modal shape, and the soften phenomenon doesn’t occur at the midpoint. With increasing excitation amplitude, a bubble appears on the primary resonance peak while another resonance peak emerges nearby it. This work explains the influence of midpoint stiffness on nonlinear resonance and enhances the study of the nonlinear behavior of buckled slender structures.

Semi-Analytical Approach and Green's Function Method: A Comparison in the Analysis of the Interaction of a Moving Mass on an Infinite Beam on a Three-Layer Viscoelastic Foundation at the Stability Limit-The Effect of Damping of Foundation Materials.

In this paper, the interaction of a mass moving uniformly on an infinite beam on a three-layer viscoelastic foundation is analyzed with the objective of determining the lowest velocity at the stability limit, called, in this context, the critical velocity. This issue is important for rail transport and, in particular, for the high-speed train, because the moving mass is the basic model of a vehicle, and the infinite beam on a three-layer viscoelastic foundation is the usual mechanical representation of the railway track. In addition to this, the advantages and disadvantages of the two implemented methods, namely, the semi-analytical approach and the Green's function method, are summarized in terms of computational time, the precision of the obtained results, limitations, and the feasibility of implementation. All results are presented in a dimensionless form to cover a wide range of possible scenarios. Some results may be considered academic, however, results related to a particular railway track are also included. Particular attention is paid to the influence of the damping of materials in the foundation upon the critical velocity of the moving mass. Regarding the semi-analytical approach, it is demonstrated that the critical velocities can be obtained in an exact manner by tracing the branches of the so-called instability lines in the velocity-moving-mass plane. This analysis can be maintained within the real domain. As for the time series, they can be determined by a numerical inverse Laplace transform. Moreover, thanks to the analytical form of the final result in the Fourier domain, each value corresponding to a specific time instant can be obtained directly, that is, without the previous time history. Regarding the Green's function method, this is used to verify a few points delimiting the stable and unstable regions of the moving mass with the help of the D-decomposition approach. Additionally, a numerical algorithm based on the Green's function and convolution integral written for dimensionless quantities is used to calculate the time series of the moving mass. In addition to identifying the critical velocity of the moving mass, its connection with the critical velocity of the moving force is emphasized, and the possibility of validating the results on long finite beams using modal expansion is presented and described.

Tuning of vibration absorbers by an effective modal coupling factor

The simplest family of vibration absorbers comprise inertia absorbers, with an inerter in series with a parallel or series dashpot–spring element, and stiffness absorbers, for which inerter and spring are interchanged. Vibration absorbers are tuned to a structure’s critical resonance, for which scalar structure-absorber equations are derived from an expansion in vibration modes with the absorber in either a free or clamped state. It is demonstrated that the influence from non-targeted residual modes is consistently represented by an effective modal coupling factor (EMCF), evaluated as the relative difference between free and clamped natural frequencies squared. While closely related to the coupling factor for shunted electromechanical transducers, the use of EMCFs determines an entirely new direction for the tuning of mechanical vibration absorbers on a flexible structure. For inertia and stiffness absorbers, the EMCF represents apparent mass or stiffness ratios that also account for the influence from residual modes. Therefore, analytical tuning expressions can be obtained from the derived modal frequency response functions, as demonstrated for a pole-placement method with the EMCF as a new governing absorber parameter. The accuracy of the proposed absorber tuning is validated by a simple numerical example, which shows that analytical tuning expressions can be used directly for vibration damping of flexible structures, provided that the EMCF is included correctly to compensate for the inherent modal interaction.

Photoinduced Co/Ni-cocatalyzed Markovnikov hydroarylation of unactivated olefins with aryl bromides.

Transition-metal-catalyzed hydroarylation of unactivated alkenes via metal hydride hydrogen atom transfer (MHAT) is an attractive approach for the construction of C(sp2)-C(sp3) bonds. However, this kind of reaction focuses mainly on using reductive hydrosilane as a hydrogen donor. Here, a novel photoinduced Co/Ni-cocatalyzed Markovnikov hydroarylation of unactivated alkenes with aryl bromides using protons as a hydrogen source has been developed. This reaction represents the first example of photoinduced MHAT via a reductive route intercepting an organometallic coreactant. The key to this transformation was that the CoIII-H species was generated from the protonation of the CoI intermediate, and the formed CoIII-C(sp3) intermediate interacted with the organometallic coreactant rather than reacting with nucleophiles, a method which has been well developed in photoinduced Co-catalyzed MHAT reactions. This reaction is characterized by its high catalytic efficiency, construction of quaternary carbons, simple reaction conditions and expansion of the reactive mode of Co-catalyzed MHAT reactions via a reductive route. Moreover, this catalytic system could also be applied to complex substrates derived from glycosides.

Photochemical dearomative skeletal modifications of heteroaromatics.

Dearomatization has emerged as a powerful tool for rapid construction of 3D molecular architectures from simple, abundant, and planar (hetero)arenes. The field has evolved beyond simple dearomatization driven by new synthetic technology development. With the renaissance of photocatalysis and expansion of the activation mode, the last few years have witnessed impressive developments in innovative photochemical dearomatization methodologies, enabling skeletal modifications of dearomatized structures. They offer truly efficient and useful tools for facile construction of highly complex structures, which are viable for natural product synthesis and drug discovery. In this review, we aim to provide a mechanistically insightful overview on these innovations based on the degree of skeletal alteration, categorized into dearomative functionalization and skeletal editing, and to highlight their synthetic utilities.

Vibration Energy Harvesting from Plates by Means of Piezoelectric Dynamic Vibration Absorbers

In this paper, the possibility of harvesting energy from the vibrations of a plate is analyzed. The harvester takes the form of a cantilever dynamic vibration absorber equipped with a piezoelectric layer and tuned by means of a tip mass to the first mode of vibration of the plate. A mathematical model of the coupled system composed of the plate and the harvester is presented. The validity of the proposed harvester is proved by means of simulations carried out with the modal expansions approach. Simulation results highlighting the effects of harvester tuning and location are presented as well. Then, the validity of the harvester is confirmed by experimental tests carried out both with a concentrated impulsive load and with a distributed pressure load. Simulations and experimental tests are performed on the cantilever piezoelectric dynamic vibration absorber and on the same piezoelectric layer directly bonded to the plate surface. Results show an improvement in terms of generated voltage when the proposed novel device is used in place of the simple layer.