Numerical Mode Research Articles

A novel method for frequency analysis of a small wind turbine with tubular guyed tower: An experimental evaluation

The present study sets out a novel methodology for the theoretical and experimental analysis required to find the natural frequencies of a small wind turbine with a guyed tower. These frequencies may cause resonance phenomena when occurring close to each other. These phenomena require precise mathematical models and experimental analysis to facilitate structural design calculations. The method uses a life-sized commercial turbine mounted on a fold-down guyed tower, the Rayleigh-Ritz numerical method, vibration modes, blade frequency, and cable stiffness. In addition, cable stiffness value depends on various factors, such as diameter, longitude, and materials. The results reveal that it is possible to shift the fundamental frequency of the cable and its harmonics. The cable is the main element that may cause resonances in other elements of the small wind turbine with a tubular guyed tower due to the range of frequencies that can be adopted depending on the cable tension. Finally, the results show a reasonable concordance between the values for the natural frequencies calculated by the mathematical model and the experimental values, obtaining an error of lower than 3.43% for the fundamental frequency system.

Tuberculosis detection using a low-loss and highly sensitive photonic crystal fiber technique in the terahertz regime

This research paper introduces a design and numerical investigation of a photonic crystal fiber (PCF) sensor with a hollow core. The sensor is specifically designed to detect Mycobacterium tuberculosis in the frequency range of 1–2 THz. The cladding region of the PCF sensor incorporates six rectangular air holes and an absorbing layer known as the perfectly matched layer (PML), which is utilized to examine various optical properties. Through a thorough investigation, our designed PCF sensor demonstrates enhanced sensitivity of 98.692%, 98.721%, 98.75%, and 98.764% for four different infected samples of tuberculosis at a frequency of 1.6 THz. The sensor exhibits minimal confinement loss and effective material loss. Furthermore, the numerical aperture and effective mode index of the proposed sensor are analyzed. An effective area of 346,550, 345,110, 343,710, and 343,020µm2 for the four different infected samples of tuberculosis is obtained. The fabrication methods employed for this sensor are mentioned. Overall, this PCF sensor can be promising for a wide range of chemical, gas, and biosensing applications.

An application of artificial neural networks for solving fractional higher-order linear integro-differential equations

This ongoing work is vehemently dedicated to the investigation of a class of ordinary linear Volterra type integro-differential equations with fractional order in numerical mode. By replacing the unknown function by an appropriate multilayered feed-forward type neural structure, the fractional problem of such initial value is changed into a course of non-linear minimization equations, to some extent. Put differently, interest was sparked in structuring an optimized iterative first-order algorithm to estimate solutions for the origin fractional problem. On top of that, some computer simulation models exemplify the preciseness and well-functioning of the indicated iterative technique. The outstanding accomplished numerical outcomes conveniently reflect the productivity and competency of artificial neural network methods compared to customary approaches.

Effects of different cladding materials on orbital angular momentum modes propagating in photonic crystal fibers.

With the development of orbital angular momentum (OAM) photonic crystal fibers (PCFs) for more efficient communication, fiber claddings are important to the performance. In this paper, the influence of S i O 2 and four new optical materials, which are amethyst, SSK2, SF11, and LaSF09, as cladding materials, on the OAM mode characteristics is studied based on a common PCF for OAM transmission. In addition, the effective index difference, dispersion, confinement loss, and other properties of OAM modes transmitted in the five materials are derived by the finite element method. After in-depth analysis, universal rules can be obtained as guidelines for optimization of PCF in the future for improving the efficiency of optical fiber communication. Through chart analysis, it can be concluded that when materials of high effective refractive indices are used as cladding materials for PCF, the dispersion, nonlinear coefficient, confinement loss, mode purity, and other properties are significantly improved. Lower dispersion and confinement loss are more conducive to long-distance communication transmission. The decrease in nonlinear coefficient represents a better effect in suppressing nonlinear effects, and the increase in numerical aperture and mode purity respectively improves the transmission efficiency and stability of OAM communication. These conclusions provide universal rules for high-quality communication in the future.

Seeing more than reading:The visual mode in utilities' sustainability reports

The analysis of semiotic modes of communication used in corporate reports is very relevant for understanding how meanings are communicated to readers or viewers. But researchers' interest has mainly focused on verbal and numerical modes of communication, and the focus on the visual mode has been very limited. This paper contributes to filling this gap through an explorative analysis of how the visual artefacts are used with the text (verbal and numerical) in utilities' corporate sustainability reports. Results show that visual artefacts are more used for captivating readers' or viewers' attention, spatializing and materializing concepts than infiltrating meanings.

Matrix product states and numerical mode decomposition for the analysis of gauge-invariant cavity quantum electrodynamics

There has been a problem of gauge ambiguities with the Rabi Hamiltonian due to the fact that it can be derived from two formally different but physically equivalent fundamental Hamiltonians. This problem has recently been resolved for models with a single quantized electromagnetic mode. In this paper, we mathematically and numerically verify this for multimode models. With this established, we combine the numerical methods, matrix product states (MPS) and numerical mode decomposition (NMD), for analyzing cavity QED systems. The MPS method is used to efficiently represent and time evolve a quantum state. However, since the coupling structure of the Rabi Hamiltonian is incompatible with MPS, it is numerically transformed into an equivalent Hamiltonian that has a chain coupling structure, which allows efficient application of MPS. The technique of NMD is used to extract the numerical electromagnetic modes of an arbitrary environment. As a proof of concept, this combined approach is demonstrated by analyzing one-dimensional cavity QED systems in various settings.

Techniques for adjusting qualities of aircraft structural models for more effective aeroelastic flutter analyses

To solve numerically the problem of aeroelastic flutter, two virtual components are required: a structural finite element model (FEM) and an aerodynamic model. MSC Software package containing Nastran with embedded flutter solution enables to perform calculations with the use of an integrated aeroelastic model. For data block including the model and the set of entry parameters, flutter equation is being solved. On the basis of postprocessed output data curves of run for resulting parameters can be plotted which gives information of flutter critical point.Numerical results may be subject to some uncertainty. Result deviation could occur as effects of various factors resulting from inaccurate geometry or poor structural qualities of mapped aircraft. Structural defects affecting mass or stiffness matrices of FEM are often hard to identify. Aspects important for effective flutter solutions are strictly connected with the coincidence of structural properties of the real aircraft and its model. In the paper, the method of numerical flutter analysis was presented with the use of techniques available in MSC Nastran. Three assessment methods were proposed to identify structural parameters usable for validating FEMs. The method of mass correction relies on adjustment of model mass values and tuning the location of the center of mass of the model to the coordinates of the location of the center of mass of the real aircraft. For adjusting stiffness of model parts, very useful are results obtained from strength test of the real airframe. The completely reliable but costly method is performing ground vibration tests (GVT) to measure precisely resonant frequencies and natural modes of free vibrations. The results obtained from experiments should be treated as the referenced, but tuning FEM to them requires both adjusting numerical eigenfrequencies and normal modes.

A Numerical Mode Matching (NMM) Method for Optical Fibers With Kerr Nonlinearity

Recently, the reshaping of the transverse light field profile in nonlinear multimode fibers (MMFs) has attracted great attentions. However, the electromagnetic (EM) fields in such nonlinear media cannot be easily and accurately calculated by using the traditional computational electromagnetics methods due to the nonlinearity of Kerr optical materials in graded-index (GRIN) MMFs. The iterative division method based on the 2.5-D spectral element numerical mode matching (SNMM) method is developed to address this problem. The SNMM method is a semi-analytical method, which can effectively reduce the computational costs to obtain highly accurate solutions. Starting from the numerical results of SNMM, the iterative division method solves electromagnetic fields of the linear-to-nonlinear transition process together iteratively. In this work, several improvements are proposed to extend the SNMM for Kerr optical nonlinear MMFs. The governing equations with anisotropic permittivity with Kerr optical nonlinear media are established in the cylindrical coordinate system. The absorbing boundary condition (ABC) is introduced to replace the perfectly matched layer (PML) so that the eigenmodes of a waveguide can be obtained accurately. Numerical results show the validity, accuracy and advantages of the proposed method in simulated MMFs.

Combined experimental–numerical mode I fracture characterization of the pultruded composite bars

In this paper, pultruded GFRP bars are investigated to determine their fracture properties. The double cantilever beam test (DCB) is used to assess fracture behavior under mode I loading conditions. However, due to the presence of the R-curve effect (variable fracture energy dependent on the length of the crack), it is necessary to introduce a nonstandard approach to determine fracture properties. The mixed experimental–numerical approach is proposed to deal with this issue. Numerical simulations were carried out in Simulia Abaqus, and with Python scripting it was possible to generate models and obtain R-curve for the material. The numerical model built based on the experimental results has very good agreement with it (force–displacement and delamination length–time characteristics) which allows the use of the mentioned model in the analysis of more complex structures. Acoustic emission analysis was introduced as an auxiliary technique. The delamination obtained from both the numerical model and the experiment complies with the registered acoustic emission events. The proposed method can be used in preparing a material model for other composite materials, which display the presence of the R-curve effect.

Experimental evaluation of a locally prestressed precast concrete wall under repeated loading histories: Seismic performance and repairability

Seismic damage and residual deformation of buildings usually lead to high repair costs and business downtime. To develop more repairable structures, the locally prestressed precast concrete wall (LPPW) has been proposed, which allows the post-tensioning (PT) tendons and dissipaters to be easily replaced. This paper conducted quasi-static tests on the LPPW to investigate the influence of the height of the upper anchorage points of the PT tendons and to evaluate the seismic performance of the LPPW under repeated loading and post-repair loading. The test results showed that the decrease in the anchorage height of the PT tendons increased the post-yield stiffness and prestress losses of the LPPW. The seismic performance of LPPW was retained well under repeated loading in terms of the bearing capacity, energy-dissipating capacity, and self-centering capacity. The post-repair LPPW restored most of the original seismic performance, validating the excellent repairability of LPPW. Moreover, a parametric analysis was conducted using the numerical mode validated through the experimental results. The analysis revealed that the drift ratio corresponding to the yielding of the PT tendons decreased with a lower anchorage point height; increasing the axial compression ratio enhanced the bearing capacity and reduced the drift ratio at the ultimate state of the LPPW; enlarging the cross-sectional area of dissipaters positively affected the bearing capacity, energy dissipation, and shear-weight ratio of the LPPW.

MAVEN Accelerometer Observations of Thermospheric Densities During Aerobraking and Deep Dip 2: Wave Features and Connections to Upward Propagating Thermal Tides

AbstractIn early 2019, the Mars Atmosphere and Volatile Evolution (MAVEN) mission underwent an ∼2‐month aerobraking campaign during which time the spacecraft periapsis altitude was lowered from its nominal altitude range of 140–160 km to as low as ∼123 km. Excluding spacecraft walk‐in/out maneuvers, accelerometer measurements were made along 272 orbits with coverage spanning Ls 340–3°, latitudes ∼5°–54°S, longitudes 0–360°, and local solar time ∼22–17 hr. In this study, we perform a diagnostic analysis of the full aerobraking data set by fitting 4‐harmonic waves to mass densities. We then study the variations of these waves as a function of latitude with an emphasis on those observed previously in Mars' thermosphere by MAVEN and other missions. Additionally, we utilize data collected during the same time period from the Mars Reconnaissance Orbiter's Mars Climate Sounder to study the vertical propagation of waves originating from the middle atmosphere. Key results indicate that normalized wave amplitudes decrease with latitude, and this is consistent with the latitudinal structure of a diurnal Kelvin mode. We also observe that waves imprinted from the middle atmosphere show normalized amplitude growth with increasing altitude. A complete summary of data sets, analysis methodology, and scientific results is given. The purpose of this study is to add to the body of knowledge surrounding Martian atmospheric wave features and to provide further constraints for future numerical modeling and subsequent tidal mode identification.

Seismic performance of novel RC shear wall with replaceable self-centering energy-dissipation components

A novel reinforced concrete (RC) shear wall with replaceable self-centering energy-dissipation components (RSECs) symmetrically installed at the bottom corner of the wall panel is proposed in this study. The RSEC consists of self-centering part and energy-dissipation part, which not only dissipates most of the seismic energy but also provides the restoring force for the wall to return initial position after yielding of the component. The RC wall with RSECs is designed to reduce the damage to the main part of structural wall and the residual deformation of the structure. The structural details and design considerations of the RC shear wall with RSECs are introduced. To verify the seismic performance of RC shear walls with the new replaceable corner components, the numerical mode is developed for the new type of shear wall and validated by experimental results. Parametric studies of RC wall with RSECs are then conducted to investigate the effects of the stiffness and pre-pressure force of disc spring group, the bearing capacity ratio of RSEC, and the thickness of embedded steel plate. The results indicate that the RC wall with RSECs has moderate bearing capacity and lateral stiffness, good energy-dissipation capacity, excellent self-centering capability and the characteristics of low damage. The function of the RC wall with RSECs can be quickly restored by replacing RSECs after the strong earthquake.

Comprehensive 3E analyses of a parabolic trough collector equipped with an innovative combined twisted turbulator

The Parabolic trough collector (PTC) is one of the most well-known equipment in renewable energy. Today, it is also a renewable source for refining and transferring power to a low-carbon economy. The present study aims to investigate the effect of the geometrical shape of the Receiver cross-section in the PTC and to investigate the effect of placing the innovative combined twisted turbulator (CTT) in it. The receiver is simulated with three different geometric shapes circular cross-section (CCS), vertical elliptical cross-section (VECS), and horizontal elliptical cross-section (HECS). The PTC contains a two-phase MWCNT-GO/Syltherm 800 hybrid nanofluid (HNF), simulated using the mixture model. In this study, numerical simulations have been conducted for Reynolds numbers (Re) of 5000 to 20,000, volume fractions (ϕ) of 1 and 2% of nanoparticles, and pitch ratios (PR) of 0.5 to 2 of the innovative CTT. The results obtained from the present study show that the geometrical change of the cross-section of the receiver is very effective in the hydrodynamic performance of the PTC. Also, placing the innovative CTT in Receiver has consistently increased thermal performance and energy efficiency. The performance evaluation criteria (PEC) index is always greater than 1 in all numerical simulation modes. Therefore, innovative CTT is always desirable in terms of the PEC index. The maximum exergy efficiency is Re = 10,000, ϕ= 0.02, and PR = 2. Based on the environmental analysis, the amount of carbon dioxide in the PTC equipped with an innovative CTT containing two-phase MWCNT-GO/Syltherm 800 HNF is 0.033 kg/day.

Statistical Analysis of Descending Open Cycles of Collatz Function

Collatz dynamic systems present a statistical space that can be studied rigorously. In a previous study, the author presented Collatz space in a unique dynamic numerical mode by tabulating a sequential correlation pattern of division by 2 of Collatz function’s even numbers until the numbers became odd with a consecutive occurrence, following an attribute of a 50:50 probability of division by 2 once (ascending behavior) as opposed to division by 2 more than once (descending behavior). In this paper, we describe the path of the Collatz function as sequences comprised of groups of the function’s iterates (open cycles) that end up with the first odd integer that is less than the starting odd integer. The descending behavior of the open cycles is attributed to a deterministic factor as observation of the cycles’ sequences shows. We do statistical analysis on 4 large samples of open cycles and orbits to 1. We define R(n) as the cycles’ deterministic variable defined as the ratio of division by 2 once to division by 2 more than once. We use statistical analysis to study the randomness of the orbits of the cycles’ starting odd positive integers as well as orbits to 1 up to 1,002,097,149.

A New Model of Temperature Field Accounting for Acid–Rock Reaction in Acid Fracturing in Shunbei Oilfield

The Shunbei oil formation is a deep, high-temperature carbonate reservoir. Acid fracturing is an effective technology to stimulate this formation. For acid fracturing, the temperature field is fundamental information for the acid system selection, acid–rock reaction, live acid penetration distance prediction, acid fracturing design, etc. Therefore, in this paper, we conduct a numerical study on the temperature field in acid fracturing to account for the acid–rock reaction in the Shunbei formation. Firstly, a new mathematical model of the fracture temperature field during acid fracturing is established based on the laws of mass and energy conservation and acid–rock reaction kinetics. The fracture model is based on a PKN model, which accounts for a few factors, such as the acid–rock reaction heat, acid–rock reaction rate dependence on the temperature, and the fracture width change with acid erosion. Then, the numerical mode is developed. Next, an extensive numerical study and a parameter analysis are conducted based on the model with the field data from the Shunbei formation. The study shows that the acid–rock reaction in acid fracturing has obvious effects on the temperature field, resulting in a 10~20 °C increase in the Shunbei formation. The acid–rock reaction dependence on temperature is a factor to be accounted for. The rock dissolution increases first and then decreases from the inlet to the tip of the fracture, unlike the monotonous decrease without temperature dependence. The temperature gradient is high near the inlet and then decreases gradually. Beyond half of the fracture, the temperature is close to the formation temperature. The temperature drops fast in the initial injection stage and tends to stabilize at about 50 min.

Effects of bootstrap current on magnetic configuration in Chinese first quasi-axisymmetric stellarator

Neoclassical properties in quasi-axisymmetric (QA) stellarators are analogous to these in tokamaks. Consequently, a substantial bootstrap current could significantly modify the MHD equilibrium properties of a QA stellarator, which is an important characteristic in this type of stellarator. This paper is dedicated to systemically investigate the effects of bootstrap current on the magnetic configuration in Chinese first quasi-axisymmetric stellarator (CFQS). For the first time, self-consistent bootstrap currents in free-boundary equilibria are calculated with an accurate Fokker–Planck neoclassical numerical mode in CFQS. Several important results are achieved: (a) as the bootstrap current grows with increasing volume-averaged normalized pressure , magnetic shear develops in the bulk plasma and meanwhile, a deep magnetic well is robustly sustained, which leads to improved stabilization of interchange modes up to . (b) In the analysis of global ideal MHD instability, as the bootstrap current rises to 39 kA (), external kink modes become destabilized and the unstable mode with m/n = 2/1 is dominant. (c) From to 1.5%, the bootstrap current hardly changes the QA property and a low neoclassical transport is maintained. However, as is enhanced beyond 2.0%, the substantial bootstrap current gives rise to an increase of non-QA magnetic field components, which weakens the neoclassical transport properties. (d) An increase of the negative magnetic shear at the core region by the bootstrap currents has a favorable effect on the properties of J (second adiabatic invariant). The maximum-J region can be extended by raising bootstrap currents.

Hundred-watt level high-order mode all-fiberized random distributed feedback Raman fiber laser with high mode purity

An all-fiberized random distributed feedback Raman fiber laser (RRFL) with LP11 mode output at 1134 nm has been demonstrated experimentally, where an intracavity acoustically induced fiber grating is employed for modal switching. The maximum output power of LP11 mode is 93.8 W with the modal purity of 82%, calculated by numerical mode decomposition technology based on stochastic parallel-gradient descent algorithm. To our best knowledge, this is the highest output power with high purity of LP11 mode generated from the RRFL. This work may pave a path towards advanced fiber lasers with special temporal and spatial characteristics for applications.

A Novel Strategy for Automatic Mode Pairing on the Model Updating of Railway Systems with Nonproportional Damping

Mode pairing is a crucial step for the stability of any model-updating strategy based on experimental modal parameters. Automatically establishing a stable and assertive correspondence between numerical and experimental modes, in many cases, proves to be a very challenging task, especially in situations where complex mode shapes are present. This article presents a novel formulation for the automatic mode pairing between experimental and numerical complex modes based on an Energy-based Modal Assurance Criterion (EMAC). The efficiency of the proposed criterion was demonstrated on the basis of a case study involving the pairing between numerical and experimental modes of a passenger railway vehicle. A highly complex detailed FE numerical model of the vehicle was developed involving the modeling of the carbody, bogies and axles. A numerical damped modal analysis allowed obtaining the main global rigid-body and flexural modes of the vehicle’s carbody, as well as several local modes associated to the vibration of specific components of the carbody. Due to the localized damping provided by the suspensions, these modes presented complex modal ordinates, especially for the rigid-body modes. The comparison between the results obtained from the application of the EMAC and the classical MAC criteria, on the pairing of five global mode shapes, proved that the EMAC criterion is much more assertive, avoiding mismatches between the experimental global modes and some of the local numerical modes with similar configurations, and, consequently, establishing the correct correspondences between experimental and numerical modes.

Evaluation of low-level jets in the southern Baltic Sea: a comparison between ship-based lidar observational data and numerical models

Abstract. In contrast to fixed measuring devices, ship-based lidar systems provide highly reliable wind observations within extensive regions. Therefore, this kind of reference dataset provides a great potential for evaluating the performance of mesoscale numerical models in resembling mesoscale flow phenomena such as low-level jets – essential for an optimal development and operation of wind turbines. This paper presents a comparison between numerical output data from two state-of-the-art numerical datasets (ERA5 and NEWA) and the ship-mounted lidar measurements from the NEWA Ferry Lidar Experiment. The comparison was performed along the route covered by the vessel, as well as in specific locations within this route, to better understand the capabilities and limitations of the numerical models to precisely resemble the occurrence and main properties of low-level jets (LLJs) in different locations. The findings of this study show that the non-stationary nature of ship-based lidar measurements allows evaluating the accuracy of the models when retrieving jets' characteristics and occurrence under different temporal and spatial effects. Numerical models underestimate the occurrence of LLJs, and they struggle to accurately describe their main characteristics, with a particularly large underestimation of the falloff. The found results are to be seen in relation to the characteristics of the observations, such as the data availability, the time–position relation of the selected vessel's route, or the profile height limitation, as well as the features of the jets, with a particular relevance of core height and falloff. Additionally, the results illustrate the temporal and spatial shift between the LLJ events detected by the measurements and the models and the potential benefit of considering such deviations when studying LLJs' climatology through numerical modes.

Novel periodic pile barrier with low-frequency wide bandgap for Rayleigh waves

This paper aims to investigate the propagation of low-frequency seismic surface waves in periodic in-filled barriers from the viewpoint of bandgaps. Based on Bloch-Flouquet theory, four configurations of periodic pile barriers with the same filling rate but different cross sections are studied. The periodic boundary conditions are imposed to derive the characteristics equation. Simultaneously, the finite element method is used to calculate the numerical dispersion relation and vibration modes of four types of periodic pile barriers with various inclusions. The sound cone and the energy parameter method are introduced to identify the surface wave modes further. Additionally, the mitigation effectiveness of a finite number of periodic barriers is evaluated using a three-dimensional transmission model. The results show that the initial frequency and bandwidth of the surface bandgaps are sensitive to the shape of the cross-section and mechanical parameters of the inclusions. The surface wave bandgaps within 9.64 ∼ 13.92 Hz are observed for the periodic barrier composed of cross-like polyfoam sections. Moreover, the radiation modes formed by the leakage of some surface waves into the sound cone are expected to widen the attenuation zones of the periodic barriers. The numerical results in frequency and time domains further validate the attenuation effect of finite barrier in the bandgap and the attenuation widening phenomenon caused by the dissipation of the leak modes into the bulk. This study provides new insights into the design of periodic pile barriers. In the future, it is expected to mitigate the low-frequency ground motion by fully designing the section shape and filling materials of pile barriers.