Three-dimensional Analytical Approach Research Articles

Mechanical Behavior of Moderately Inflated Tubular Organs: A Three-Dimensional Analytical Approach

Mechanical Behavior of Moderately Inflated Tubular Organs: A Three-Dimensional Analytical Approach

Influence of Hole-to-Hole Interaction on the Acoustic Behavior of Multi-Orifice Perforated Plates

Abstract A key factor for developing low-emission combustion systems in modern gas turbines and aero-engines is the acoustic liner's optimized design. Several models are available in the literature for the acoustic impedance of perforated acoustic liners. Most of these impedance models neglect the interaction effect between the orifices. In practice, the orifices are generally closely distributed such that the interactions between acoustic radiation from neighboring orifices can affect their acoustical behavior. The hole-to-hole interaction effect may change the resonance frequency of the resonator due to the nonplanar wave propagation in the cavity, the orifices in the perforated plate, and the near-wall region in the combustor. Considering this effect may help to predict the resonance frequency of the resonator accurately. In this work, a three-dimensional (3D) analytical approach is developed to account for the nonplanar wave propagation in the cavity and orifices on the perforated plate. The present study employs the proposed 3D analytical method to determine the hole-to-hole interaction end correction of multi-orifice perforated plates. Additionally, the hole-to-hole interaction end correction from a series of perforated plates with different orifice radii and spacings is obtained via the finite element method. Perforated plate specimens with different center-to-center hole spacing are tested using an impedance tube. Experimental results show that the resonance frequency is shifted toward a lower frequency with decreasing holes' spacing. The resulting model is compared with the experiments and the end-correction models available in the literature. The comparison shows that the available end-correction models cannot capture the hole-to-hole interaction effect, which is observed in experiments. In contrast, the proposed model can reproduce measurements with high quality. The resulting model demonstrates that the acoustic end-correction length for orifices is closely related to the perforated plate's porosity ratio and orifice radius. The proposed model is readily applicable in the design of multi-orifice perforated plates.

A three-dimensional analytical approach for large rectangular splitter silencers in the presence of mean flow

The dissipative splitter silencer is a common means for broadband noise attenuation in flow ducts such as ventilation and gas turbine systems where many higher order modes are cut-on. To predict the effect of a splitter silencer, analytical approaches have obvious advantages over the numerical methods on computation efficiency, but the development of analytical approaches are often based on many simplifications like the infinite length assumption. This paper presents a three-dimensional analytical method to solve the sound propagation in a duct with a finite length splitter silencer in the presence of mean flow. In the developed method, the convergence problem, which is often encountered by using the existing mode-based methods for high-frequency computations of soft-wall eigenmodes, is overcome by applying the equivalent surface source concept. With very low computational cost, the present method is validated to give consistent transmission loss predictions with the numerical results and experimental measurements available in the literature. Further, the performance of a splitter silencer is studied with different higher order incident modes, and reflection versus dissipation analysis is conducted by using the developed method. It is found that the sound attenuation is dependent on the sound energy spatial distributions of the incident sound modes, and the dissipation dominates the transmission loss behavior of the splitter silencer.

A three-dimensional semi-quantitative method to monitor the evolution of polycyclic aromatic hydrocarbons from vacuum gas oil feedstocks to lighter products

Formation and accumulation of polycyclic aromatic hydrocarbons (PAHs) are responsible of major topical issues related to the conversion of petroleum vacuum gas oils (VGOs) in transportation fuels through hydrocracking process. To achieve an efficient management of these hydrocarbons, a detailed semi-quantitative description of PAHs contained in VGOs was provided by a three-dimensional off-line analytical approach based on centrifugal partition chromatography (CPC), supercritical fluid chromatography (SFC) and high-resolution mass spectrometry (HRMS). As a result, well-organised CPCxSFC chromatograms provided a relevant separation of PAHs according to both unsaturation level (DBE) and alkylation degree. This dedicated methodology allowed the semi-quantification of PAHs having a DBE superior to 12. For the first time, PAHs were quantified in six VGOs allowing to highlight differences in composition depending on the origin of the samples. Then, the evolution of PAH concentration was monitored during hydrotreating and hydrocracking processes. For the hydrotreated/hydrocracked (HDT/HCK) products, their sulphur and nitrogen contents were low enough to make possible semi-quantification of PAHs directly by SFC/HRMS. An accumulation of PAHs was observed when a recycle stream from the unconverted oil to HDT reactor was applied. This work demonstrates that valuable analytical data could be obtained leading a step forward in the overall understanding of a process from native VGO feedstocks to the HDT/HCK products.

A Novel Three-Dimensional Analytical Approach for Acoustic Noise Modeling in Switched Reluctance Machines

Acoustic noise modeling, analysis, and reduction are critical in the design of switched reluctance machines for noise-sensitive applications. Although the analytical method can provide a fast simulation of the acoustic noise, it is generally less accurate compared to the numerical method. In order to improve the simulation accuracy, a novel analytical method is presented in this paper. The proposed method considers the excitation of the high-axial-order vibration modes to simulate the vibration behavior and the acoustic noise in the three-dimensional (3D) domain. Methods of obtaining the input data for the 3D analytical simulations are presented. The acoustic noise results obtained from the numerical simulations and experiments from an 8/6 switched reluctance motor drive are used to validate the analytical method presented in this paper.

Black Lives Matter: Race Discourse and the Semiotics of History Reconstruction

The death of unarmed black male George Floyd, who was killed by a white police officer in Minneapolis, May 25, 2020, has given momentum to the Black Lives Matter (BLM) movement whose activists rallied in different parts of the world to remove or deface monuments to historic figures associated with racism, slavery, and colonialism. These social practices of toppling statues have a discursive value and, since they are meant to communicate a message to the broader society, these actions are incorporated into a semiotic system. This study examines signs and, therefore, the system of representations involved in toppling statues performed by BLM activists and documented in photos. The research employs a critical approach to semiotics based on Roland Barthes’ (1964) semiotic model of levels of signification. However, for a comprehensive analytical understanding, the study also makes use of a multidisciplinary Critical Discourse Analysis CDA approach which provides a systematic method to examine and expose power relations, inequality, dominance, and oppression in social practices. Besides its general analytical framework, the integrated CDA approach combines Fairclough’s (1995) three-dimensional analytical approach, which presupposes examining text, discursive practice, and sociocultural practice, with Reisigl and Wodak’s (2001, 2017) Discourse Historical Analysis (DHA), which investigates ideology and racism within their socio-cultural and historic context. The analysis of the images reveals a common thematic structure and encoded messages produced in order to change the cultural and social norms of the USA national discourse generated and cultivated within a specific ideological and historical context. These social actions consist of signs that make up a coherent communicative system which provides BLM activists with instruments in the struggle over the memory of slavery, white supremacy and oppression of the past for the rights of the black minority in the present in a better society of racial equality, human rights, and liberation.

Statistical Properties and Configurational Entropy of a Two-Dimensional Néel Magnetic Skyrmions Population

The study of the thermodynamic properties of topological defects is important not only for understanding their magnetic properties but also for suggesting novel applications. In this paper, the statistical and statistical thermodynamic properties of a population of Néel magnetic skyrmion diameters hosted in an ultrathin cylindrical dot is determined within a two-dimensional analytical approach. The statistical properties such as the skyrmion size are calculated in the region of skyrmion metastability and are compared with the ones obtained using a recent three-dimensional analytical approach based on the analogy with the Maxwell–Boltzmann distribution of dilute gas molecules. The investigation of the statistical thermodynamic properties focus on the calculation of the configurational entropy at thermodynamic equilibrium determined in the continuous limit from the Boltzmann order function. While the statistical properties are quantitatively similar passing from the two-dimensional to the three-dimensional approach, the configurational entropy calculated from the two-dimensional skyrmions distribution is considerably lower than the one obtained from the three-dimensional skyrmions distribution. Because of the strong resemblance between the statistical configurational entropy and Jaynes’s information entropy, it is suggested to use magnetic skyrmions as temperature and external field dependent information entropy carriers for a future potential technological application in the field of low-dimensional magnetic systems and skyrmionics.

Internal instability as a possible failure mechanism for layered composites.

This paper revisits a three-dimensional analytical approach to study internal instability in layered composites, when the behaviour of each component of the material is described by the three-dimensional equations of solid mechanics. It shows the development of a unified computational procedure for numerical realization of the three-dimensional analytical method as applied to various constitutive equations of the layers and fibres, and different loading schemes (uniaxial or biaxial loading). The paper also contains many examples of calculation of critical controlled parameters for particular composites as well as analysis of different buckling modes. The results of this method can be used as a benchmark for simplified models. This article is part of the themed issue 'Multiscale modelling of the structural integrity of composite materials'.

The Brazilian Disc Test Under a Non-Uniform Contact Pressure Along Its Thickness

Using a three-dimensional analytical approach, the sensitivity of the Brazilian test to its standard testing recommendations was investigated. It was concluded that the tensile stress induced in a Brazilian disc is significantly affected by the distribution of the applied load along its thickness rather than its circumferential condition. Under a non-uniform contact pressure along the BTS thickness, it was evident that both the numerical value and the location of the maximum tensile stress varied as a function of the geometrical aspect ratio of the disc specimen. For test conditions in which load distribution in the contact region along the thickness does not follow the standards or the uncertainty of its exact nature is large, e.g. in testing of super hard materials with relatively high stiffness and hardness greater than the contact testing platens, great care should be taken in regard to the interpretation of the Brazilian test result.

The age-related maturational pattern of the human subarcuate fossa (petromastoid canal). Preliminary results from the application of a new three-dimensional analytical approach

The subarcuate fossa, or petromastoid canal, is a hypostotic feature of the temporal bone used for assessing the age at death of immature individuals. The present study uses the high-resolution micro-CT record of 20 extant human infant and juvenile temporal bones to more precisely assess the age-related maturational pattern of this bony structure. In the perspective of the application of our analytical protocol to the study of the hominid fossil record, the main goals of this contribution are to extend the amount and to improve the quality of the linear and volumetric information on the human subarcuate fossa by the application of new 3D imaging techniques.

An analytical approach to 3D orthodontic load systems

To present and demonstrate a pseudo three-dimensional (3D) analytical approach for the characterization of orthodontic load (force and moment) systems. Previously measured 3D load systems were evaluated and compared using the traditional two-dimensional (2D) plane approach and the newly proposed vector method. Although both methods demonstrated that the loop designs were not ideal for translatory space closure, they did so for entirely different and conflicting reasons. The traditional 2D approach to the analysis of 3D load systems is flawed, but the established 2D orthodontic concepts can be substantially preserved and adapted to 3D with the use of a modified coordinate system that is aligned with the desired tooth translation.

Three-dimensional clustered speckle fields: theory, simulations and experimental verification

Clustered speckle patterns are a particular type of speckles that appear when a coherently illuminated diffuser is imaged through a multiple aperture pupil mask attached to a lens. The cluster formation is the result of the complex speckle modulations of the multiple interferences produced by the apertures. In this paper, a three-dimensional analytical approach to simulate cluster speckles everywhere after the lens is presented. This approach has the possibility of including multiple aperture masks at the lens and at the diffuser, in contrast to previous works which were also limited to the description of the patterns only at the image plane. This model contributes to the development of tailor made speckle patterns that can be used in diverse optical applications, including those lying in the focus region. The approach is validated under different conditions by comparing experimental results with simulations on a statistical basis. Some aspects of possible uses of these clusters are briefly revised, such as optical trapping, manipulation and metrology.

Three-dimensional analysis of combination effect of ellagitannins and acyclovir on herpes simplex virus types 1 and 2

The effects of combinations of three nonahydroxyterphenoyl-bearing C-glucosidic ellagitannins (castalagin, vescalagin and grandinin) with acyclovir (ACV) on the replication of type-1 and type-2 herpes simplex viruses in MDBK cells were tested by the focus-forming units reduction test. Ellagitannins included in these combinations possess a high individual antiviral activity: selectivity index of castalagin and vescalagin versus HSV-1 was similar to that of ACV, and relatively lower against HSV-2. The three-dimensional analytical approach of Prichard and Shipman was used to evaluate the impact of drug–drug interactions. The combination effects of ellagitannins with acyclovir were markedly synergistic.

Analytical Design of Permanent Magnet Radial Couplings

This paper presents a three-dimensional analytical approach for computing the torque transmitted by synchronous radial couplings with radially polarized tile permanent magnets. An expression is given as a finite sum of elliptic functions, which has no underlying simplificating assumptions. Such an expression allows parametric studies and optimizations of coupling structures. It is applied first to the study of conventional radial couplings. Then, structures with “short pitch” magnets are considered and compared with conventional ones. Eventually, special designs are presented, as the ones dedicated to screwing applications, for instance, which require creating an asymmetrical torque.

Radial Stiffness of a Ferrofluid Seal

This paper presents an analytical model for calculating the shape and the radial stiffness of ferrofluid seals used as radial bearings and this theoretical value of the radial stiffness is compared to measured values. This approach is interesting for the design of loudspeakers. Moreover, the concept of magnetic pressure is used to determine the seal shape as well as its energy. This paper corresponds to the case in which the ferrofluid seal is submitted to a high magnetic field. Furthermore, the calculation of the seal shape when the moving part is decentred is discussed. Indeed, the variation of the seal energy is evaluated with a three-dimensional analytical approach and both the restoring force exerted by the seal and the radial stiffness are calculated. The results obtained with an experimental setting confirm the validity of the model.

Magnetic pressure and shape of ferrofluid seals in cylindrical structures

This paper presents a three-dimensional analytical model for studying the shape and the pressure of ferrofluid seals in totally ironless structures. This three-dimensional analytical approach is based on the exact calculation of the magnetic field components created by ring permanent magnets whose polarizations are either radial or axial. We assume that the ferromagnetic particles of the ferrofluid are saturated. Moreover, the permanent magnets (neodymium iron boron) used in the considered applications create a magnetic field which is much higher than the magnetic field created by the magnetic particles in the ferrofluid so the latter is neglected. Nevertheless, the static behavior of the ferrofluid seal depends on both the magnetic field produced by the permanent magnets and the saturation magnetization of the ferrofluid particles. Furthermore, the accurate knowledge of the ferrofluid seal shape as well as the magnetic pressure inside the ferrofluid seal is very useful for the design of devices using both permanent magnets and ferrofluid seals. It is emphasized here that our structures are completely ironless and thus, there are no iron-base piston for these structures. Then, this paper makes a review of the main structures using ring permanent magnets and ferrofluid seals. For each ironless structure, the shape and the pressure of the ferrofluid seals are determined.

DISCUSSION ABOUT THE MAGNETIC FIELD PRODUCED BY CYLINDRICAL HALBACH STRUCTURES

This paper uses a three-dimensional analytical approach based on the Coulombian model for studying the magnetic field produced by cylindrical Halbach structures. Such structures, commonly used in magnetic couplings or in electrical machines, are composed of tile permanent magnets with rotating magnetizations. Such assemblies of tile permanent magnets allow one to easily optimize the radial field shape in the air gap of electrical machines. In addition, Halbach structures can be used in magnetic couplings for improving the torque transmitted between the two rotors. Analytical studies dealing with the optimization of such structures generally use a two- dimensional analytical approach for calculating either the magnetic field produced by tile permanent magnets or the forces exerted between them. These two-dimensional expressions are useful because they have a very low computational cost. However, their accuracy depends greatly on the structure dimensions. We propose in this paper to use a three-dimensional analytical model based on the Coulombian model for determining the exact shape of the magnetic field produced by a Halbach structure. Such an approach also allows one to determine the demagnetizing magnetic field inside the tile permanent magnets. This element of information is important for the design of tile permanent magnets. In addition, we show that some effects cannot be predicted with the linearized analytical model. This implies that a linearized dimensional optimization is not accurate. This study has been carried out without any simplifying assumptions. Therefore, the calculations of the three magnetic field components are exact for all points in space, whatever the magnet dimensions. We can say that such a three-dimensional analytical approach is a good alternative to a finite element one because it has a lower computational cost and is more accurate.

MECHANICAL PROPERTIES OF A FERROFLUID SEAL: THREE-DIMENSIONAL ANALYTICAL STUDY BASED ON THE COULOMBIAN MODEL

This paper presents a general method for studying the mechanical properties of a ferrofluid seal by using a three-dimensional analytical approach based on the coulombian model of a magnet. The fundamental Maxwell's equations lead us to define the concept of magnetic energy of the ferrofluid seal by using only the three- dimensional equations of the magnetic field created by ring permanent magnets radially magnetized. Our study corresponds to the specific case when the ferrofluid is submitted to a very high magnetic field. Under these conditions, we assume that the mechanical properties of the ferrofluid depend only on the magnetic field created by the permanent magnets. Throughout this paper, the remanence polarization J of the magnets used is higher than 1 T. The magnetic field we use in order to align the magnetic particles is very intense, greater than 400 kA/m. Consequently, the magnetic particles are assumed to be saturated and the magnetic field they create can be omitted. In this paper, a cylindrical structure consisting of two outer ring permanent magnets radially magnetized and an inner non- magnetic cylinder is considered. In addition, a ferrofluid seal is placed between them. The calculation of the magnetic pressure of the ferrofluid seal has been analytically established in three dimensions in order to determine its shape. Moreover, the geometrical evolution of the ferrofluid seal shape is presented when the inner non-magnetic cylinder crushes the ferrofluid seal. The radial stiffness of the ferrofluid seal is determined in three dimensions when the inner cylinder is decentered. Furthermore, a way of obtaining the ferrofluid seal static capacity is discussed.

Limit equilibrium analysis of large-scale reinforced and unreinforced embankments loaded by a strip footing

The paper describes limit equilibrium analyses of two large-scale geosynthetic reinforced soil embankments and one unreinforced soil embankment that were taken to collapse under a strip footing placed close to the crest. One reinforced embankment was constructed with a relatively extensible and weak polypropylene geogrid and the second with a relatively strong and stiff high-density polyethylene geogrid. The geometry of the embankments and the loading arrangement were the same for all three structures. The focus of the paper is on a comparison of the predicted collapse load for the three structures and the actual observed values. A three-dimensional analytical approach is used to account for possible side-wall friction effects due to the test facility in which the large-scale experimental models were built. The paper also reports details on the interpretation of in-isolation constant load tests and strain measurements used to infer tensile loads in the reinforcement at failure. An important conclusion is that a general two-part wedge analysis approach can be used to predict the collapse footing load for both unreinforced and reinforced sand embankments in this investigation provided careful attention is paid to the selection of soil shear strength and reinforcement tensile capacity.Key words: geosynthetics, reinforced embankments, strip footing, large scale, limit equilibrium analyses.

Circular asymmetric Helmholtz resonators

A three-dimensional (3D) analytical approach is developed to account for the nonplanar wave propagation in the cavity and neck of "piston-driven" circular asymmetric Helmholtz resonators. The present 3D analytical results are compared with (1) the numerical predictions from the boundary element method (BEM) to evaluate the analytical approach; and (2) the one-dimensional (1D) solution to examine the effect of nonplanar waves at area discontinuity between the neck and the cavity. In order to improve the 1D solution, the end correction is also determined by using the 3D analytical approach. The effect of neck offset on the resonance frequency of circular asymmetric Helmholtz resonators is investigated. Predictions of resonance frequency and transmission loss from the present 3D and corrected 1D analytical approaches are, respectively, identical and close to the BEM results, while the corrected 1D approach provides a better accuracy compared to the 1D solutions with Ingard's correction. Finally, the boundary element method is employed to determine the wave attenuation performance of the "pipe-mounted" Helmholtz resonators to examine the effect of multidimensional waves in the vicinity of the main duct and neck junction.