Harmonic Shape Research Articles

A numerical and experimental investigation on passive piezoelectric shunt damping of mistuned blisks

In a previous study, we proposed a method for the damping of rotationally periodic structures, when a specific mode with n nodal diameters is targeted. The proposed method considers 4 n lead zirconate titanate patches (or a multiple of) which can be, either, shunted independently on 4 n identical resistor–inductor circuits, or mounted in two parallel loops and shunted on only two resistor–inductor circuits. Both configurations offer the same performance; however, the parallel configuration requires only two inductors and it is aimed to reduce the demand on inductors; it works actually like a spatial filter and assumes a perfectly symmetric structure with harmonic mode shapes in the circumferential direction. The study presented in this article is aimed at evaluating the proposed damping technique in the presence of blade mistuning. In the first part, the parallel and the independent configurations are compared numerically on a set of mistuned bladed drums with controlled level of mistuning. In the second part, the parallel and the independent shunts are implemented experimentally on a mistuned bladed drum mock-up. For the considered mock-up, the numerical results show that for moderate levels of mistuning, the parallel shunt performs almost like the independent shunt, while the experimental results confirm this fact.

First harmonic shape analysis of Brazilian free-tailed bat calls during emergence

Echolocating bats can adapt calls when facing challenging echolocation tasks. Previous studies have shown that bats can change their pulse duration, pulse repetition rate, or vary their start/end/peak frequencies depending on behavior. Even though this kind of signal investigation reveals important findings, these approaches to analysis use bulk parameters that may hide subtleties in the call structure that could be important to the bat. In some cases, calls may have the same start and end frequencies but have different FM shapes and meet different sensory needs. In the present study, we demonstrate an algorithm for extracting the first harmonics of the Brazilian free-tailed bat (Tadarida brasiliensis) to investigate how the shape of the call changes. High pass filtering, power banded time-frequency analysis, and search algorithms were used to isolate the first harmonics. By tracking the first harmonics, the detailed frequency modulation shapes of different bat group sizes were obtained, and the difference among those traces was measured. The detailed shape analysis will provide a new insight into the adaptive call design of bats.

The public multi-coil information (PUMCIN) policy.

Multi-coil (MC) magnetic field modeling has emerged as a viable alternative to conventional field generation based on spherical harmonic shapes, and an active MC community is forming. Although all MC applications share the same modeling concept, the specific MC designs can largely differ as a result of disparities in region of interest (eg, human versus rodent), intended MR application (eg, B0 shimming versus spatial encoding), or other experimental constraints (eg, available bore space or integration with radiofrequency technology). To date, a lack of detailed information on existing MC designs complicates the assessment and precludes a meaningful comparison. Here, we suggest that future publications involving the MC technique not only report the benefits for the application at hand, but also include an explicit description of the MC wire pattern used. This public multi-coil information (PUMCIN) policy represents a voluntary commitment to promoting free public access to the details necessary for reproducing and benefiting from MC research. The PUMCIN policy is expected to initiate a paradigm shift with respect to the way MC innovation is reported. By setting an example, we hope to encourage the evolving MC community to maximize the benefits for science and society by embracing it. Magn Reson Med 78:2042-2047, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Wing Geometry and Kinematic Parameters Optimization of Flapping Wing Hovering Flight

How to efficiently mimic the wing shape and kinematics pattern of an able hovering living flier is always a concern of researchers from the flapping wing micro aerial vehicles community. In this work, the separate or combined optimizations of wing geometry or/and wing kinematic parameters are systematically performed to minimize the energy of hovering flight, firstly on the basis of analytically extended quasi-steady aerodynamic model by using hybrid genetic algorithm. Before the elaboration of the optimization problem, the parametrization description of dynamically scaled wing with non-dimensional conformal feature of insect-scale rigid wing is firstly proposed. The optimization results show that the combined optimization of wing geometry and kinematic parameters can obtain lower flapping frequency, larger wing geometry parameters and lower power density in comparison with those from other cases of optimization. Moreover, the flapping angle for the optimization involving wing kinematic parameters manifests harmonic shape profile and the pitch angle possesses round trapezoidal profile with certain faster time scale of pitch reversal. The combined optimization framework provides a novel method for the conceptual design of fundamental parameters of biomimetic flapping wing micro aerial vehicle.

Few strongly interacting ultracold fermions in one-dimensional traps of different shapes

The ground-state properties of a few spin-1/2 fermions with different masses and interacting via short-range contact forces are studied within an exact diagonalization approach. It is shown that, depending on the shape of the external confinement, different scenarios of the spatial separation between components manifested by specific shapes of the density profiles can be obtained in the strong interaction limit. We find that the ground-state of the system undergoes a specific transition between orderings when the confinement is changed adiabatically from a uniform box to a harmonic oscillator shape. We study the properties of this transition in the framework of the finite-size scaling method adopted to few-body systems.

Bounded distortion harmonic shape interpolation

Planar shape interpolation is a classic problem in computer graphics. We present a novel shape interpolation method that blends C ∞ planar harmonic mappings represented in closed-form. The intermediate mappings in the blending are guaranteed to be locally injective C ∞ harmonic mappings, with conformal and isometric distortion bounded by that of the input mappings. The key to the success of our method is the fact that the blended differentials of our interpolated mapping have a simple closed-form expression, so they can be evaluated with unprecedented efficiency and accuracy. Moreover, in contrast to previous approaches, these differentials are integrable, and result in an actual mapping without further modification. Our algorithm is embarrassingly parallel and is orders of magnitude faster than state-of-the-art methods due to its simplicity, yet it still produces mappings that are superior to those of existing techniques due to its guaranteed bounds on geometric distortion.

NFAL Prototype Design and Feasibility Analysis for Self-Levitated Conveying

ABSTRACTIn order to avoid friction and scratching when conveying object, an acoustic levitation prototype was designed to verify the feasibility. The modal shapes and the forced harmonic shapes of the prototype are obtained by an ANSYS coupled field computation with a one-quarter symmetry model and the levitation capacity was assessed by the use of groups of simulation and physical testing. The simulation results showed that the pure flexural and mixed flexural wave shapes with different wave numbers existed at some specific frequency. The amplitude in the central point of an aluminum plate having four piezo-electric discs glued to the bottom surface was simulated for a frequency spectrum. The experimental results confirmed the theoretical results and the feasibility of the prototype and confirm that objects can be floated at several resonant frequencies under forced vibrating condition. The system can provide largest bearing capacity when both the piezoelectric disc and the plate resonances coincide.

FILTRATIONAL PRESSURE WAVES AS A METHOD OF RESERVOIR FLOW PARAMETERS INVESTIGATION

The control of the oil fields development requires knowledge of the reservoirs filtration parameters in the borehole environment and in the inter-well space. These parameters can be evaluated based on geophysical data and laboratory studies of the cores, but reliable information about the filtration parameters can be obtained only from hydrodynamic experiments. Studies of the reservoirs are carried out under conditions of both steady and unsteady filtration. This paper describes one of unsteady methods for studying reservoirs, i.e. the method of filtration waves of pressure, which can be regarded as a kind of pulse test or cyclic flow rate variation. In this research, the method of filtration waves of pressure as a method for determining the hydrodynamic parameters of fluid-saturated reservoirs is considered. The concept of this method suggests stimulation of periodic changes of flow rate and, respectively, pressure in one of the wells, this resulting in propagation of waves of diffusion type in the fluid-saturated reservoir; and in the neighboring wells responses to the initial disturbance in the form of pressure change with the same period as in the active well will be recorded. Phase velocity and damping coefficient of these waves, as well as the parameters of the filtration medium can be determined based on the measured values of amplitudes and phases of the pressure waves. If, using a device for flow control in the active well, to set change of flow rate q (t) in the value close to harmonic shape, then a quasi-harmonic change in pressure P (t) will take place in the bottom hole with the same period, as well. This kind of research of the wellbore environment represents a periodic self-listening of the wells. The analysis results of the dispersion relations will make it possible to establish a type of filtration and an adequate mathematical model. The study of the type of pressure change curves will allow assessing the degree of medium's nonlinearity, to draw conclusions regarding anisotropy of the reservoir and discontinuity of distribution of the filtration parameters in the borehole environment.

Harmonic shapes in isotropic laminated plates

Harmonic shapes in isotropic laminated plates

Analysis of regional deformation of the heart's left ventricle using invariant SPHARM descriptors

This paper presents a method to analyze the regional deformation of the heart left ventricle (LV). It consists of two steps. First, based on previous work a global analysis is carried out in order to detect any pathological cases using 3D spherical harmonic (SPHARM) shape description process. The computed invariant SPHARM shape descriptors are used to compute the distance between the LV anatomical structures namely the endocardium and epicardium. Secondly, to accurately determine the site and the extent of the disease, a regional analysis is achieved. For this purpose, a 3D division into 17 regions’ 3D closed surfaces according to the AHA standard is carried out and a surface closing process is proposed. Each resulting region is then decomposed into a spherical harmonic basis. The regional invariant SPHARM descriptors are generated and used to quantify regional deformations. This method has been validated on deformable surfaces synthesized using an ellipsoidal model and real data obtained from myocardial scintigraphy imaging techniques.

Analytical investigation of the SAFE diagram for bladed wheels, numerical and experimental validation

Compressor and turbine bladed wheels interact with the fluid distributed by the stator vanes. They are subject to vibration and fatigue loading, especially when resonance conditions are excited. Avoiding resonance is fundamental when designing bladed wheels. The Campbell diagram approach is too conservative since bladed wheels show many close frequency natural modes, thus it is almost impossible to avoid frequency matching. Singh׳s Advanced Frequency Evaluation (SAFE) diagram, or interference diagram, also introduces shape matching in addition to the frequency, for resonance prediction, therefore many frequency matching cases can be identified as non-critical and thus tolerated. The present paper explains and demonstrates the SAFE diagram by introducing an analytical expression to identify bladed wheel resonance conditions. The mode shape matching with a harmonic component is investigated by means of specific examples. Symmetry properties of the matching distribution of harmonic indices and mode shapes are also introduced and demonstrated. Finally, a bladed wheel analysis is used for validation, both in FE simulations and experiments.

A displacement‐based finite element formulation for general polyhedra using harmonic shape functions

SUMMARYA displacement‐based continuous‐Galerkin finite element formulation for general polyhedra is presented for applications in nonlinear solid mechanics. The polyhedra can have an arbitrary number of vertices or faces. The faces of the polyhedra can have an arbitrary number of edges and can be nonplanar. The polyhedra can be nonconvex with only the mild restriction of star convexity with respect to the vertex‐averaged centroid. Conforming shape functions are constructed using harmonic functions defined on the undeformed configuration, thus requiring the use of a total‐Lagrangian finite element formulation in large deformation applications. For nonlinear applications with computationally intensive constitutive models, it is important to minimize the number of element quadrature points. For this reason, an integration scheme is adopted in which the number of quadrature points is equal to the number of vertices. As a first step toward verifying the element behavior in the general nonlinear setting, several linear verification examples are presented using both random Voronoi meshes and distorted hexahedral meshes. For the hexahedral meshes, results for the polyhedral formulation are compared to those of the standard trilinear hexahedral formulation. The element behavior in the nearly incompressible regime is also examined. Copyright © 2013 John Wiley & Sons, Ltd.

Enhancement of Second Harmonic Signal in Nanofabricated Cones

Geometrical effects in optical nanostructures on nanoscale can lead to interesting phenomena such as inhibition of spontaneous emission,1,2 high-reflecting omnidirectional mirrors, structures that exhibit low-loss-waveguiding,3 and light confinement.4,5 Here, we demonstrate a similar concept of exploiting the geometrical effects on nanoscale through precisely fabricating lithium niobate (LiNbO3) nanocones arrays devices. We show a strong second harmonic generation (SHG) enhancement, shape and arrangement dependent, up to 4 times bigger than the bulk one. These devices allow below diffraction limited observation, being perfect platforms for single molecule fluorescence microscopy6 or single cell endoscopy.7 Nanocones create a confined illumination volume, devoid from blinking and bleaching, which can excite molecules in nanocones proximity. Illumination volume can be increased by combining the SH enhancement effect with plasmon resonances, excited thanks to a gold plasmonic shell deposited around the nanostructures. This results in a local further enhancement of the SH signal up to 20 times. The global SH enhancement can be rationally designed and tuned through the means of simulations.

An Engineering Drawing Retrieval Method Based on Spherical Harmonics

In this paper, an engineering drawing retrieval method based on spherical harmonics is proposed. Firstly, the sample points are uniformly generated by computing the interaction points between the rays and the engineering drawing. Secondly, the sampled points are transformed from the 2D space into the 3D space to get the spherical harmonics shape descriptors. Finally, the Euclidean distance is adopted to compute the distance between the two feature vectors, which can give the similarity coefficient for two compared engineering drawings. Experimental results show that the proposed method is good at retrieving engineering drawings and the retrieval performance can meet the requirement of the practical retrieval.

Third harmonic shear horizontal and Rayleigh Lamb waves in weakly nonlinear plates

The third order harmonic generation (third harmonics as well as cubic sum and difference harmonics) due to the cubic interaction of two collimated elastic waves in a homogeneous, isotropic, weakly nonlinear plate is investigated by using a fourth order expansion of strain energy density to formulate the nonlinear boundary problems. Waves with both shear horizontal (SH) and Rayleigh Lamb (RL) nature are considered as primary or tertiary wave fields. The non-zero power flux condition is evaluated using characteristic parity matrices of the cubic nonlinear forcing terms and third order harmonic mode shapes. Results indicate that waves with either SH or RL nature receive power flux from a specific pattern of primary mode interaction. Further analytical evaluation of the synchronism condition enables identification of primary SH and RL modes that are able to generate cumulative third harmonics. The primary SH modes are shown to be holo-internal-resonant with third harmonic SH fields. This simply means that all points on the primary dispersion curves are internally resonant with third harmonics, which is not the case for second harmonics. Such flexibility will be advantageous for laboratory and field measurements.

Multi-coil magnetic field modeling

The performance of multi-coil (MC) magnetic field modeling is compared to dedicated wire patterns for the generation of spherical harmonic (SH) shapes as these are the workhorse for spatial encoding and magnetic field homogenization in MR imaging and spectroscopy. To this end, an example 48 channel MC setup is analyzed and shown to be capable of generating all first through fourth order SH shapes over small and large regions-of-interest relevant for MR investigations. The MC efficiency for the generation of linear gradient fields shares the same order of magnitude with classic and state-of-the-art SH gradient coils. MC field modeling becomes progressively more efficient with the synthesis of more complex field shapes that require the combination of multiple SH terms. The possibility of a region-specific optimization of both magnetic field shapes and generation performance with the MC approach are discussed with emphasis on the possible trade-off between the field accuracy and generation efficiency.MC shimming has been shown previously to outperform current SH shimming. Along with the efficiency gains of MC shimming shown here, the MC concept has the potential to (1) replace conventional shim systems that are based on sets of dedicated SH coils and (2) allow optimal object-specific shim solutions similar to object-specific RF coils.

Analyzing mistuned multi-stage turbomachinery rotors with aerodynamic effects

A great deal of research has been conducted on accurately modeling large cyclic structures such as turbomachinery rotors. Accurate modeling of realistic industrial turbomachinery requires overcoming several challenges. The first is the excessively large size of the finite element models (FEMs) needed, which can contain millions of degrees of freedom per stage of the rotor. The second challenge is the presence of small random variations in the structural properties known as mistuning, which arise from operational wear and/or manufacturing tolerances, and destroy the cyclic symmetry of the FEMs. The third is the complexity of turbomachinery models, which often include multiple stages that often have a mismatched computational grid at the interface between stages. The fourth challenge is associated with modeling the aerodynamic loads on the turbomachinery rotor. Much research has been conducted to overcome the first two challenges. By combining cyclic symmetry analysis and component mode mistuning (CMM), compact single-stage reduced order models (ROMs) can be created to accurately capture the free and forced response of these systems. These highly efficient ROMs can be developed from single sector calculations and can be of the order of the number of sectors in the stage. Recently, the third challenge associated with the complexity of modeling multiple stages has been addressed by the authors. Their method uses cyclic symmetry and CMM to form single-stage ROMs (using only single sector models and single sector calculations), and then combines these single-stage ROMs by projecting the motion along the interface between stages along a set of harmonic shape functions. This method allows for the creation of compact ROMs of multi-stage systems with mistuning using sector only calculations. The fourth challenge has been addressed only for single-stage systems by computing a complex aerodynamic matrix (which contains stiffness and damping terms) using an iterative approach. In this work, some of the effects of the aerodynamics on multi-stage systems are explored. The methodology consists of first creating efficient structural ROMs of a multi-stage rotor using the method previously developed, and then iteratively calculating the complex aerodynamic matrices for each stage. A new way to account for the effects of a shift in frequency due to mistuning on the complex aerodynamic matrix is also proposed. Additionally, a new classification of complex multi-stage aeroelastic modes is introduced. The presented results focus on exploring the influences of the aerodynamics and mistuning on the multi-stage response. A variety of numerical results are analyzed for two stages of an industrial rotor.

Shape Abnormalities of the Caudate Nucleus Correlate with Poorer Gait and Balance: Results from a Subset of the LADIS Study

Functional deficits seen in several neurodegenerative disorders have been linked with dysfunction in frontostriatal circuits and with associated shape alterations in striatal structures. The severity of visible white matter hyperintensities (WMHs) on magnetic resonance imaging has been found to correlate with poorer performance on measures of gait and balance. This study aimed to determine whether striatal volume and shape changes were correlated with gait dysfunction. Magnetic resonance imaging scans and clinical gait/balance data (scores from the Short Physical Performance Battery [SPPB]) were sourced from 66 subjects in the previously published LADIS trial, performed in nondisabled individuals older than age 65 years with WMHs at study entry. Data were obtained at study entry and at 3-year follow-up. Caudate nuclei and putamina were manually traced using a previously published method and volumes calculated. The relationships between volume and physical performance on the SPPB were investigated with shape analysis using the spherical harmonic shape description toolkit. There was no correlation between the severity of WMHs and striatal volumes. Caudate nuclei volume correlated with performance on the SPPB at baseline but not at follow-up, with subsequent shape analysis showing left caudate changes occurred in areas corresponding to inputs of the dorsolateral prefrontal, premotor, and motor cortex. There was no correlation between putamen volumes and performance on the SPPB. Disruption in frontostriatal circuits may play a role in mediating poorer physical performance in individuals with WMHs. Striatal volume and shape changes may be suitable biomarkers for functional changes in this population.

Dependence of Harmonic Spectrum Shape on Laser Beam Intensity in Interaction With Atoms

We present a method to calculate the harmonic spectrum of the radiation emitted at the interactions between intense laser beams and atoms. Our relations describe accurately, in good agreement with the experiment, important features of the harmonic spectrum and the evolution of its shape with the increase of the laser beam intensity. More specifically, for low intensities, of the order of $10^{13}~{\rm W}/{\rm cm}^{2}$ , the spectrum has the well-known plateau shape, after which follows a sharp decrease at the cutoff edge. When the beam intensity is increased, toward $10^{15}~{\rm W}/{\rm cm}^{2}$ , the slope of the plateau increases, corresponding to a decrease by one or two orders of magnitude of the harmonic intensities. When the beam intensity is increased more, toward $10^{17}~{\rm W}/{\rm cm}^{2}$ , there is a maximum at the left edge of the spectrum, which is followed by a strong decrease of many orders of magnitude, and the spectrum concentrates in a very limited domain, under a certain frequency, far lower than the theoretical cutoff frequency. These theoretical results are in good agreement with numerous experimental data from the literature, for many atoms and ions, and for a large spectrum of intensities of laser beams. This result has important implications in the emerging field of generation of high intensity hard X-rays.

Lateral ventricle morphology analysis via mean latitude axis.

Statistical shape analysis has emerged as an insightful method for evaluating brain structures in neuroimaging studies, however most shape frameworks are surface based and thus directly depend on the quality of surface alignment. In contrast, medial descriptions employ thickness information as alignment-independent shape metric. We propose a joint framework that computes local medial thickness information via a mean latitude axis from the well-known spherical harmonic (SPHARM-PDM) shape framework. In this work, we applied SPHARM derived medial representations to the morphological analysis of lateral ventricles in neonates. Mild ventriculomegaly (MVM) subjects are compared to healthy controls to highlight the potential of the methodology. Lateral ventricles were obtained from MRI scans of neonates (9-144 days of age) from 30 MVM subjects as well as age- and sex-matched normal controls (60 total). SPHARM-PDM shape analysis was extended to compute a mean latitude axis directly from the spherical parameterization. Local thickness and area was straightforwardly determined. MVM and healthy controls were compared using local MANOVA and compared with the traditional SPHARM-PDM analysis. Both surface and mean latitude axis findings differentiate successfully MVM and healthy lateral ventricle morphology. Lateral ventricles in MVM neonates show enlarged shapes in tail and head. Mean latitude axis is able to find significant differences all along the lateral ventricle shape, demonstrating that local thickness analysis provides significant insight over traditional SPHARM-PDM. This study is the first to precisely quantify 3D lateral ventricle morphology in MVM neonates using shape analysis.