scholarly journals Modal dynamics of structures with bladed isotropic rotors and its complexity for two-bladed rotors

2016 ◽  
Vol 1 (2) ◽  
pp. 271-296 ◽  
Author(s):  
Morten Hartvig Hansen
Keyword(s):  
Fourier Series ◽  
Degrees Of Freedom ◽  
Mass Matrix ◽  
Single Mode ◽  
Model Parameters ◽  
System Matrix ◽  
Resonance Frequencies ◽  
Set Up ◽  
Truncated Fourier Series ◽  
Modal Dynamics

Abstract. The modal dynamics of structures with bladed isotropic rotors is analyzed using Hill's method. First, analytical derivation of the periodic system matrix shows that isotropic rotors with more than two blades can be represented by an exact Fourier series with 3/rev (three per rotor revolution) as the highest order. For two-bladed rotors, the inverse mass matrix has an infinite Fourier series with harmonic components of decreasing norm; thus, the system matrix can be approximated by a truncated Fourier series of predictable accuracy. Second, a novel method for automatically identifying the principal solutions of Hill's eigenvalue problem is introduced. The corresponding periodic eigenvectors can be used to compute symmetric and antisymmetric components of the two-bladed rotor motion, as well as the additional forward and backward whirling components for rotors with more than two blades. To illustrate the use of these generic methods, a simple wind turbine model is set up with three degrees of freedom for each blade and seven degrees of freedom for the nacelle and drivetrain. First, the model parameters are tuned such that the low-order modal dynamics of a three-bladed 10 MW turbine from previous studies is recaptured. Second, one blade is removed, leading to larger and higher harmonic terms in the system matrix. These harmonic terms lead to modal couplings for the two-bladed turbine that do not exist for the three-bladed turbine. A single mode of a two-bladed turbine will also have several resonance frequencies in both the ground-fixed and rotating frames of reference, which complicates the interpretation of simulated or measured turbine responses.

scholarly journals Modal dynamics of structures with bladed isotropic rotors and its complexity for 2-bladed rotors

2016 ◽  
Author(s):  
Morten Hartvig Hansen
Keyword(s):  
Fourier Series ◽  
Degrees Of Freedom ◽  
Mass Matrix ◽  
Single Mode ◽  
System Matrix ◽  
Rotating Blade ◽  
Bladed Rotor ◽  
Harmonic Components ◽  
Truncated Fourier Series ◽  
Modal Dynamics

Abstract. The modal dynamics of structures with bladed isotropic rotors is analyzed using Hill's method. First, analytical derivation of the periodic system matrix shows that isotropic rotors with more than two blades can be represented by an exact Fourier series with 3/rev as the highest order. For 2-bladed rotors, the inverse mass matrix has an infinite Fourier series with harmonic components of decreasing norm, thus the system matrix can be approximated by a truncated Fourier series of predictable accuracy. Second, a novel method for automatically identifying the principal solutions of Hill's eigenvalue problem is introduced. The corresponding periodic eigenvectors can be used to compute symmetric and anti-symmetric components of the 2-bladed rotor motion, and the additional forward and backward whirling components for rotors with more than two blades. Finally, the generic methods are used on a simple wind turbine model consisting of three degrees of freedom for each blade and seven degrees of freedom for the nacelle and drivetrain. The modal dynamics of a 3-bladed 10MW turbine from previous studies is recaptured. Removing one blade, the larger and higher harmonic terms in the system matrix lead to resonant modal couplings for the 2-bladed turbine that do not exist for the 3-bladed turbine, and that excitation of a single mode of a 2-bladed turbine leads to responses at several frequencies in both the ground-fixed and rotating blade frames of reference which complicates the interpretation of simulated or measured turbine responses.

Application of Error Analysis Method in the Complex Vehicle Model

2012 ◽  
Vol 591-593 ◽  
pp. 584-587
Author(s):  
Shui Rong Liao ◽  
Tao Yang
Keyword(s):  
Error Analysis ◽  
Degrees Of Freedom ◽  
Lateral Acceleration ◽  
Steering Wheel ◽  
Model Parameters ◽  
Vehicle Model ◽  
Two Degrees Of Freedom ◽  
Input Amplitude ◽  
Sinusoidal Input ◽  
Set Up

A two degree of freedom input vehicle model is set up. Based on driver modeling analytical method of error analysis, step signal is taken as the input of steering angle to complex vehicle model based on CarSim, vehicle lateral acceleration is taken as as output. Meanwhile, the same steering wheel angle is taken as input as equivalent two degrees of freedom vehicle model, vehicle model parameters are optimized based on the minimum objective function. The results show that, in the same kind of speed, for steering wheel angle step input and sinusoidal input , when the input amplitude increases, the equivalent accuracy of the complex vehicle model and two degrees of freedom vehicle model will be reduced.

Investigation of discontinuous periodic signals using the measuring labview complex

2020 ◽  
pp. 72-79
Author(s):  
E.B. Solovyeva ◽  
◽  
Yu.M. Inshakov ◽  
Keyword(s):  
Fourier Series ◽  
Laboratory Experiment ◽  
Gibbs Phenomenon ◽  
Electrical Signals ◽  
Measuring Complex ◽  
Universal Measuring ◽  
Depth Study ◽  
Periodic Signals ◽  
Truncated Fourier Series

General approaches to the analysis of the Gibbs phenomenon for discontinuous periodic signals approximated by the truncated Fourier series are considered. Methods for smoothing the truncated Fourier series and improving its convergence are discussed. The software means for modeling is a universal measuring complex LabVIEW, which possesses a convenient environment for analyzing electrical signals, on the basis of this complex a laboratory experiment is carried out. The advantages of the measuring LabVIEW complex and its capabilities for in-depth study of discontinuous periodic signals are noted.

scholarly journals Dynamics of Fourier Modes in Torus Generative Adversarial Networks

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 325
Author(s):  
Ángel González-Prieto ◽  
Alberto Mozo ◽  
Edgar Talavera ◽  
Sandra Gómez-Canaval
Keyword(s):  
Fourier Series ◽  
Generative Adversarial Networks ◽  
Learning Models ◽  
Training Process ◽  
Small Perturbations ◽  
Adversarial Networks ◽  
Novel Method ◽  
Truncated Fourier Series ◽  
Real Flow ◽  
Machine Learning Models

Generative Adversarial Networks (GANs) are powerful machine learning models capable of generating fully synthetic samples of a desired phenomenon with a high resolution. Despite their success, the training process of a GAN is highly unstable, and typically, it is necessary to implement several accessory heuristics to the networks to reach acceptable convergence of the model. In this paper, we introduce a novel method to analyze the convergence and stability in the training of generative adversarial networks. For this purpose, we propose to decompose the objective function of the adversary min–max game defining a periodic GAN into its Fourier series. By studying the dynamics of the truncated Fourier series for the continuous alternating gradient descend algorithm, we are able to approximate the real flow and to identify the main features of the convergence of GAN. This approach is confirmed empirically by studying the training flow in a 2-parametric GAN, aiming to generate an unknown exponential distribution. As a by-product, we show that convergent orbits in GANs are small perturbations of periodic orbits so the Nash equillibria are spiral attractors. This theoretically justifies the slow and unstable training observed in GANs.

scholarly journals Designing of Drive Systems in the Aspect of the Desired Spectrum of Operation

Energies ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2562
Author(s):  
Tomasz Dzitkowski ◽  
Andrzej Dymarek ◽  
Jerzy Margielewicz ◽  
Damian Gąska ◽  
Lukasz Orzech ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Dynamic Parameters ◽  
Synthesis Algorithm ◽  
Moments Of Inertia ◽  
Driving System ◽  
Six Degrees Of Freedom ◽  
Resonance Frequencies ◽  
Drive Systems ◽  
Power Component

A method for selecting dynamic parameters and structures of drive systems using the synthesis algorithm is presented. The dynamic parameters of the system with six degrees of freedom, consisting of a power component (motor) and a two-speed gearbox, were determined, based on a formalized methodology. The required gearbox is to work in specific resonance zones, i.e., meet the required dynamic properties such as the required resonance frequencies. In the result of the tests, a series of parameters of the drive system, defining the required dynamic properties such as the resonance and anti-resonance frequencies were recorded. Mass moments of inertia of the wheels and elastic components, contained in the required structure of the driving system, were determined for the selected parameters obtained during the synthesis.

scholarly journals Galloping Stability and Wind Tunnel Test of Iced Quad Bundled Conductors considering Wake Effect

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Xiaohui Liu ◽  
Ming Zou ◽  
Chuan Wu ◽  
Mengqi Cai ◽  
Guangyun Min ◽  
...  
Keyword(s):  
Wind Tunnel ◽  
Transmission Lines ◽  
Degrees Of Freedom ◽  
Wind Tunnel Test ◽  
Aerodynamic Coefficients ◽  
Wake Effect ◽  
Aerodynamic Coefficient ◽  
Set Up ◽  
The Stability ◽  
Three Degrees Of Freedom

A new quad bundle conductor galloping model considering wake effect is proposed to solve the problem of different aerodynamic coefficients of each subconductor of iced quad bundle conductor. Based on the quasistatic theory, a new 3-DOF (three degrees of freedom) galloping model of iced quad bundle conductors is established, which can accurately reflect the energy transfer and galloping of quad bundle conductor in three directions. After a series of formula derivations, the conductor stability judgment formula is obtained. In the wind tunnel test, according to the actual engineering situation, different variables are set up to accurately simulate the galloping of iced quad bundle conductor under the wind, and the aerodynamic coefficient is obtained. Finally, according to the stability judgment formula of this paper, calculate the critical wind speed of conductor galloping through programming. The dates of wind tunnel test and calculation in this paper can be used in the antigalloping design of transmission lines.

scholarly journals An enhanced set of displacement parameter restraints in CRYSTALS

2018 ◽  
Vol 51 (4) ◽  
pp. 1059-1068 ◽  
Author(s):  
Pascal Parois ◽  
James Arnold ◽  
Richard Cooper
Keyword(s):  
Structural Model ◽  
Rigid Bodies ◽  
Model Parameters ◽  
Coordinate Systems ◽  
Principal Axes ◽  
Anisotropic Displacement Parameters ◽  
Set Up ◽  
Meaningful Relationships ◽  
Parameter Values ◽  
Total Model

Crystallographic restraints are widely used during refinement of small-molecule and macromolecular crystal structures. They can be especially useful for introducing additional observations and information into structure refinements against low-quality or low-resolution data (e.g. data obtained at high pressure) or to retain physically meaningful parameter values in disordered or unstable refinements. However, despite the fact that the anisotropic displacement parameters (ADPs) often constitute more than half of the total model parameters determined in a structure analysis, there are relatively few useful restraints for them, examples being Hirshfeld rigid-bond restraints, direct equivalence of parameters and SHELXL RIGU-type restraints. Conversely, geometric parameters can be subject to a multitude of restraints (e.g. absolute or relative distance, angle, planarity, chiral volume, and geometric similarity). This article presents a series of new ADP restraints implemented in CRYSTALS [Parois, Cooper & Thompson (2015), Chem. Cent. J. 9, 30] to give more control over ADPs by restraining, in a variety of ways, the directions and magnitudes of the principal axes of the ellipsoids in locally defined coordinate systems. The use of these new ADPs results in more realistic models, as well as a better user experience, through restraints that are more efficient and faster to set up. The use of these restraints is recommended to preserve physically meaningful relationships between displacement parameters in a structural model for rigid bodies, rotationally disordered groups and low-completeness data.

scholarly journals Melting and freezing under Antarctic ice shelves from a combination of ice-sheet modelling and observations

2017 ◽  
Vol 63 (240) ◽  
pp. 731-744 ◽  
Author(s):  
JORGE BERNALES ◽  
IRINA ROGOZHINA ◽  
MAIK THOMAS
Keyword(s):  
Mass Balance ◽  
Ice Sheet ◽  
Model Parameters ◽  
Ice Shelf ◽  
Ice Shelves ◽  
Continental Scale ◽  
Model Set ◽  
Set Up ◽  
Basal Melting ◽  
The Antarctic

ABSTRACTIce-shelf basal melting is the largest contributor to the negative mass balance of the Antarctic ice sheet. However, current implementations of ice/ocean interactions in ice-sheet models disagree with the distribution of sub-shelf melt and freezing rates revealed by recent observational studies. Here we present a novel combination of a continental-scale ice flow model and a calibration technique to derive the spatial distribution of basal melting and freezing rates for the whole Antarctic ice-shelf system. The modelled ice-sheet equilibrium state is evaluated against topographic and velocity observations. Our high-resolution (10-km spacing) simulation predicts an equilibrium ice-shelf basal mass balance of −1648.7 Gt a−1 that increases to −1917.0 Gt a−1 when the observed ice-shelf thinning rates are taken into account. Our estimates reproduce the complexity of the basal mass balance of Antarctic ice shelves, providing a reference for parameterisations of sub-shelf ocean/ice interactions in continental ice-sheet models. We perform a sensitivity analysis to assess the effects of variations in the model set-up, showing that the retrieved estimates of basal melting and freezing rates are largely insensitive to changes in the internal model parameters, but respond strongly to a reduction of model resolution and the uncertainty in the input datasets.

LOWER LIMB REHABILITATION ROBOT FOR GAIT TRAINING

2014 ◽  
Vol 14 (06) ◽  
pp. 1440004 ◽  
Author(s):  
SHUAI GUO ◽  
JIANCHENG JI ◽  
GUANGWEI MA ◽  
TAO SONG ◽  
JING WANG
Keyword(s):  
Lower Limb ◽  
Degrees Of Freedom ◽  
Balance Training ◽  
Gait Training ◽  
Rehabilitation Robot ◽  
Stroke Patients ◽  
Motion Characteristics ◽  
Set Up ◽  
Limb Rehabilitation ◽  
Lower Limb Rehabilitation

After analyzing the rehabilitation needs of stroke patients and the previous studies on lower limb rehabilitation robot, our lower limb rehabilitation robot is designed for stroke patients' gait and balance training. The robot consists of the mobile chassis, the support column and the pelvis mechanism and it is described in detail. As the pelvis mechanism allows most of the patient's motion degrees of freedom (DOFs), the kinematics model of the mechanism is set up, and kinematics simulation is carried out to study the motion characteristics of the mechanism. After analyzing the calculation and simulation results, the pelvis mechanism is proven to measure up to the movement needs of the paralytic's waist and pelvis in walking rehabilitation process.

scholarly journals Dielectric Elastomer Actuator Driven Soft Robotic Structures With Bioinspired Skeletal and Muscular Reinforcement

2020 ◽  
Vol 7 ◽  
Author(s):  
M. Franke ◽  
A. Ehrenhofer ◽  
S. Lahiri ◽  
E.-F. M. Henke ◽  
T. Wallmersperger ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Aerosol Deposition ◽  
Dielectric Elastomer ◽  
Artificial Muscles ◽  
Soft Systems ◽  
Natural Motion ◽  
Dielectric Elastomer Actuators ◽  
Resonance Frequencies ◽  
Wide Range ◽  
Laminate Theory

Natural motion types found in skeletal and muscular systems of vertebrate animals inspire researchers to transfer this ability into engineered motion, which is highly desired in robotic systems. Dielectric elastomer actuators (DEAs) have shown promising capabilities as artificial muscles for driving such structures, as they are soft, lightweight, and can generate large strokes. For maximum performance, dielectric elastomer membranes need to be sufficiently pre-stretched. This fact is challenging, because it is difficult to integrate pre-stretched membranes into entirely soft systems, since the stored strain energy can significantly deform soft elements. Here, we present a soft robotic structure, possessing a bioinspired skeleton integrated into a soft body element, driven by an antagonistic pair of DEA artificial muscles, that enable the robot bending. In its equilibrium state, the setup maintains optimum isotropic pre-stretch. The robot itself has a length of 60 mm and is based on a flexible silicone body, possessing embedded transverse 3D printed struts. These rigid bone-like elements lead to an anisotropic bending stiffness, which only allows bending in one plane while maintaining the DEA's necessary pre-stretch in the other planes. The bones, therefore, define the degrees of freedom and stabilize the system. The DEAs are manufactured by aerosol deposition of a carbon-silicone-composite ink onto a stretchable membrane that is heat cured. Afterwards, the actuators are bonded to the top and bottom of the silicone body. The robotic structure shows large and defined bimorph bending curvature and operates in static as well as dynamic motion. Our experiments describe the influence of membrane pre-stretch and varied stiffness of the silicone body on the static and dynamic bending displacement, resonance frequencies and blocking forces. We also present an analytical model based on the Classical Laminate Theory for the identification of the main influencing parameters. Due to the simple design and processing, our new concept of a bioinspired DEA based robotic structure, with skeletal and muscular reinforcement, offers a wide range of robotic application.

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