Rigid Body Degrees Of Freedom Research Articles

ANCF-based modelling of rigid-flexible coupling of helicopter flexible rotor blades

Abstract A high-precision rotor structure dynamic model applicable to a variety of helicopter blade hub structures is established considering rotor blade flexible deformation. The absolute nodal coordinate method is applied to the traditional rotor blade rigid-flexible coupling dynamics model, making the new model applicable to both fully articulated rotor blades and other advanced blade hub structures. No small-volume assumptions were made in the modelling process. Both Green’s strain expression under finite deformation and the geometrical relation of elastic deformation motion based on the absolute nodal coordinate method are used to derive the blade strain energy, kinetic energy, and the external load virtual work. The rotation angle at the articulation constraint at the root of the blade coupled with the elastic deformation degrees of freedom of the blade in three independent rigid body degrees of freedom, respectively. The rotor blade rigid-flexible coupling dynamics equations were established according to the Hamilton action principle. The time-domain simulation is carried out under a free single pendulum and fixed rotational speed/fixed torque for the established flexible blade model, which verifies the validity and high accuracy of the rigid-flexible coupling articulation model of the flexible rotor blade and the blade hub.

Nonlinear Helicopter Rigid-Elastic Coupled Modeling with Its Applications on Aeroservoelasticity Analysis

This paper represents a new mathematical model for helicopters with flexible fuselages. The theory connects the two commonly separated research areas of flight, dynamics and structural dynamics, by considering all necessary effects of a flexible fuselage on helicopter flight dynamic characteristics. They are rigid-elastic couplings of the flexible fuselage between six rigid-body degrees of freedom and elastic deformations, along with inertial and kinematic couplings between subcomponents and the fuselage. This is achieved by using the floating frame theory and deriving the acceleration coupling matrices of subcomponents analytically. In addition, the obtained formulation is explicitly decoupled such that all unknown absolute accelerations could be obtained in a single step without iterations, which could improve computational efficiency greatly. This model is suited for aeroservoelastic analysis, and is particularly suited for heavy lift helicopters (HLH) because they usually have slower turning rotors and more flexible fuselages due to their larger scale, leading to closer frequency ranges between rigid body motions and high-frequency rotor and structural modes. The model is validated before being applied to a numerical example of a sample HLH with a feedback loop for stability augmentation. The results show that the feedback loop connects actuators, fuselage deformation, and rigid body motion and induces divergent oscillation, which is the aeroservoelastic instability that cannot be predicted without the additional sensor measurements feedback caused by dynamic deformation. Since the 10-second step response could be calculated in three seconds, the presented helicopter mathematical model is expected to be used in real-time simulations or even further in pilot-in-the-loop simulations, ultimately helping with the design of modern helicopters with nonnegligible fuselage flexibility.

Machine Learning Methods for Rapid Prediction of Thermostabilizing Mutants of G‐protein‐coupled receptors in Detergents

G protein‐coupled receptors (GPCRs) are highly dynamic and often denature when extracted in detergents. Deriving thermostable mutants has been a successful strategy to stabilize GPCRs in detergents, but this process is experimentally tedious. We have developed a computational method that scans the entire receptor for alanine or leucine mutations and calculates the stability score for mutation of each position in the GPCR structural model. The method involves generating homology models of the receptors of varying accuracies and an ensemble of conformations by sampling the rigid body degrees of freedom of transmembrane helices. Then, an all‐atom force field function is used to calculate the enthalpy gain, known as the “stability score” upon mutation of every residue, in these receptor structures, to alanine. Inclusion of conformational sampling to account for structural perturbations improves the thermostability predictions compared to using a single structure. We have validated the method against experimentally measured thermostability data for single mutants of the β1‐adrenergic receptor (β1AR), adenosine A2A receptor (A2AR) and neurotensin receptor 1 (NTSR1). We will present some of our recent results on blind predictions of thermostabilizing mutations on NTSR1.Using the computed energy components in our dataset, we have recently tested several machine learning algorithms for rapid and reliable prediction of thermostable and non‐thermostable mutants. We used Matlab to build a binary classification model (thermostable vs. non‐thermostable) trained on data from an ensemble of three proteins (25% of dataset used for holdout cross‐validation), and tested against a fourth protein omitted from the training set. Initial dataset was heavily imbalanced to the “non‐thermostable” class. This was balanced by random replication of the undersampled “thermostable” class. Models trained by decision tree algorithms performed best in our study compared to k‐nearest neighbor (k‐NN) algorithms. Our precision and recall statistics for the best performing ensemble dataset were as follows: Boosted Trees – 62% precision, 34% recall, Simple Trees – 30% precision, 90% recall, Complex Trees – 36% precision, 73% recall, Medium k‐NN – 28% precision, 34% recall.These results are promising for predicting true thermostable mutants, and we are working to improve our methods for reducing the number of false positive predictions. This requires testing different training algorithms such as Support Vector Machines and other k‐NN and Decision Tree models, and potentially ensemble training models combining multiples of these algorithms. Our method is the first step toward a computational method for rapid prediction of thermostable mutants of GPCRs. These tools are critical for reliable and quick prediction of thermostabilizing mutations of GPCRs for drug discovery.Support or Funding InformationFunding for this work was from NIH‐RO1GM097261 to N.V.This abstract is from the Experimental Biology 2018 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Fault condition effects on the dynamic response of V-shaped offshore wind turbine

Offshore wind is an extensive renewable energy resource appropriate for fulfilling the increasing energy needs and increasing the security of energy supply. The issues related to the design of the support structure, installation, grid connection, operation, and maintenance in normal and fault conditions significantly influence the levelized cost of the produced energy. The feasibility of different concepts should be numerically calculated and assessed for all aforementioned issues. In this paper, the dynamic response of the V-shaped semisubmersible under different possible fault conditions is examined. Different response quantities of the floating wind turbine are compared for the case that the system operates under operational and fault conditions. The response quantities include motions of the platform in all six rigid-body degrees of freedom, mooring line tension, tower base-bending moment, and functionality of the wind turbine. A numerical model accounting for fully coupled dynamic analysis of the offshore wind turbine under different fault conditions has been developed. It is found that for the V-shaped semisubmersible, the mooring line tension is significantly affected by different fault conditions compared to the rest examined response quantities; the maximum value of the tension of the mooring lines is increased by a factor of 1.6 due to fault conditions. Among the different fault conditions, shutdown case seems to have the largest influence on the functionality and responses of the V-shaped floating wind turbine. For emergency shutdown fault conditions, backlash occurs that results in large variation of tower-bending moment.

Dynamics and control of robotic spacecrafts for the transportation of flexible elements

The technology of robotic spacecrafts has been identified as one of the most appealing solutions to the on-orbit construction of large space structures in future space missions. As a prerequisite of a successful on-orbit construction, it is needed to use small autonomous spacecrafts for the transportation of flexible elements. To this end, the paper presents an energy-based scheme to control a couple of robotic spacecrafts carrying a flexible slender structure to its desired position. The flexible structure is modelled as a long beam based on the formulation of absolute nodal coordinates to account for the geometrical nonlinearity due to large displacement. Meanwhile, the robotic spacecrafts are actuated on their rigid-body degrees of freedom and modelled as two rigid bodies attached to the flexible beam. The energy-based controller is designed using the technique of energy shaping and damping injection such that translational and rotational maneuvers can be achieved with the suppression of the flexible vibrations of the beam. Finally, numerical case studies are performed to demonstrate the proposed schemes.

Experimental and numerical study of the response of the offshore combined wind/wave energy concept SFC in extreme environmental conditions

This paper deals with an experimental study of the survivability of the offshore combined concept Semisubmersible wind energy and Flap-type wave energy Converter (SFC) and with comparisons of the experimental data with numerical predictions. The SFC is a combined energy concept consisting of a braceless semisubmersible type floating wind turbine and three fully submerged rotating flap-type Wave Energy Converters (WECs). In order to study the survivability of the concept the focus is on extreme environmental conditions. In these conditions the SFC will not produce wind or wave power; the wind turbine is parked with the blades feathered into the wind and the WECs are released to freely rotate about their axis of rotation. Firstly the development and set-up of the physical model are presented. Static, quasi-static, decay, regular waves and irregular waves with wind loading tests are conducted on an 1:50 scale physical model. Aligned and oblique wave with wind loading conditions are considered. Measured variables that are presented include motions of the semisubmersible platform in six rigid body degrees of freedom, rotation of the flap-type WECs, tension of mooring lines, internal loads of the arms that connect the flap with the pontoon of the platform and tower base bending moment. The experimental data are compared with numerical predictions obtained by a fully coupled numerical model. The comparison is made at model scale. A good agreement between experimental data and numerical predictions is observed confirming the accuracy of the numerical models and tools that are used. The discrepancy between numerical and experimental results is smaller for regular than irregular waves. Compared to oblique conditions a better agreement between experimental and numerical results is obtained for the case of aligned wave and wind loadings. The results obtained demonstrate the good performance of the SFC concept in extreme environmental conditions. No strong nonlinear hydrodynamic phenomena are observed in the tests.

Hybrid simulation approach incorporating microscopic interaction along with rigid body degrees of freedom for stacking between base pairs.

Stacking interaction between the aromatic heterocyclic bases plays an important role in the double helical structures of nucleic acids. Considering the base as rigid body, there are total of 18 degrees of freedom of a dinucleotide step. Some of these parameters show sequence preferences, indicating that the detailed atomic interactions are important in the stacking. Large variants of non-canonical base pairs have been seen in the crystallographic structures of RNA. However, their stacking preferences are not thoroughly deciphered yet from experimental results. The current theoretical approaches use either the rigid body degrees of freedom where the atomic information are lost or computationally expensive all atom simulations. We have used a hybrid simulation approach incorporating Monte-Carlo Metropolis sampling in the hyperspace of 18 stacking parameters where the interaction energies using AMBER-parm99bsc0 and CHARMM-36 force-fields were calculated from atomic positions. We have also performed stacking energy calculations for structures from Monte-Carlo ensemble by Dispersion corrected density functional theory. The available experimental data with Watson-Crick base pairs are compared to establish the validity of the method. Stacking interaction involving A:U and G:C base pairs with non-canonical G:U base pairs also were calculated and showed that these structures were also sequence dependent. This approach could be useful to generate multiscale modeling of nucleic acids in terms of coarse-grained parameters where the atomic interactions are preserved. This method would also be useful to predict structure and dynamics of different base pair steps containing non Watson-Crick base pairs, as found often in the non-coding RNA structures. © 2015 Wiley Periodicals, Inc. Biopolymers 105: 212-226, 2016.

Rapid Computational Prediction of Thermostabilizing Mutations for G Protein-Coupled Receptors.

G protein-coupled receptors (GPCRs) are highly dynamic and often denature when extracted in detergents. Deriving thermostable mutants has been a successful strategy to stabilize GPCRs in detergents, but this process is experimentally tedious. We have developed a computational method to predict the position of the thermostabilizing mutations for a given GPCR sequence. We have validated the method against experimentally measured thermostability data for single mutants of the β1-adrenergic receptor (β1AR), adenosine A2A receptor (A2AR) and neurotensin receptor 1 (NTSR1). To make these predictions we started from homology models of these receptors of varying accuracies and generated an ensemble of conformations by sampling the rigid body degrees of freedom of transmembrane helices. Then, an all-atom force field function was used to calculate the enthalpy gain, known as the “stability score” upon mutation of every residue, in these receptor structures, to alanine. For all three receptors, β1AR, A2AR, and NTSR1, we observed that mutations of hydrophobic residues in the transmembrane domain to alanine that have high stability scores correlate with high experimental thermostability. The prediction using the stability score improves when using an ensemble of receptor conformations compared to a single structure, showing that receptor flexibility is important. We also find that our previously developed LITiCon method for generating conformation ensembles is similar in performance to predictions using ensembles obtained from microseconds of molecular dynamics simulations (which is computationally hundred times slower than LITiCon). We improved the thermostability prediction by including other properties such as residue-based stress and the extent of allosteric communication by each residue in the stability score. Our method is the first step toward a computational method for rapid prediction of thermostable mutants of GPCRs.

The equations of Lagrange for a continuous deformable body with rigid body degrees of freedom, written in a momentum based formulation

The present paper is concerned with Lagrange׳s Equations, applied to a deformable body in the presence of rigid body degrees of freedom. The Lagrange description of Continuum Mechanics is used. An exact version of the Equations is derived first. This version, which represents an identical extension of the Fundamental Law of Dynamics, does involve the idea of virtual motions. The virtual motion is described in the framework of the Ritz-Ansatz, but our derivation does not make use of D׳Alemberts principle, the principle of virtual work, or variational principles. From the exact version, by involving arguments related to the Galerkin approximation technique, we derive an approximate Ritz type version of Lagrange׳s Equations. This approximate version coincides with the traditional one, which is based on the notion of kinetic energy. However, since our derivation stems from the Fundamental Law of Dynamics, we have at our disposal an alternative formulation, which is based on the notion of local momentum. This momentum based version, which is the main topic of the present contribution, can be used for the purpose of performing independent checks of the energy based version of Lagrange׳s Equations. The momentum based version also clarifies that and how certain terms in the energy based version do cancel out. The momentum based version is worked out in the framework of the Floating Frame of Reference Formulation of Multibody Dynamics. Explicit formulas for the single terms of Lagrange׳s Equations are derived for the translational, rotational and flexible degrees of freedom of the deformable body, respectively. Corresponding Lagrange׳s Equations are explained in the light of the relations of Balance of Total Momentum, Balance of Total Moment of Momentum, of the Mean Stress Theorem and the notion of Virial of Forces. An embedding into the literature is given.

I-ATTRACT: a New Flexible Docking Approach for Investigating Protein Protein Interactions

Many of the most important processes in the cell are carried out by large molecular machines built up from multiple proteins. However, structural data for a large fraction of known and putative complexes is still lacking. Computational docking methods aim at predicting protein complexes based on the structure of the individual constituents. A new protein-protein docking approach, i-ATTRACT has been evaluated on a large benchmark. The docking combines rigid body degrees of freedom and fully flexible interface residues in a simultaneous potential energy minimization. To our knowledge this is the first docking method performing an energy minimization in degrees of freedom of multiple scale. Procedures combining Monte Carlo sampling and energy minimization were applied as well. Refinement of rigid body docking solutions from a systematic search with unbound protein structures using ATTRACT [1] shows promising results on a large number of cases. i-ATTRACT is able to significantly improve results for initial structural deviations of up to 8 A from bound geometries. Compared to molecular dynamics this refinement procedure comes at low computational cost but shows more efficient sampling by combining small-scale conformational rearrangements and large-scale center-of-mass displacements.Reference:[1] de Vries, S., Zacharias, M. (2012), ATTRACT-EM: A New Method for the Computational Assembly of Large Molecular Machines Using Cryo-EM Maps. PLOS ONE 7(12): e49733. doi:10.1371/journal.pone.0049733.

Final Approach and Flare Control of a Flexible Aircraft in Crosswind Landings

In this paper, the flight simulation and control of a flexible aircraft in landing is presented. The discrete form of hybrid-state equations of motion in terms of quasi coordinates takes into account the coupling between elastic and rigid-body degrees of freedom and provides the framework for the controller design and simulation. The wings of the aircraft are modeled as cantilever beams undergoing bending and torsion about their elastic axis. Distributed variables are discretized in space using the Galerkin method, and unsteady aerodynamic forces are computed using strip theory and finite state induced-flow theory. A landing condition in which the elastic aircraft encounters a crosswind all the way before touchdown is considered. To design the control system, nonlinear coupled equations of motion are linearized about the trim condition and separated into two sets of decoupled equations, in which the elastic variables affect lateral-directional equations. The landing phase is divided into the final approach and flare phases and, for each phase, separate controllers are designed for longitudinal- and lateral-directional channels. An optimal-integral feedforward control scheme is implemented to accomplish the autolanding, while suppressing the wind effects on the flight path. The performance of the control system is examined through nonlinear simulation.

Nonlinear Gust Response Analysis of Free Flexible Aircraft

Gust response analysis plays a very important role in large aircraft design. This paper presents a methodology for calculating the flight dynamic characteristics and gust response of free flexible aircraft. A multidisciplinary coupled numerical tool is developed to simulate detailed aircraft models undergoing arbitrary free flight motion in the time domain, by Computational Fluid Dynamics (CFD), Computational Structure Dynamics (CSD) and Computational Flight Mechanics (CFM) coupling. To achieve this objective, a structured, time-accurate flow- solver is coupled with a computational module solving the flight mechanics equations of motion and a structural mechanics code determining the structural deformations. A novel method to determine the trim state of flexible aircraft is also stated. First, the field velocity approach is validated, after the trim state is attained, gust responses for the one-minus-cosine gust profile are analyzed for the longitudinal motion of a slender-wing aircraft configuration with and without the consideration of structural deformation. RBA), while the second aims mainly to the analysis of elastic aircraft experiencing relatively small deformations. The idea to not consider cross-coupling effects between these two disciplines has been commonly justified by the large frequency separation of the characteristic motion which is typical of conventional structures. Nowadays, the focus on weight minimization for aircraft, leads toward more and more flexible vehicles. The resulting underlying structures may not exhibit the usual wide frequency separation among the rigid body degrees of freedom and the remaining elastic modes. So that the approach mentioned above can lead to mistakes/errors in analyses of flight performance, flying qualities, and control systems design. In these cases, an integrated analysis of flight mechanics and aeroelasticity is necessary from the very early stages of preliminary design (6).

Various Structural Approaches to Analyze an Aircraft with High Aspect Ratio Wings

Aeroelastic analysis of an aircraft with a high aspect ratio wing for medium altitude and long endurance capability was attempted in this paper. In order to achieve such an objective, various structural models were adopted. The traditional approach has been based on a one-dimensional Euler-Bernoulli beam model. The structural analysis results of the present beam model were compared with those by the three-dimensional NASTRAN finite element model. In it, a taper ratio of 0.5 was applied; it was comprised of 21 ribs and 3 spars, and included two control surfaces. The relevant unsteady aerodynamic forces were obtained by using ZAERO, which is based on the doublet lattice method that considers flow compressibility. To obtain the unsteady aerodynamic force, the structural mode shapes and natural frequencies were transferred to ZAERO. Two types of unsteady aerodynamic forces were considered. The first was the unsteady aerodynamic forces which were based on the one-dimensional beam shape; the other was based on the three-dimensional FEM model shape. These two types of aerodynamic forces were compared, and applied to the foregoing flutter analysis. The ultimate goal of the present research is to analyze the possible interaction between the rigid-body degrees of freedom and the aeroelastic modes. This will be achieved after the development of a reliable nonlinear beam formulation that would validate the current results as well as enable a thorough investigation of the nonlinearity. Moreover, such analysis will allow for an examination of the above-mentioned interaction between the flight dynamics and aeroelastic modes with the inclusion of the rigid body degrees of freedom.

Vibration Characteristics of Guided Circular Saws: Experimental and Numerical Analyses

Studying the vibrational characteristics of guided circular saws is of particular interest in the current study. Guided circular saws are free in both the inner and outer rim. They are restrained from having axial motion by using two space-fixed guide pads in either side of the blade. Because of the small clearance between the guide pads and the saw blade, the blade is capable of having rigid body tilting and a translational degree of freedom. At first, we attempted to develop an understanding regarding the vibrational characteristics of such disks through experimental investigations. An electromagnet was used to generate random white noise for the purpose of exciting the bending waves. Using inductance displacement probes, the frequencies and amplitudes of the disk vibrations were measured and the mean deflections were plotted. In the next step, a space-fixed external force (air jet) was used to excite the disks in the lateral direction. The experimental results indicate that the blade frequencies show a significant change as a result of the initial lateral displacement imposed by the external force. It was also seen that due to the presence of the external force, a stationary wave develops and collapses at a higher speed. For the numerical simulations, the nonlinear governing equations based on Von Kármán plate theory were used. The effect of rigid body degrees of freedom was taken into account. As an approximation, the guide pads were modeled with four space-fixed springs. Using Galerkin’s method, the governing equations were discretized and their equilibrium solutions were found. After linearizing the governing equations around the equilibrium solution, the effect of nonlinearity on the amplitude and frequency response of the guided blade was investigated. It was seen that the numerical results were in close agreement with the experimental results.

Multibody Simulation of Integrated Tiltrotor FlightMechanics, Aeroelasticity and Control

This work describes the application of an adaptive control algorithm based on the generalized predictive control paradigmtoadetailednonlinearaeroelasticmodelofatiltrotoraircraftthatincludesrigid-bodydegreesoffreedom, restrictedtotheplaneofsymmetry.Theanalysisisbasedonanoriginalmultibodydynamicsformulation.Themodel is augmented by an autopilot and a stability augmentation system; in relevant cases, a model of the passive biomechanics of the pilot is considered as well. The interaction of rigid-body and deformable degrees of freedom alters the aeroelastic behavior of the system compared with that of the clamped wing rotor, discussed in a previous work. The flutter mechanism, originally consisting in whirl flutter, changes after considering rigid-body degrees of freedom;the short-period flight mechanics mode nowdominates high-speedstability. Thisissue ismainlyaddressed by the stability augmentation system, whereas the generalized predictive control is mainly used to reduce gustinducedwingloads,althoughitsinterventionforwhirl-fluttersuppressionisstillneededtoextendthe flightenvelope at very high speed. The capability of the adaptive regulator to reduce wing loads is assessed in hover and in highspeed forward flight. In the latter condition, the capability to suppress whirl flutter is assessed as well. HE use of active control in aerospace promises structural loads reduction and flutter suppression. However, setting aside all issues related to reliability, redundancy, and certification for a moment, modern aircraft (and rotorcraft) may not allow control designers to rely on the (sometimes abused) frequency separation paradigm that separately considers the dynamics of the aeroelastic and flight mechanics problems, thus significantly simplifying the analysis, since linearized models usually suffice for aeroelastic problems. In fact, airframe elastic modes with low frequencies interacting with low-frequency rotor modes may result in significant dynamic loading and reduced aeroelastic stability. This work focuses on the numerical analysis of the active aeroelastic control of a tiltrotor aircraft by means of an adaptive controller based on generalized predictive control (GPC), as discussed in [1], considering its interaction with flight mechanics dynamics, including the automatic flight control system (AFCS) and the passive dynamics of the pilot. Current generation tiltrotor aircraft mount two rotors on tilting nacelles that are located at the wing tips of an otherwise relatively conventional fixed wing aircraft design. Nacelle tilt changes the orientation of the rotor thrust about the pitch axis of the aircraft. As a consequence, tiltrotor aircraft can fly in two operating modes. In the helicopter mode (Fig. 1a) the nacelles are in the vertical position to provide the rotor thrust required to lift the aircraft. In helicopter mode, pitch control moments are generated by symmetrically tilting the rotor disks longitudinally, like conventional helicopters. Yaw control moment is produced in helicopter mode by differentially

Consistent structural linearisation in flexible-body dynamics with large rigid-body motion

A consistent linearisation, using perturbation methods, is obtained for the structural degrees of freedom of flexible slender bodies with large rigid-body motions. The resulting system preserves all couplings between rigid and elastic motions and can be projected onto a few vibration modes of a reference configuration. This gives equations of motion with cubic terms in the rigid-body degrees of freedom and constant coefficients which can be pre-computed prior to the time-marching simulation. Numerical results are presented to illustrate the approach and to show its advantages with respect to mean-axes approximations.

Precomputed acceleration noise for improved rigid-body sound

We introduce an efficient method for synthesizing acceleration noise -- sound produced when an object experiences abrupt rigid-body acceleration due to collisions or other contact events. We approach this in two main steps. First, we estimate continuous contact force profiles from rigid-body impulses using a simple model based on Hertz contact theory. Next, we compute solutions to the acoustic wave equation due to short acceleration pulses in each rigid-body degree of freedom. We introduce an efficient representation for these solutions -- Precomputed Acceleration Noise -- which allows us to accurately estimate sound due to arbitrary rigid-body accelerations. We find that the addition of acceleration noise significantly complements the standard modal sound algorithm, especially for small objects.

Precomputed acceleration noise for improved rigid-body sound

We introduce an efficient method for synthesizing acceleration noise -- sound produced when an object experiences abrupt rigid-body acceleration due to collisions or other contact events. We approach this in two main steps. First, we estimate continuous contact force profiles from rigid-body impulses using a simple model based on Hertz contact theory. Next, we compute solutions to the acoustic wave equation due to short acceleration pulses in each rigid-body degree of freedom. We introduce an efficient representation for these solutions -- Precomputed Acceleration Noise -- which allows us to accurately estimate sound due to arbitrary rigid-body accelerations. We find that the addition of acceleration noise significantly complements the standard modal sound algorithm, especially for small objects.

Modeling railroad track structures using the finite segment method

In the finite segment method, the dynamics of a deformable body is described using a set of rigid bodies that are connected by elastic force elements. This approach can be used, as demonstrated in this investigation, in the simulation of some rail movements. In order to ensure that the rail geometry is not distorted as the result of the finite segment displacements, a new track model that consistently integrates the absolute nodal coordinate formulation (ANCF) geometry and the finite segment method is developed. ANCF finite elements define the track geometry in the reference configuration as well as the change in the geometry due to the movement of the finite segments of the track. Using ANCF geometry and the finite segment kinematics, the location of the wheel/rail contact point is predicted online and used to update the creepage expressions due to the finite segment displacements and rotations. The location of the wheel/rail contact point and the updated creepage expressions are used to evaluate the creep forces. A three-dimensional elastic contact formulation (ECF-A) which allows for wheel/rail separation is used in this investigation. The rail displacement due to the applied loads is modeled by a set of rigid finite segments that are connected by a set of spring-damper elements. Each rail finite segment is assumed to have six rigid body degrees of freedom. The equations of motion of the finite segments are integrated with the railroad vehicle system equations of motion in a sparse matrix formulation. The resulting dynamic equations are solved using a predictor–corrector numerical integration method that has a variable order and variable step size. The finite segments may be used to model specific phenomena that occur in railroad vehicle applications, including rail rotations and gauge widening. The procedure used in this investigation to implement the finite segment method in a general purpose multibody system (MBS) computer program is described. Two simple models are presented in order to demonstrate the implementation of the finite segment method in MBS algorithms. The limitations of using the finite segments approach for modeling the track structure and rail flexibility are also discussed.

Conservation Issues for Reynolds-Averaged Navier-Stokes–Based Rotor Aeroelastic Simulations

AbstractAeroelastic simulations that are computed by coupling separate computational fluid dynamics (CFD) and computational structural dynamics (CSD) codes will include not only numerical errors in both the CFD and CSD methods, but also errors associated with the data exchange among the codes of the aerodynamic loads and moments and structural deflections. Whereas the numerical errors associated with the data interface have been investigated and quantified for fixed-wing applications, their effect has not been quantified for rotational applications, such as rotors and wind turbines, in which rigid body degrees of freedom cannot be separated from flexible motion of the blades. This paper provides a systematic analysis of the numerical errors introduced by the data interface for high-aspect ratio blades undergoing multibody dynamic motion including rotation. It is demonstrated that the failure to consider conservation of work or energy during the CFD-CSD data exchange can lead to a shift in the mean loading...