Application of the First Order Generalized-α Method to the Solution of an Intrinsic Geometrically Exact Model of Rotor Blade Systems

2008 ◽  
Vol 4 (1) ◽  
Author(s):  
F. Khouli ◽  
F. F. Afagh ◽  
R. G. Langlois
Keyword(s):  
Rotor Blade ◽  
Mixed Model ◽  
Transient Behavior ◽  
Mathematical Structure ◽  
Weak Form ◽  
Integration Scheme ◽  
State Variables ◽  
Nonlinear Mixed Model ◽  
First Order ◽  
Blade System

An energy decaying integration scheme for an intrinsic, geometrically exact, multibody dynamics model with composite, dimensionally reducible, active beamlike structures is proposed. The scheme is based on the first order generalized-α method that was proposed and successfully applied to various nonlinear dynamics models. The similarities and the differences between the mathematical structure of the nonlinear intrinsic model and a parallel nonlinear mixed model of chains are highlighted to demonstrate the effect of the form of the governing equation on the stability of the integration scheme. Simple C° shape functions are used in the spatial discretization of the state variables owing to the weak form of the model. Numerical solution of the transient behavior of multibody systems, representative of various rotor blade system configurations, is presented to highlight the advantages and the drawbacks of the integration scheme. Simulation predictions are compared against experimental results whenever the latter is available to verify the implementation. The suitability and the robustness of the proposed integration scheme are then established based on satisfying two conservational laws derived from the intrinsic model, which demonstrate the retained energy decaying characteristic of the scheme and its unconditional stability when applied to the intrinsic nonlinear problem, and the dependance of its success on the form of the governing equations.

Numerical Integration of a New Set of Equations of Motion for Mechanical Systems With Scleronomic Constraints

2015 ◽  
Author(s):  
Nikolaos Potosakis ◽  
Elias Paraskevopoulos ◽  
Sotirios Natsiavas
Keyword(s):  
Equations Of Motion ◽  
Time Integration ◽  
Mechanical Systems ◽  
Nonholonomic Constraints ◽  
Weak Form ◽  
Integration Scheme ◽  
Weak Formulation ◽  
First Order ◽  
Motion Constraints ◽  
Time Integration Scheme

Some new theoretical and numerical results are presented on the dynamic response of a class of mechanical systems with equality motion constraints. At the beginning, the equations of motion of the corresponding unconstrained system are presented, first in strong and then in a weak form. Next, the formulation is extended to systems with holonomic and/or nonholonomic constraints. The formulation is based on a new set of equations of motion, represented by a system of second order ordinary differential equations (ODEs) in both the coordinates and the Lagrange multipliers associated to the motion constraints. Moreover, the position, velocity and momentum type quantities are assumed to be independent, forming a three field set of equations. The weak formulation developed was first used to cast the equations of motion as a set of first order ODEs in the coordinates and the corresponding momenta. Then, the same formulation was also employed as a basis for producing a suitable time integration scheme for the systems examined. The validity and efficiency of this scheme was tested and illustrated by applying it to a number of characteristic example systems.

An Analytical Transient Tire Model

2001 ◽  
Vol 29 (2) ◽  
pp. 108-132 ◽  
Author(s):  
A. Ghazi Zadeh ◽  
A. Fahim
Keyword(s):  
Transient Behavior ◽  
Stability Control ◽  
Vehicle Stability ◽  
Tire Model ◽  
Steering Angle ◽  
First Order ◽  
Vehicle Stability Control ◽  
Proposed Model ◽  
Depth Study ◽  
And Performance

Abstract The dynamics of a vehicle's tires is a major contributor to the vehicle stability, control, and performance. A better understanding of the handling performance and lateral stability of the vehicle can be achieved by an in-depth study of the transient behavior of the tire. In this article, the transient response of the tire to a steering angle input is examined and an analytical second order tire model is proposed. This model provides a means for a better understanding of the transient behavior of the tire. The proposed model is also applied to a vehicle model and its performance is compared with a first order tire model.

An improved dynamic load-strength interference model for the reliability analysis of aero-engine rotor blade system

2020 ◽  
pp. 095441002097289
Author(s):  
Bingfeng Zhao ◽  
Liyang Xie ◽  
Yu Zhang ◽  
Jungang Ren ◽  
Xin Bai ◽  
...  
Keyword(s):  
Reliability Analysis ◽  
Dynamic Load ◽  
Rotor Blade ◽  
Engineering Application ◽  
Weight Ratio ◽  
System Component ◽  
Aero Engine ◽  
Blade System ◽  
Improved Model ◽  
Engine Rotor

As the power source of an aircraft, aero-engine tends to meet many rigorous requirements for high thrust-weight ratio and reliability with the continuous improvement of aero-engine performance. In this paper, based on the order statistics and stochastic process theory, an improved dynamic load-strength interference (LSI) model was proposed for the reliability analysis of aero-engine rotor blade system, with strength degradation and catastrophic failure involved. In presented model, the “unconventional active” characteristic of rotor blade system, changeable functioning relationships and system-component configurations, was fully considered, which is necessary for both theoretical analysis and engineering application. In addition, to reduce the computation cost, a simplified form of the improved LSI model was also built for convenience of engineering application. To verify the effectiveness of the improved model, reliability of turbojet 7 engine rotor blade system was calculated by the improved LSI model based on the results of static finite element analysis. Compared with the traditional LSI model, the result showed that there were significant differences between the calculation results of the two models, in which the improved model was more appropriate to the practical condition.

System Properties of One-Dimensional Distributed Systems

1977 ◽  
Vol 99 (2) ◽  
pp. 85-90 ◽  
Author(s):  
L. S. Bonderson
Keyword(s):  
Distributed Systems ◽  
Sufficient Conditions ◽  
State Variables ◽  
One Dimensional ◽  
First Order ◽  
Lumped Element ◽  
Order Form ◽  
Power Product ◽  
System Properties ◽  
Necessary And Sufficient

The system properties of passivity, losslessness, and reciprocity are defined and their necessary and sufficient conditions are derived for a class of linear one-dimensional multipower distributed systems. The utilization of power product pairs as state variables and the representation of the dynamics in first-order form allows results completely analogous to those for lumped-element systems.

scholarly journals Skill Transference of a Probe-Tube Placement Training Simulator

2020 ◽  
Vol 31 (01) ◽  
pp. 040-049 ◽  
Author(s):  
Robert W. Koch ◽  
Hasan Saleh ◽  
Paula Folkeard ◽  
Sheila Moodie ◽  
Conner Janeteas ◽  
...  
Keyword(s):  
Mixed Model ◽  
Tracking System ◽  
Optical Tracking ◽  
Tube Placement ◽  
Control Group ◽  
Educational Settings ◽  
Training Simulator ◽  
Nonlinear Mixed Model ◽  
Optical Tracking System ◽  
Clinical Scenarios

AbstractProbe-tube placement is a necessary step in hearing aid verification which needs ample hands-on experience and confidence before performing in clinic. To improve the methods of training in probe-tube placement, a manikin-based training simulator was developed consisting of a 3D-printed head, a flexible silicone ear, and a mounted optical tracking system. The system is designed to provide feedback to the user on the depth and orientation of the probe tube, and the time required to finish the task. Although a previous validation study was performed to determine its realism and teachability with experts, further validation is required before implementation into educational settings.This study aimed to examine the skill transference of a newly updated probe-tube placement training simulator to determine if skills learned on this simulator successfully translate to clinical scenarios.All participants underwent a pretest in which they were evaluated while performing a probe-tube placement and real-ear-to-coupler difference (RECD) measurement on a volunteer. Participants were randomized into one of two groups: the simulator group or the control group. During a two-week training period, all participants practiced their probe-tube placement according to their randomly assigned group. After two weeks, each participant completed a probe-tube placement on the same volunteer as a posttest scenario.Twenty-five novice graduate-level student clinicians.Participants completed a self-efficacy questionnaire and an expert observer completed a questionnaire evaluating each participant’s performance during the pre- and posttest sessions. RECD measurements were taken after placing the probe tube and foam tip in the volunteer’s ear. Questionnaire results were analyzed through nonparametric t-tests and analysis of variance, whereas RECD results were analyzed using a nonlinear mixed model method.Results suggested students in the simulator group were less likely to contact the tympanic membrane when placing a probe tube, appeared more confident, and had better use of the occluding foam tip, resulting in more improved RECD measurements.The improved outcomes for trainees in the simulator group suggest that supplementing traditional training with the simulator provides useful benefits for the trainees, thereby encouraging its usage and implementation in educational settings.

scholarly journals Numerical Integration of Multibody Dynamic Systems Involving Nonholonomic Equality Constraints

2021 ◽  
Author(s):  
Sotirios Natsiavas ◽  
Panagiotis Passas ◽  
Elias Paraskevopoulos
Keyword(s):  
Dynamic Systems ◽  
Equations Of Motion ◽  
Time Integration ◽  
Nonholonomic Constraints ◽  
Coupled System ◽  
Weak Form ◽  
Integration Scheme ◽  
Motion Constraints ◽  
Multibody Dynamic ◽  
Time Integration Scheme

Abstract This work considers a class of multibody dynamic systems involving bilateral nonholonomic constraints. An appropriate set of equations of motion is employed first. This set is derived by application of Newton’s second law and appears as a coupled system of strongly nonlinear second order ordinary differential equations in both the generalized coordinates and the Lagrange multipliers associated to the motion constraints. Next, these equations are manipulated properly and converted to a weak form. Furthermore, the position, velocity and momentum type quantities are subsequently treated as independent. This yields a three-field set of equations of motion, which is then used as a basis for performing a suitable temporal discretization, leading to a complete time integration scheme. In order to test and validate its accuracy and numerical efficiency, this scheme is applied next to challenging mechanical examples, exhibiting rich dynamics. In all cases, the emphasis is put on highlighting the advantages of the new method by direct comparison with existing analytical solutions as well as with results of current state of the art numerical methods. Finally, a comparison is also performed with results available for a benchmark problem.

Modeling of a Wind Turbine Rotor Blade System

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Dayuan Ju ◽  
Qiao Sun
Keyword(s):  
Wind Turbine ◽  
Rotor Blade ◽  
Simulation Software ◽  
Wind Flow ◽  
Coupling Effects ◽  
Horizontal Axis Wind Turbine ◽  
Blade Vibration ◽  
Proposed Model ◽  
Blade System ◽  
Coupling Terms

In wind turbine blade modeling, the coupling between rotor rotational motion and blade vibration has not been thoroughly investigated. The inclusion of the coupling terms in the wind turbine dynamics equations helps us understand the phenomenon of rotor oscillation due to blade vibration and possibly diagnose faults. In this study, a dynamics model of a rotor-blade system for a horizontal axis wind turbine (HAWT), which describes the coupling terms between the blade elastic movement and rotor gross rotation, is developed. The model is developed by using Lagrange's approach and the finite-element method has been adopted to discretize the blade. This model captures two-way interactions between aerodynamic wind flow and structural response. On the aerodynamic side, both steady and unsteady wind flow conditions are considered. On the structural side, blades are considered to deflect in both flap and edge directions while the rotor is treated as a rigid body. The proposed model is cross-validated against a model developed in the simulation software fatigue, aerodynamics, structure, and turbulence (fast). The coupling effects are excluded during the comparison since fast does not include these terms. Once verified, we added coupling terms to our model to investigate the effects of blade vibration on rotor movement, which has direct influence on the generator behavior. It is illustrated that the inclusion of coupling effects can increase the sensitivity of blade fault detection methods. The proposed model can be used to investigate the effects of different terms as well as analyze fluid–structure interaction.

scholarly journals Reaction rate coefficient k20 and temperature coefficient Θ in organic waste thermal disintegration

2018 ◽  
Vol 23 ◽  
pp. 00026
Author(s):  
Sylwia Myszograj
Keyword(s):  
Activated Sludge ◽  
Mixed Model ◽  
Heating Temperature ◽  
Treatment Plant ◽  
Oxygen Demand ◽  
Rate Of Change ◽  
Waste Activated Sludge ◽  
Nonlinear Mixed Model ◽  
The Difference ◽  
Reaction Speed

It was described the test of sewage sludge and organic fraction of municipal mixed solid waste thermal disintegration process. The waste activated sludge used during the tests was collected from the secondary settlement tank in a mechanical-biological wastewater treatment plant. The biowaste used in the studies was collected from an area of new buildings. It was noticed from means values of Soluble Chemical Oxygen Demand (SCOD) plot that both heating temperature and time, influence the amount of dissolved COD. The observations indicate that changes of SCOD can be described by an increasing, differentiable function of time and the rate of change of the soluble COD in the hydrolysates, in time is proportional to the difference of the maximum values of SCOD and its value in time, which leads to the relationship of the first-order ordinary differential equation. The process effectiveness depending on the temperature was described with the mathematical model including Van't Hoff-Arrhenius equation. Inspection of the data and some preliminary fits indicates, that for the description of changes in SCOD terms of time and temperature were adopted the form of nonlinear mixed model. Values of k20 indicator and Θ parameter depend on the substrate type. For waste activated sludge thermal disintegration, value of reaction speed indicator k20 was 0.028 h-1 (0,67 d-1), and value of temperature indicator equalled Θ = 1.024. For thermal disintegration of biological waste, value of reaction speed indicator k20 was 0.016 h-1 (0,38 d-1), and value of temperature indicator equalled Θ = 1.016.

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