An accurate singularity-free geometrically exact beam formulation using Euler parameters

2017 ◽  
Vol 91 (2) ◽  
pp. 1095-1112 ◽  
Author(s):  
W. Fan ◽  
W. D. Zhu
Keyword(s):  
Euler Parameters ◽  
Geometrically Exact Beam ◽  
Geometrically Exact Beam Formulation

Experimental Validation of Flexible Multibody Dynamics Beam Formulations

2013 ◽  
Author(s):  
Olivier A. Bauchau ◽  
Shilei Han ◽  
Aki Mikkola ◽  
Marko K. Matikainen ◽  
Johannes Gerstmayr
Keyword(s):  
Experimental Data ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Multibody Dynamics ◽  
Absolute Nodal Coordinate ◽  
Beam Elements ◽  
Beam Experiment ◽  
Geometrically Exact Beam ◽  
Cantilevered Beam ◽  
The Absolute ◽  
Geometrically Exact Beam Formulation

In this paper, the accuracy of the geometrically exact beam formulation and absolute nodal coordinate formulation are studied by comparing their predictions against experimental data referred to as the “Princeton beam experiment.” The experiment deals with a cantilevered beam experiencing coupled flap, lag, and twist deformations. In the absolute nodal coordinate formulation, two different beam elements are used. The first is based on a shear deformable approach in which the element kinematics are described using two nodes. The second is based on a recently proposed approach in which three nodes are used. The numerical results for the geometrically exact beam formulation and the recently proposed three-node absolute nodal coordinate formulation agree well with the experimental data. The two-node beam element predictions are similarly to linear theory. This study suggests that the latest developments of the absolute nodal coordinate formulation must be used to ensure accuracy under complicated loading conditions involving by twist deformation.

scholarly journals Aeroelastic Stability Analysis of Electric Aircraft Wings with Distributed Electric Propulsors

Aerospace ◽  
2021 ◽  
Vol 8 (4) ◽  
pp. 100
Author(s):  
Mohammadreza Amoozgar ◽  
Michael I. Friswell ◽  
Seyed Ahmad Fazelzadeh ◽  
Hamed Haddad Khodaparast ◽  
Abbas Mazidi ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Electric Propulsion ◽  
Aeroelastic Stability ◽  
Concentrated Mass ◽  
High Lift ◽  
Aircraft Wings ◽  
Time Space ◽  
Beam Equations ◽  
Geometrically Exact Beam ◽  
Electric Aircraft

In this paper, the effect of distributed electric propulsion on the aeroelastic stability of an electric aircraft wing was investigated. All the electric propulsors, which are of different properties, are attached to the wing of the aircraft in different positions. The wing structural dynamics was modelled by using geometrically exact beam equations, while the aerodynamic loads were simulated by using an unsteady aerodynamic theory. The electric propulsors were modelled by using a concentrated mass attached to the wing, and the motor’s thrust and angular momentum were taken into account. The thrust of each propulsor was modelled as a follower force acting exactly at the centre of gravity of the propulsor. The nonlinear aeroelastic governing equations were discretised using a time–space scheme, and the obtained results were verified against available results and very good agreement was observed. Two case studies were considered throughout the paper, resembling two flight conditions of the electric aircraft. The numerical results show that the tip propulsor thrust, mass, and angular momentum had the most impact on the aeroelastic stability of the wing. In addition, it was observed that the high-lift motors had a minimal effect on the aeroelastic stability of the wing.

scholarly journals A Numerical Solution for Modelling Mooring Dynamics, Including Bending and Shearing Effects, Using a Geometrically Exact Beam Model

2021 ◽  
Vol 9 (5) ◽  
pp. 486
Author(s):  
Tobias Martin ◽  
Hans Bihs
Keyword(s):  
Numerical Solution ◽  
Offshore Wind ◽  
Mooring Line ◽  
Beam Model ◽  
Tight Coupling ◽  
Energy Propagation ◽  
Two Phase ◽  
Geometrically Exact Beam ◽  
Mooring Dynamics ◽  
Rotational Deformation

During the operation of moored, floating devices in the renewable energy sector, the tight coupling between the mooring system and floater motion results in snap load conditions. Before snap events occur, the mooring line is typically slack. Here, the mechanism of energy propagation changes from axial to bending dominant, and the correct modelling of the rotational deformation of the lines becomes important. In this paper, a new numerical solution for modelling the mooring dynamics that includes bending and shearing effects is proposed for this purpose. The approach is based on a geometrically exact beam model and quaternion representations for the rotational deformations. Further, the model is coupled to a two-phase numerical wave tank to simulate the motion of a moored, floating offshore wind platform in waves. A good agreement between the proposed numerical model and reference solutions was found. The influence of the bending stiffness on the motion of the structure was studied subsequently. We found that increased stiffness increased the amplitudes of the heave and surge motion, whereas the motion frequencies were less altered.

STABILITY OF SPATIAL ELASTICA IN A GRAVITATIONAL FIELD

2012 ◽  
Vol 12 (02) ◽  
pp. 403-421 ◽  
Author(s):  
BOONCHAI PHUNGPAINGAM ◽  
LAWRENCE N. VIRGIN ◽  
SOMCHAI CHUCHEEPSAKUL
Keyword(s):  
Gravitational Field ◽  
Elastic Equilibrium ◽  
Experimental System ◽  
Primary Control ◽  
Arc Length ◽  
Euler Parameters ◽  
Reference Analysis ◽  
Horizontal Orientation ◽  
Equilibrium Configurations ◽  
Out Of Plane

This paper considers the behavior of a spatial elastica in a gravitational field. The slenderness of the system considered is such that the weight becomes an important consideration in determining elastic equilibrium configurations. Both ends of the elastica are clamped in an initially (planar) horizontal orientation at a fixed distance apart. However, one of the ends allows an increase in arc-length, that is, it is a sleeve joint. Thus, the total arc-length is the primary control parameter. This kind of elastica typically loses stability, resulting in out-of-plane deflections, when the total arc-length is increased beyond a critical value. A small mid-length torque can used to perturb a planar equilibrium configuration in order to test for stability. The aim of this study is to assess the effect of self-weight of the elastica (which is typically ignored) on promoting or delaying the loss of stability. To this end, it is useful to compare and contrast the results of orientation, that is, the system is configured in both an initial "upright" orientation and then in an "upside-down" orientation to highlight the influence of gravity. The results of the weightless elastica are used as a reference. Analysis is based on Kirchhoff's rod theory and Euler parameters, and the resulting set of governing differential equations are solved using a shooting method. The results from an experimental system using a slender superelastic wire made from Nitinol (Nickel Titanium Naval Ordnance Laboratory) exhibit close agreement with the analytical results.

Mechanical Power Losses of Ball Bearings: Model and Experimental Validation

2021 ◽  
pp. 1-29
Author(s):  
Ahmet Dindar ◽  
Amit Chimanpure ◽  
Ahmet Kahraman
Keyword(s):  
Dynamic Model ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Mechanical Power ◽  
Ball Bearings ◽  
Power Losses ◽  
Euler Parameters ◽  
Surface Shear ◽  
Axial Forces ◽  
Set Up

Abstract A tribo-dynamic model of ball bearings is proposed to predict their load-dependent (mechanical) power losses. The model combines (i) a transient, point contact mixed elastohydrodynamic lubrication (EHL) formulation to simulate the mechanics of the load carrying lubricated ball-race interfaces, and (ii) a singularity-free dynamics model, and establishes the two-way coupling between them that dictates power losses. The dynamic model employs a vectoral formulation with Euler parameters. The EHL model is capable of capturing two-dimensional contact kinematics, velocity variations across the contact as well as asperity interactions of rough contact surfaces. Resultant contact surface shear distributions are processed to predict mechanical power losses of example ball bearings operating under combined radial and axial forces. An experimental set-up is introduced for measurement of the power losses of rolling-element bearings. Sets of measurements taken by using the same example ball bearings are compared to those predicted by the model to assess its accuracy in predicting mechanical power loss of a ball bearing within wide ranges of axial and radial forces.

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