Modeling Controlled Articulated Flexible Systems Using Assumed Modes: Part II — Numerical Investigation

2001 ◽  
Author(s):  
Theodore G. Mordfin ◽  
Sivakumar S. K. Tadikonda
Keyword(s):  
Multibody Dynamics ◽  
Dynamic Systems ◽  
Flexible Multibody Dynamics ◽  
Companion Paper ◽  
Parameter Variation ◽  
Flexible Bodies ◽  
Simulation Efficiency ◽  
Multibody Dynamic ◽  
Flexible Multibody ◽  
Assumed Mode

Abstract Guidelines are sought for generating component body models for use in controlled, articulated, flexible multibody dynamics system simulations. In support of this effort, exact truth models and linearized large-articulation models are developed in a companion paper. The purpose of the truth models is to aid in evaluating the use of various types of component body assumed modes in the large-articulation models. The assumed mode models are analytically evaluated from the perspectives of both structural dynamics and multibody dynamics. In this paper, component body assumed modes are tested in a linearized large-articulation model. The numerical behavior of the model and its performance in the presence of parameter variation is investigated and explained. The results show that high accuracy, high simulation efficiency, and numerical robustness cannot be simultaneously achieved. However, in many cases, satisfactory levels of all three are achievable. Guidelines are proposed for modeling the flexible bodies in controlled-articulation flexible multibody dynamic systems.

On Selecting Assumed Modes in a Controlled Articulated Flexible Multibody Dynamics System

2007 ◽  
Author(s):  
Theodore G. Mordfin ◽  
Sivakumar Tadikonda
Keyword(s):  
Exact Solutions ◽  
Numerical Solutions ◽  
Structural Characteristics ◽  
Flexible Multibody Dynamics ◽  
Control Laws ◽  
Simulation Efficiency ◽  
Multibody Dynamic ◽  
Non Linear ◽  
Flexible Multibody ◽  
Constituent Component

The modeling and simulation of controlled-articulation flexible multibody dynamic systems often involves the use of approximating functions, or assumed modes, to represent the structural characteristics of the constituent component bodies. However, clear and complete guidance on appropriate component body modeling techniques is lacking. As a result, researchers and applications engineers encounter severe and unexplained numerical problems when simulating such systems. Earlier studies demonstrated these problems, explained their causes, and developed modeling guidelines from the perspective of accuracy, robustness, and simulation efficiency. In this study, the guidelines are tested and confirmed for a controlled-articulation flexible multibody dynamic system. In support of this effort, exact closed-form and numerical solutions are developed for the small elastic motions of a planar, flexible, two-link system in which each link is represented by an Euler-Bernoulli bar in transverse vibration. The inboard link is pinned to the ground, and the outboard link is pinned to the outboard end of the first link in an arbitrary configuration. Articulation is controlled by proportional and proportional/derivative feedback control laws. The exact solutions are “truth models” for the linear characteristics of an analogous non-linear large articulation model in which link deformations are represented by assumed modes. Using a linearized version of the non-linear large-articulation model as an assumed modes testbed, the modeling guidelines are tested against the exact solutions. The numerical results conform with expectation, and the efficacy of the guidelines is successfully confirmed.

Translational Joints in Flexible Multibody Dynamics

1988 ◽  
Author(s):  
R. S. Hwang ◽  
E. J. Haug
Keyword(s):  
Multibody Dynamics ◽  
Flexible Multibody Dynamics ◽  
Local Deformation ◽  
Kinematic Constraints ◽  
Flexible Bodies ◽  
Numerical Examples ◽  
Flexible Multibody ◽  
Global Deformation ◽  
Deformation Modes ◽  
Joint Formulations

Abstract Formulations of translational kinematic constraints between flexible bodies are developed to model deformatioin of flexible surfaces that move relative to one another. Three types of flexible translational articulated joints are presented The joint formulations are illustrated in analysis of prototype systems with translational joints. Global deformation modes and substructure local deformation modes are used and compared in numerical examples.

A Uniform Rotationless Formulation of Flexible Multibody Dynamics: Conserving Integration of Rigid Bodies, Nonlinear Beams and Shells

2007 ◽  
Author(s):  
Peter Betsch ◽  
Nicolas Sa¨nger
Keyword(s):  
Multibody Dynamics ◽  
Flexible Multibody Dynamics ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Flexible Bodies ◽  
Finite Dimensional ◽  
Nonlinear Beams ◽  
Body Dynamics ◽  
Flexible Multibody ◽  
Additional Constraints

A uniform framework for rigid body dynamics and nonlinear structural dynamics is presented. The advocated approach is based on a rotationless formulation of rigid bodies, nonlinear beams and shells. In this connection, the specific kinematic assumptions are taken into account by the explicit incorporation of holonomic constraints. This approach facilitates the straightforward extension to flexible multibody dynamics by including additional constraints due to the interconnection of rigid and flexible bodies. We further address the design of energy-momentum schemes for the stable numerical integration of the underlying finite-dimensional mechanical systems.

scholarly journals Iterative Coordinate Reduction Algorithm of Flexible Multibody Dynamics Using a Posteriori Eigenvalue Error Estimation

2020 ◽  
Vol 10 (20) ◽  
pp. 7143
Author(s):  
Seongji Han ◽  
Jin-Gyun Kim ◽  
Juhwan Choi ◽  
Jin Hwan Choi
Keyword(s):  
Multibody Dynamics ◽  
Reduction Process ◽  
Flexible Multibody Dynamics ◽  
Dynamics Simulation ◽  
Iteration Step ◽  
Error Estimator ◽  
A Posteriori ◽  
Flexible Bodies ◽  
Flexible Multibody ◽  
Coordinate Reduction

Coordinate reduction has been widely used for efficient simulation of flexible multibody dynamics. To achieve the reduction of flexible bodies with reasonable accuracy, the appropriate number of dominant modes used for the reduction process must be selected. To handle this issue, an iterative coordinate reduction strategy is introduced. In the iteration step, more dominant modes of flexible bodies are selected than the ones in the previous step. Among the various methods, the conventional frequency cut-off rule is here considered. As a stop criterion, a novel a posteriori error estimator that can evaluate the relative eigenvalue error between full and reduced flexible bodies is proposed. Through the estimated relative eigenvalue error obtained, the number of dominant modes is automatically selected to satisfy the error tolerance up to the desired mode range. The applicability to the automation process is verified through numerical examples. It is also evaluated that efficient and accurate flexible multibody dynamics simulation is available with the reduced flexible body, generated by the proposed algorithm.

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