Vibration of Moving Flexible Bodies (Formulation of Dynamics by Using Normal Modes and a Local Observer Frame)

1999 ◽  
Author(s):  
Atsushi Kawamoto ◽  
Mizuho Inagaki ◽  
Takayuki Aoyama ◽  
Nobuyuki Mori ◽  
Kimihiko Yasuda
Keyword(s):  
Rigid Body ◽  
Elastic Deformation ◽  
Multibody Systems ◽  
Elastic Vibration ◽  
Rigid Body Motion ◽  
Flexible Multibody Systems ◽  
Body Motion ◽  
Flexible Multibody ◽  
Local Observer ◽  
New Formulation

Abstract This paper deals with the formulation that can analyze vibration noise problems practically in the flexible multibody systems. Many kinds of formulations have been proposed on the flexible multibody systems so far. They are categorized into several groups according to their purposes and coordinate systems. The floating frame of reference formulation is at present the most popular method for general purpose simulations among them. The formulation uses Cartesian coordinates for the position of a body, Euler angles or Euler parameters for the orientations, and modal coordinates for the elastic degrees of freedom. The equations of motion with these different kinds of coordinates are complicated because of coupling between rigid body motion and elastic vibration. On the other hand, the linear theory of elasto-dynamics appears to be simple and could be practical for some limited uses. But it neglects the effect of the elastic deformation on the rigid body motion. In many cases, the effect is significant and essential. In this paper, we propose a new formulation with rigid body modes and a local observer frame (LOF) for large amplitude rigid body motion, and with elastic modes for small amplitude elastic vibration. The LOF is updated properly to compensate the gap between rigid body motion and the LOF motion. The new formulation makes the coupling terms as simple as possible without any loss of the effect of the elastic deformation on the rigid body motion and gives the uniform description in each modal coordinate.

A Partitioned Iteration Method Employing CG-Following Reference Frames for Distributed Simulation of Flexible Multibody Systems

2007 ◽  
Author(s):  
Geunsoo Ryu ◽  
Zheng-Dong Ma ◽  
Gregory M. Hulbert
Keyword(s):  
Rigid Body ◽  
Elastic Deformation ◽  
Iteration Method ◽  
Multibody Systems ◽  
Distributed Simulation ◽  
Rigid Body Motion ◽  
Flexible Multibody Systems ◽  
Body Motion ◽  
Flexible Multibody ◽  
Gluing Algorithm

A distributed simulation platform, denoted as D-Sim, has been developed previously by our research group, which comprises three essential attributes: a general XML description for models suitable for both leaf and integrated models, a gluing algorithm, which only relies on the interface information to integrate subsystem models, and a logical distributed simulation architecture that can be realized using any connection-oriented distributed technology. The overarching research focus is to integrate heterogeneous subsystem models, e.g., multibody dynamics subsystems models and finite element subsystems models and to conduct seamlessly integrated simulation and design tasks in a distributed computing environment. A Partitioned Iteration Method (PIM) is proposed in this paper, which decouples the rigid body motion from elastic deformation of the simulated system using an iteration scheme. The method employs a CG-following reference frame for each deformable body in the distributed simulation of flexible multibody systems. The resultant simulation system can be used to integrate distributed deformable bodies D-Sim, while allowing large rigid body motions among the bodies or subsystems. It also enables using independent simulation servers; where each server can run commercially available or research-based MBD and/or FEM codes. Examples are provided that demonstrate the performance of the method and also how to decouple and integrate rigid body motion and elastic deformation using the developed gluing algorithm.

A Generalized Component Mode Synthesis Approach for Flexible Multibody Systems With a Constant Mass Matrix

2012 ◽  
Vol 8 (1) ◽  
Author(s):  
Astrid Pechstein ◽  
Daniel Reischl ◽  
Johannes Gerstmayr
Keyword(s):  
Rigid Body ◽  
Multibody Systems ◽  
Mass Matrix ◽  
Rigid Body Motion ◽  
Flexible Multibody Systems ◽  
Component Mode Synthesis ◽  
Body Motion ◽  
Mode Shapes ◽  
Flexible Multibody ◽  
Flexible Deformation

A standard technique to reduce the system size of flexible multibody systems is the component mode synthesis. Selected mode shapes are used to approximate the flexible deformation of each single body numerically. Conventionally, the (small) flexible deformation is added relatively to a body-local reference frame which results in the floating frame of reference formulation (FFRF). The coupling between large rigid body motion and small relative deformation is nonlinear, which leads to computationally expensive nonconstant mass matrices and quadratic velocity vectors. In the present work, the total (absolute) displacements are directly approximated by means of global (inertial) mode shapes, without a splitting into rigid body motion and superimposed flexible deformation. As the main advantage of the proposed method, the mass matrix is constant, the quadratic velocity vector vanishes, and the stiffness matrix is a co-rotated constant matrix. Numerical experiments show the equivalence of the proposed method to the FFRF approach.

Performance of the Incremental and Non-Incremental Finite Element Formulations in Flexible Multibody Problems

1999 ◽  
Vol 122 (4) ◽  
pp. 498-507 ◽  
Author(s):  
Marcello Campanelli ◽  
Marcello Berzeri ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Multibody Systems ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Multibody Systems ◽  
Large Displacement ◽  
Body Motion ◽  
Absolute Nodal Coordinate ◽  
Flexible Multibody ◽  
The Absolute ◽  
Finite Element Formulations

Many flexible multibody applications are characterized by high inertia forces and motion discontinuities. Because of these characteristics, problems can be encountered when large displacement finite element formulations are used in the simulation of flexible multibody systems. In this investigation, the performance of two different large displacement finite element formulations in the analysis of flexible multibody systems is investigated. These are the incremental corotational procedure proposed in an earlier article (Rankin, C. C., and Brogan, F. A., 1986, ASME J. Pressure Vessel Technol., 108, pp. 165–174) and the non-incremental absolute nodal coordinate formulation recently proposed (Shabana, A. A., 1998, Dynamics of Multibody Systems, 2nd ed., Cambridge University Press, Cambridge). It is demonstrated in this investigation that the limitation resulting from the use of the infinitesmal nodal rotations in the incremental corotational procedure can lead to simulation problems even when simple flexible multibody applications are considered. The absolute nodal coordinate formulation, on the other hand, does not employ infinitesimal or finite rotation coordinates and leads to a constant mass matrix. Despite the fact that the absolute nodal coordinate formulation leads to a non-linear expression for the elastic forces, the results presented in this study, surprisingly, demonstrate that such a formulation is efficient in static problems as compared to the incremental corotational procedure. The excellent performance of the absolute nodal coordinate formulation in static and dynamic problems can be attributed to the fact that such a formulation does not employ rotations and leads to exact representation of the rigid body motion of the finite element. [S1050-0472(00)00604-8]

Flexible Multibody Systems With Large Deformations Using Absolute Nodal Coordinates for Isoparametric Solid Brick Elements

2003 ◽  
Author(s):  
Lars Ku¨bler ◽  
Peter Eberhard ◽  
Johannes Geisler
Keyword(s):  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Large Deformations ◽  
Flexible Multibody Systems ◽  
Body Motion ◽  
Absolute Nodal Coordinates ◽  
Shell Elements ◽  
Flexible Multibody ◽  
Absolute Coordinates ◽  
Solid Bodies

In this paper a formulation for flexible Multibody Systems (MBS) is proposed where flexible bodies are described using absolute coordinates for isoparametric brick elements. The use of absolute coordinates allows for large deformations and provides an accurate description of rigid body motion and inertia in the case of large rotations without additional considerations. Further, constant mass matrices are obtained for isoparametric elements. Brick elements are important, e. g. if general solid bodies with low stiffness, i. e. not negligible large deformations, are part of the MBS and cannot be modeled using beam, plate, or shell elements. Since only nodal translational degrees of freedom are used for brick elements additional questions arise. For example, imposing joint constraints for relative rotations between two bodies requires a nodal reference frame at connection points. An approach is proposed to define such a reference system utilizing displacement information of three finite element nodes.

A General Method for the Dynamic Modeling of Ball Bearing–Rotor Systems

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Yamin Li ◽  
Hongrui Cao ◽  
Linkai Niu ◽  
Xiaoliang Jin
Keyword(s):  
Rigid Body ◽  
Dynamic Modeling ◽  
Ball Bearing ◽  
Elastic Vibration ◽  
Rigid Body Motion ◽  
Rotor System ◽  
Body Motion ◽  
Rotor Systems ◽  
Proposed Model ◽  
Vibration Responses

A general dynamic modeling method of ball bearing–rotor systems is proposed. Gupta's bearing model is applied to predict the rigid body motion of the system considering the three-dimensional motions of each part (i.e., outer ring, inner ring, ball, and rotor), lubrication tractions, and bearing clearances. The finite element method is used to model the elastic deformation of the rotor. The dynamic model of the whole ball bearing–rotor system is proposed by integrating the rigid body motion and the elastic vibration of the rotor. An experiment is conducted on a test rig of rotor supported by two angular contact ball bearings. The simulation results are compared with the measured vibration responses to validate the proposed model. Good agreements show the accuracy of the proposed model and its ability to predict the dynamic behavior of ball bearing–rotor systems. Based on the proposed model, vibration responses of a two bearing–rotor system under different bearing clearances were simulated and their characteristics were discussed. The proposed model may provide guidance for structural optimization, fault diagnosis, dynamic balancing, and other applications.

On the Rigid-Body Motion of Traveling, Sagged, Elastic Cables

2002 ◽  
Author(s):  
Albert C. J. Luo ◽  
Yuefang Wang
Keyword(s):  
Analytical Solution ◽  
Rigid Body ◽  
Elastic Deformation ◽  
Flexible Structures ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Cable Model ◽  
Cable Structures ◽  
Elastic Cables

This paper presents a methodology for modeling very flexible structures. A theory for the dynamics of traveling, arbitrarily sagged, elastic cables is developed for demonstration of this methodology. In this theory, the cable motion is modeled through the rigid-body motion and elastic deformation, and the rigid-body motion of cable configuration is modeled as an inextensible cable model. The dynamic, rigid-body configuration of a cable is a referenced base to describe its elastic deformation motion for any instantaneous moment. In this paper, the analytical solution for the rigid-body motion of the cable under a certain loading is developed as Part I of this investigation. From the dynamical configuration of the rigid-body motion of cable, an elastic motion of nonlinear cables is further investigated in sequel as the part II. This theory can be applied any cable structures and the methodology is useful for the perfectly flexible structures such as membranes.

On the Use of Virtual Work in a Graph-Theoretic Formulation for Multibody Dynamics

1997 ◽  
Author(s):  
Pengfei Shi ◽  
John McPhee
Keyword(s):  
Multibody Systems ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Flexible Multibody Systems ◽  
Theoretic Approach ◽  
Computer Implementation ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
Flexible Multibody ◽  
New Formulation

Abstract In this paper, graph-theoretic and virtual work methods are combined in a new formulation of the equations of motion for rigid and flexible multibody systems. In addition to extending the theory for existing graph-theoretic approaches, this new formulation offers two distinct improvements. First, the set of differential-algebraic dynamic equations are smaller in number than those obtained using conventional formulations. Secondly, the equations of motion for rigid and flexible multibody systems can be generated using a consistent graph-theoretic approach, thereby leading to an efficient and modular computer implementation.

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