scholarly journals Global modes for the reduction of flexible multibody systems

2021 ◽  
Author(s):  
Alessandro Cammarata
Keyword(s):  
Multibody System ◽  
Equations Of Motion ◽  
Computational Effort ◽  
System Level ◽  
Component Level ◽  
Planar Case ◽  
Local Modes ◽  
Flexible Multibody ◽  
Global Modes ◽  
Computational Resources

AbstractModeling a flexible multibody system employing the floating frame of reference formulation (FFRF) requires significant computational resources when the flexible components are represented through finite elements. Reducing the complexity of the governing equations of motion through component-level reduced-order models (ROM) can be an effective strategy. Usually, the assumed field of deformation is created considering local modes, such as normal, static, or attachment modes, obtained from a single component. A different approach has been proposed in Cammarata (J. Sound Vibr. 489, 115668, 2020) for planar systems only and involves a reduction based on global flexible modes of the whole mechanism. Through the use of global modes, i.e., obtained from an eigenvalue analysis performed on the linearized dynamic system around a certain configuration, it is possible to obtain a modal basis for the flexible coordinates of the multibody system. Here, the same method is extended to spatial mechanisms to verify its applicability and reliability. It is demonstrated that global modes can be used to create ROM both at the system and component levels. Studies on the complexity of the method reveal this approach can significantly reduce the calculation times and the computational effort compared to the unreduced model. Unlike the planar case, the numerical experiments reveal that the system-level approach based on global modes can suffer from slow convergence speed and low accuracy in results.

Flexible Multibody Dynamics Formulation by Hamilton’s Equations

2010 ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Multibody Dynamics ◽  
Multibody System ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Flexible Multibody Dynamics ◽  
Flexible Body ◽  
Flexible Multibody System ◽  
Generalized Coordinates ◽  
Flexible Multibody ◽  
The Matrix

Numerical solution of the dynamics equations of a flexible multibody system as represented by Hamilton’s canonical equations requires that its generalized velocities q˙ be solved from the generalized momenta p. The relation between them is p = J(q)q˙, where J is the system mass matrix and q is the generalized coordinates. This paper presents the dynamics equations for a generic flexible multibody system as represented by p˙ and gives emphasis to a systematic way of constructing the matrix J for solving q˙. The mass matrix is shown to be separable into four submatrices Jrr, Jrf, Jfr and Jff relating the joint momenta and flexible body mementa to the joint coordinate rates and the flexible body deformation coordinate rates. Explicit formulas are given for these submatrices. The equations of motion presented here lend insight to the structure of the flexible multibody dynamics equations. They are also a versatile alternative to the acceleration-based dynamics equations for modeling mechanical systems.

Design Optimization With System-Level Reliability Constraints

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
M. McDonald ◽  
S. Mahadevan
Keyword(s):  
Design Optimization ◽  
Individual Component ◽  
Limit State ◽  
Computational Effort ◽  
Reliability Estimation ◽  
System Level ◽  
Component Level ◽  
Limit States ◽  
Single Loop ◽  
Solution Algorithms

Reliability-based design optimization (RBDO) of mechanical systems is computationally intensive due to the presence of two types of iterative procedures—design optimization and reliability estimation. Single-loop RBDO algorithms offer tremendous savings in computational effort, but they have so far only been able to consider individual component reliability constraints. This paper presents a single-loop RBDO formulation and an equivalent formulation that can also include system-level reliability constraints. The formulations allow the allocation of optimal reliability levels to individual component limit states in order to satisfy both system-level and component-level reliability requirements. Four solution algorithms to implement the second, more efficient formulation are developed. A key feature of these algorithms is to remove the most probable points from the decision space, thus avoiding the need to calculate Hessians or gradients of limit state gradients. It is shown that with the proposed methods, system-level RBDO can be accomplished with computational expense equivalent to several cycles of computationally inexpensive single-loop RBDO based on second-moment methods. Examples of this new approach applied to series, parallel, and combined systems are provided.

Aspects of Symbolic Formulations in Flexible Multibody Systems

2014 ◽  
Vol 9 (4) ◽  
Author(s):  
Markus Burkhardt ◽  
Robert Seifried ◽  
Peter Eberhard
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Flexible Multibody Systems ◽  
Fem Model ◽  
Local Shape ◽  
Flexible Bodies ◽  
Elastic Bodies ◽  
Flexible Multibody

The symbolic modeling of flexible multibody systems is a challenging task. This is especially the case for complex-shaped elastic bodies, which are described by a numerical model, e.g., an FEM model. The kinematic and dynamic properties of the flexible body are in this case numerical and the elastic deformations are described with a certain number of local shape functions, which results in a large amount of data that have to be handled. Both attributes do not suggest the usage of symbolic tools to model a flexible multibody system. Nevertheless, there are several symbolic multibody codes that can treat flexible multibody systems in a very efficient way. In this paper, we present some of the modifications of the symbolic research code Neweul-M2 which are needed to support flexible bodies. On the basis of these modifications, the mentioned restrictions due to the numerical flexible bodies can be eliminated. Furthermore, it is possible to re-establish the symbolic character of the created equations of motion even in the presence of these solely numerical flexible bodies.

scholarly journals Parameter Identification on Flexible Multibody Models Using the Adjoint Variable Method and Flexible Natural Coordinate Formulation

2020 ◽  
Vol 15 (7) ◽  
Author(s):  
Simon Vanpaemel ◽  
Frank Naets ◽  
Martijn Vermaut ◽  
Wim Desmet
Keyword(s):  
Parameter Identification ◽  
Computational Cost ◽  
Variable Method ◽  
System Level ◽  
Model Parameters ◽  
Adjoint Variable Method ◽  
Adjoint Variable ◽  
Component Level ◽  
Flexible Multibody

Abstract This work proposes a methodology for in situ parameter identification using system-level measurements of (flexible) multibody systems, opposed to dedicated component-level identification. The sensitivity information employed for the optimization is obtained using the adjoint variable method (AVM). This method has the advantage of obtaining sensitivity information at a computational cost independent of the amount of model parameters. The underlying flexible multibody formulation employed is a novel approach called the flexible natural coordinates formulation (FNCF). This formulation combines the advantageous properties of the floating frame of reference formulation (FFRF) and the generalized component mode synthesis (GCMS) methods and results in a constant mass and stiffness matrix with quadratic constraint equations. This work shows how the specific structure of equations obtained through FNCF drastically reduces the complexity of the AVM as the simulation derivatives can be readily obtained and are of limited order. The proposed approach has been implemented in an in-house object-oriented matlab multibody code. The methodology is illustrated by identifying 13 model parameters of a MacPherson suspension model, in situ and using system-level measurements.

Dynamic Characteristics for a Planar Two-Link Flexible Multibody System Including the Gravity Effects

1992 ◽  
Author(s):  
G. J. Wiens ◽  
H. Tsai
Keyword(s):  
Eigenvalue Problems ◽  
Multibody System ◽  
Nonlinear Differential Equations ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Field Method ◽  
Space Applications ◽  
Flexible Multibody ◽  
Gravity Effects ◽  
The Stability

Abstract This paper addresses modeling issues that arise in the formulation of the equations of motion for the flexible multibody mechanical systems intended for space applications and designed according to ground test results. A planar multibody system consisting of two flexible links interconnected by two revolute joints and a payload at its free end is proposed for the investigations. In addition to the gravity and transverse deflections (most common two conditions adopted for the research in this field), the foreshortening effects, the axial deflections and the work done by the system’s own weight on the elastic deflections are also taken into consideration. Since the slender link assumption is made, the Euler-Bernoulli Beam theory is considered sufficient and satisfactory for describing the behavior of the deformed link components. The Lagrangian formulation in conjunction with assumed displacement field method is then implemented to develop the equations of motion for the system. After achieving the analytical model for the system, a linearization about various system configurations transforms the fully coupled nonlinear differential equations into standard eigenvalue problems. In doing so, the roles played by gravity, foreshortening and system’s own weight (‘weight-load’) on the dynamic behavior of the system undergoing ground testing are examined. For analysis, the fundamental frequency of the system is chosen as a measurement index. Finally, parametric studies focusing on the mass properties of payload, lower and upper links, and actuators are undertaken to address the stability problems. Results indicate that the ‘weight-load’ exhibits interesting effects on the ‘foreshortening and stability’, hence, merits further investigation.

scholarly journals Cone complementarity approach for dynamic analysis of multiple pendulums

2019 ◽  
Vol 11 (6) ◽  
pp. 168781401985674 ◽  
Author(s):  
Xinxin Yu ◽  
Oleg Dmitrochenko ◽  
Marko K Matikainen ◽  
Grzegorz Orzechowski ◽  
Aki Mikkola
Keyword(s):  
Multibody Dynamics ◽  
Multibody System ◽  
Equations Of Motion ◽  
Straightforward Manner ◽  
Planar Case ◽  
Multiple Contacts ◽  
Granular Chains ◽  
Complementarity Approach ◽  
Planar Approach ◽  
Straightforward Approach

The multibody system dynamics approach allows describing equations of motion for a dynamic system in a straightforward manner. This approach can be applied to a wide variety of applications that consist of interconnected components which may be rigid or deformable. Even though there are a number of applications in multibody dynamics, the contact description within multibody dynamics still remains challenging. A user of the multibody approach may face the problem of thousands or millions of contacts between particles and bodies. The objective of this article is to demonstrate a computationally straightforward approach for a planar case with multiple contacts. To this end, this article introduces a planar approach based on the cone complementarity problem and applies it to a practical problem of granular chains.

Application of Fractional Scaling Analysis to Loss of Coolant Accidents: Component Level Scaling for Peak Clad Temperature

2009 ◽  
Vol 131 (12) ◽  
Author(s):  
Ivan Catton ◽  
Wolfgang Wulff ◽  
Novak Zuber ◽  
Upendra Rohatgi
Keyword(s):  
Computational Effort ◽  
System Level ◽  
System Component ◽  
Scaling Analysis ◽  
Primary System ◽  
Component Level ◽  
Single Experiment ◽  
Pressurized Water ◽  
Loss Of Coolant Accident ◽  
Loss Of Coolant

Fractional scaling analysis (FSA) is demonstrated here at the component level for depressurization of nuclear reactor primary systems undergoing a large-break loss of coolant accident. This paper is the third of a three-part sequence. The first paper by Zuber et al. (2005, “Application of Fractional Scaling Analysis (FSA) to Loss of Coolant Accidents (LOCA), Part 1. Methodology Development,” Nucl. Eng. Des., 237, pp. 1593–1607) introduces the FSA method; the second by Wulff et al. (2005, “Application of Fractional Scaling Methodology (FSM) to Loss of Coolant Accidents (LOCA), Part 2. System Level Scaling for System Depressurization,” ASME J. Fluid Eng., to be published) demonstrates FSA at the system level. This paper demonstrates that a single experiment or trustworthy computer simulation, when properly scaled, suffices for large break loss of coolant accident (LBOCAs) in the primary system of a pressurized water reactor and of all related test facilities. FSA, when applied at the system, component, and process levels, serves to synthesize the world-wide wealth of results from analyses and experiments into compact form for efficient storage, transfer, and retrieval of information. This is demonstrated at the component level. It is shown that during LBOCAs, the fuel rod stored energy is the dominant agent of change and that FSA can rank processes quantitatively and thereby objectively in the order of their importance. FSA readily identifies scale distortions. FSA is shown to supercede use of the subjectively implemented phenomena identification and ranking table and to minimize the number of experiments, analyses and computational effort by reducing the evaluation of peak clad temperature (PCT) to a single parameter problem, thus, greatly simplifying uncertainty analysis.

Dynamic Infrared System Level Fault Isolation

2003 ◽  
Author(s):  
John A. Naoum ◽  
Johan Rahardjo ◽  
Yitages Taffese ◽  
Marie Chagny ◽  
Jeff Birdsley ◽  
...  
Keyword(s):  
Fault Isolation ◽  
System Level ◽  
System Component ◽  
Component Level ◽  
Ir Imaging ◽  
Non Destructive

Abstract The use of Dynamic Infrared (IR) Imaging is presented as a novel, valuable and non-destructive approach for the analysis and isolation of failures at a system/component level.

Analysis of Linear Nonconservative Vibrations

1995 ◽  
Vol 62 (3) ◽  
pp. 685-691 ◽  
Author(s):  
F. Ma ◽  
T. K. Caughey
Keyword(s):  
Modal Analysis ◽  
Equations Of Motion ◽  
Substantial Reduction ◽  
Computational Effort ◽  
Equivalence Transformations ◽  
State Space Approach ◽  
Nonconservative System ◽  
First Order ◽  
Physical Insight ◽  
Space Approach

The coefficients of a linear nonconservative system are arbitrary matrices lacking the usual properties of symmetry and definiteness. Classical modal analysis is extended in this paper so as to apply to systems with nonsymmetric coefficients. The extension utilizes equivalence transformations and does not require conversion of the equations of motion to first-order forms. Compared with the state-space approach, the generalized modal analysis can offer substantial reduction in computational effort and ample physical insight.

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