On the modal analysis of flexible multibody systems with singular mass and stiffness matrices

PAMM ◽  
2018 ◽  
Vol 18 (1) ◽  
Author(s):  
Christian Hente ◽  
Cristian G. Gebhardt ◽  
Benedikt Hofmeister ◽  
Raimund Rolfes
Keyword(s):  
Modal Analysis ◽  
Multibody Systems ◽  
Flexible Multibody Systems ◽  
Stiffness Matrices ◽  
Flexible Multibody

Modal analysis of active flexible multibody systems

2011 ◽  
Vol 89 (9-10) ◽  
pp. 750-761 ◽  
Author(s):  
Magne Bratland ◽  
Bjørn Haugen ◽  
Terje Rølvåg
Keyword(s):  
Modal Analysis ◽  
Multibody Systems ◽  
Flexible Multibody Systems ◽  
Flexible Multibody

scholarly journals Flexible-Link Multibody System Eigenvalue Analysis Parameterized with Respect to Rigid-Body Motion

2019 ◽  
Vol 9 (23) ◽  
pp. 5156 ◽  
Author(s):  
Ilaria Palomba ◽  
Renato Vidoni
Keyword(s):  
Eigenvalue Problem ◽  
Motion Planning ◽  
Modal Analysis ◽  
Multibody Systems ◽  
Multibody System ◽  
Differential Algebraic Equations ◽  
Flexible Multibody Systems ◽  
System Configuration ◽  
Modal Characteristics ◽  
Flexible Multibody

The dynamics of flexible multibody systems (FMBSs) is governed by ordinary differential equations or differential-algebraic equations, depending on the modeling approach chosen. In both the cases, the resulting models are highly nonlinear. Thus, they are not directly suitable for the application of the modal analysis and the development of modal models, which are very useful for several advanced engineering techniques (e.g., motion planning, control, and stability analysis of flexible multibody systems). To define and solve an eigenvalue problem for FMBSs, the system dynamics has to be linearized about a selected configuration. However, as modal parameters vary nonlinearly with the system configuration, they should be recomputed for each change of the operating point. This procedure is computationally demanding. Additionally, it does not provide any numerical or analytical correlation between the eigenpairs computed in the different operating points. This paper discusses a parametric modal analysis approach for FMBSs, which allows to derive an analytical polynomial expression for the eigenpairs as function of the system configuration, by solving a single eigenvalue problem and using only matrix operations. The availability of a similar modal model, which explicitly depends on the system configuration, can be very helpful for, e.g., model-based motion planning and control strategies towards to zero residual vibration employing the system modal characteristics. Moreover, it allows for an easy sensitivity analysis of modal characteristics to parameter uncertainties. After the theoretical development, the method is applied and validated on a flexible multibody system, specifically using the Equivalent Rigid Link System dynamic formulation. Finally, numerical results are presented and discussed.

Active vibration control of spatial flexible multibody systems

2013 ◽  
Vol 30 (1) ◽  
pp. 13-35 ◽  
Author(s):  
Maria Augusta Neto ◽  
Jorge A. C. Ambrósio ◽  
Luis M. Roseiro ◽  
A. Amaro ◽  
C. M. A. Vasques
Keyword(s):  
Vibration Control ◽  
Multibody Systems ◽  
Active Vibration Control ◽  
Flexible Multibody Systems ◽  
Flexible Multibody ◽  
Active Vibration

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]

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