Component mode synthesis with constant mass and stiffness matrices applied to flexible multibody systems

2008 ◽  
Vol 73 (11) ◽  
pp. 1518-1546 ◽  
Author(s):  
J. Gerstmayr ◽  
J. A. C. Ambrósio
Keyword(s):  
Multibody Systems ◽  
Flexible Multibody Systems ◽  
Component Mode Synthesis ◽  
Constant Mass ◽  
Stiffness Matrices ◽  
Flexible Multibody

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

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.

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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