scholarly journals An Approximation-Based Design Optimization Approach to Eigenfrequency Assignment for Flexible Multibody Systems

2021 ◽  
Vol 11 (23) ◽  
pp. 11558
Author(s):  
Roberto Belotti ◽  
Ilaria Palomba ◽  
Erich Wehrle ◽  
Renato Vidoni
Keyword(s):  
Multibody Systems ◽  
Mechanical Systems ◽  
Computational Effort ◽  
Flexible Multibody Systems ◽  
Optimization Approach ◽  
Multibody Simulation ◽  
Assignment Method ◽  
Modal Model ◽  
Flexible Multibody ◽  
Lightweight Engineering

The use of flexible multibody simulation has increased significantly over recent years due to the increasingly lightweight nature of mechanical systems. The prominence of lightweight engineering design in mechanical systems is driven by the desire to require less energy in operation and to reach higher speeds. However, flexible lightweight systems are prone to vibration, which can affect reliability and overall system performance. Whether such issues are critical depends largely on the system eigenfrequencies, which should be correctly assigned by the proper choice of the inertial and elastic properties of the system. In this paper, an eigenfrequency assignment method for flexible multibody systems is proposed. This relies on a parametric modal model which is a Taylor expansion approximation of the eigenfrequencies in the neighborhood of a configuration of choice. Eigenfrequency assignment is recast as a quadratic programming problem which can be solved with low computational effort. The method is validated by assigning the lowest eigenfrequency of a two-bar linkage by properly adding point masses. The obtained results indicate that the proposed method can effectively assign the desired eigenfrequency.

Discrete Adjoint Method for the Sensitivity Analysis of Flexible Multibody Systems

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Alfonso Callejo ◽  
Valentin Sonneville ◽  
Olivier A. Bauchau
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Adjoint Method ◽  
Mechanical Systems ◽  
Rigid Bodies ◽  
Flexible Multibody Systems ◽  
Design Parameters ◽  
Integration Scheme ◽  
Discrete Version ◽  
Flexible Multibody

The gradient-based design optimization of mechanical systems requires robust and efficient sensitivity analysis tools. The adjoint method is regarded as the most efficient semi-analytical method to evaluate sensitivity derivatives for problems involving numerous design parameters and relatively few objective functions. This paper presents a discrete version of the adjoint method based on the generalized-alpha time integration scheme, which is applied to the dynamic simulation of flexible multibody systems. Rather than using an ad hoc backward integration solver, the proposed approach leads to a straightforward algebraic procedure that provides design sensitivities evaluated to machine accuracy. The approach is based on an intrinsic representation of motion that does not require a global parameterization of rotation. Design parameters associated with rigid bodies, kinematic joints, and beam sectional properties are considered. Rigid and flexible mechanical systems are investigated to validate the proposed approach and demonstrate its accuracy, efficiency, and robustness.

A Recursive Algorithm for Solving the Generalized Velocities From the Momenta of Flexible Multibody Systems

2010 ◽  
Vol 5 (4) ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Multibody Systems ◽  
Recursive Algorithm ◽  
Time Derivative ◽  
Computational Effort ◽  
Open Loop ◽  
Flexible Multibody Systems ◽  
Arithmetic Operations ◽  
Flexible Multibody ◽  
Hamilton's Equations ◽  
Hamilton’S Equations

Hamilton’s equations can be used to define the dynamics of a tree configured flexible multibody system. Their states are the generalized coordinates and momenta (p,q). Numerical solution of these equations requires the time derivatives of the states be defined. Hamilton’s equations have the benefit that the time derivative of the system momenta are easy to compute. However, the generalized velocities q̇ need be solved from the system momenta as defined by p=J(q)q̇ to support the computation of ṗ and the propagation of q. Because of the size of J, the determination of q̇ by linear equation solution schemes requires order ([N+∑i=1Nni]3) arithmetic operations, where N is the number of bodies and ni is the number of mode shape functions used to model the ith body deformations. It has been shown that q̇ can be solved recursively from the momentum equations for rigid multibody systems (Naudet, Lefeber, and Terze, 2003, “Forward Dynamics of Open-Loop Multibody Mechanisms Using An Efficient Recursive Algorithm Based On Canonical Momenta,” Multibody Syst. Dyn., 10, pp. 45–59). This paper extends that result to flexible multibody systems. The overall arithmetic operations to solve for q̇ in this case is proportional to N if the effort to solve for the flexible coordinate rates for each body is weighted the same as that for the joint rate. However, each time the flexible coordinates rate of a body is solved an order (ni3) operations is incurred. Thus, the total computational effort for flexible multibody systems includes an additional order (∑i=1Nni3) operations.

scholarly journals Reduced-Order Observers for Nonlinear State Estimation in Flexible Multibody Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Ilaria Palomba ◽  
Dario Richiedei ◽  
Alberto Trevisani
Keyword(s):  
Model Reduction ◽  
Multibody Systems ◽  
Numerical Test ◽  
Computational Effort ◽  
Flexible Multibody Systems ◽  
Large Set ◽  
State Variables ◽  
Reduced Order ◽  
Flexible Multibody ◽  
Nonlinear State

Modern control schemes adopted in multibody systems take advantage of the knowledge of a large set of measurements of the most important state variables to improve system performances. In the case of flexible-link multibody systems, however, the direct measurement of these state variables is not usually possible or convenient. Hence, it is necessary to estimate them through accurate models and a reduced set of measurements ensuring observability. In order to cope with the large dimension of models adopted for flexible multibody systems, this paper exploits model reduction for synthesizing reduced-order nonlinear state observers. Model reduction is done through a modified Craig-Bampton strategy that handles effectively nonlinearities due to large displacements of the mechanism and through a wise selection of the most important coordinates to be retained in the model. Starting from such a reduced nonlinear model, a nonlinear state observer is developed through the extended Kalman filter (EKF). The method is applied to the numerical test case of a six-bar planar mechanism. The smaller size of the model, compared with the original one, preserves accuracy of the estimates while reducing the computational effort.

A Null Space Projection Approach for Modally Reduced Flexible Multibody Systems

2016 ◽  
Author(s):  
Robert G. Winkler ◽  
Dimitrios Plakomytis ◽  
Johannes Gerstmayr
Keyword(s):  
Multibody Systems ◽  
Large Scale ◽  
Null Space ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
The Body ◽  
Flexible Multibody Systems ◽  
Flexible Mode ◽  
Flexible Multibody ◽  
Space Projection

Light-weight structures and high-performance mechanical systems lead to an increasing amount of vibrations. In order to comply with standards in noise and vibration limits, the simulation of flexible multibody systems is inevitable. Due to the size of the finite element models of real-life mechanical systems, a model order reduction is necessary for the efficient simulation of such large scale flexible multibody systems. Currently, the most widely used technique for modelling and simulation of large scale flexible multibody systems is based on the Floating Frame of Reference Formulation (FFRF) of the modally reduced bodies. Recently, alternatives to the FFRF have been proposed, e.g. the Generalized Component Mode Synthesis (GCMS) which uses an absolute or inertial description of the modes. GCMS leads to a concise form of the equations of motion and a constant mass matrix. Within the context of the GCMS method, the rigid body motion is described with twelve coordinates while the deformation of the body is represented with nine coordinates for each flexible mode. The main drawback of the GCMS method is that the number of flexible coordinates is nine times higher as compared to the classic FFRF and therefore when more modes are needed the efficiency of the method can be impaired. Therefore, the objective of the present paper is the further reduction of the new flexible coordinates by means of a null space projection method. Null space methods have been extensively used in order to develop efficient integration algorithms for rigid bodies, flexible beams and shells; however their applicability to modally reduced flexible multibody systems has not been studied intensively. In the paper herein, we develop a new formulation for modally reduced flexible multibody systems which involves a projection onto the null space of properly defined (internal) constraint conditions imposed to the flexible coordinates. It is important to note that focus is put on the description of the projection in the continuous case rather than the discrete which will be addressed in later developments. The proposed formulation is derived in great detail and it is shown that the simple form of the equations of motion of the GCMS method is almost retained. Finally, the applicability and performance of the method is assessed by means of a numerical example.

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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