A Practical Approach for the Linearization of the Constrained Multibody Dynamics Equations

Negrut, Dan; Ortiz, José Luis Luviano

doi:10.1115/1.2198876

Cited by 54 publications

(31 citation statements)

References 16 publications

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“…The best way of acquiring modal characteristics or frequency response functions for such systems would be to linearize the system equations of motion, express them in standard matrix form, + + = ,   y y y M C K Q and apply appropriate harmonic input/response assumptions. For more details on linearization methods, the interested reader is referred to the work of Negrut and Ortiz [17].…”

Section: Resultsmentioning

confidence: 99%

Derivation of Rigid Body Analysis Models From Vehicle Architecture Abstractions

Lesiv

Prater

Osborne

et al. 2011

Volume 9: Transportation Systems; Safety Engineering, Risk Analysis and Reliability Methods; Applied Stochastic Optimization, U

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Vehicle analysis models of every type have their basis in some type of physical representation of the design domain. Rather than describing three-dimensional continua of a collection of components as is done in detail-level CAD models, an architecture-level abstraction describes fundamental function and arrangement, while capturing just enough physical detail to be used as the basis for a meaningful representation of the design, and eventually, analyses that permit architecture assessment. The design information captured by the abstractions is available at the very earliest stages of the vehicle developing process, so the model itself can function as a "design space for ideas". In this paper we describe a generalized process for analysis model extraction from vehicle architecture abstractions, and then apply that process to the specific case of rigid body response models. We also discuss implementation of a rigid body analysis engine that forms part of the analysis suite of a software package supporting all aspects of vehicle architecture design. UNCLASSIFIED: Distribution Statement A. Approved for public release. Report Documentation Page Form Approved OMB No. 0704-0188Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

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Section: Resultsmentioning

confidence: 99%

Derivation of Rigid Body Analysis Models From Vehicle Architecture Abstractions

Lesiv

Prater

Osborne

et al. 2011

Volume 9: Transportation Systems; Safety Engineering, Risk Analysis and Reliability Methods; Applied Stochastic Optimization, U

View full text Add to dashboard Cite

show abstract

“…Avoidance of linearization of nonlinear equations of motion. The ODEs generated by conventional methods are nonlinear ones that need to be linearized before perform vibration calculation [6][7][8][9][10]. Instead, the ODEs obtained by using the proposed method are a minimal set of second-order linear ODEs which can be directly used for vibration calculation.…”

Section: Reduction Of Trigonometric Functions Computingmentioning

confidence: 99%

“…Dynamic modeling and vibration analysis based on multibody dynamics are essential to design, optimization and control of these systems [3,4]. Vibration calculation of SR-MBS are usually started by solving large-scale nonlinear equations of motion combined with constraint equations [5], and then linearization is carried out to obtain a set of linearized differentialalgebraic equations (DAEs) or second-order ordinary differential equations (ODEs) [6][7][8][9][10]. This kind of method is necessary for solving the dynamics of nonlinear systems with large deformation.…”

Section: Introductionmentioning

confidence: 99%

Vibration Calculation of Spatial Multibody Systems Based on Constraint-Topology Transformation

et al. 2011

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Many kinds of mechanical systems can be modeled as spatial rigid multibody systems (SR-MBS), which consist of a set of rigid bodies interconnected by joints, springs and dampers. Vibration calculation of SR-MBS is conventionally conducted by approximately linearizing the nonlinear equations of motion and constraint, which is very complicated and inconvenient for sensitivity analysis. A new algorithm based on constraint-topology transformation is presented to derive the oscillatory differential equations in three steps, that is, vibration equations for free SR-MBS are derived using Lagrangian method at first; then, an open-loop constraint matrix is derived to obtain the vibration equations for open-loop SR-MBS via quadric transformation; finally, a cut-joint constraint matrix is derived to obtain the vibration equations for closed-loop SR-MBS via quadric transformation. Through mentioned above, the vibration calculation can be significantly simplified and the sensitivity analysis can be conducted conveniently. The correctness of the proposed method has been verified by numerical experiments in comparison with the traditional approaches.

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“…When multi-body system dynamics is concerned, some authors address the problem by projecting the co-ordinates of the system on the constraint manifolds [25]. This is the case of the popular solver MSC/ADAMS [26].…”

Section: Eigenanalysismentioning

confidence: 99%

Reduced Order Models Using Generalized Eigenanalysis

Ripepi

Masarati

2011

Proceedings of the Institution of Mechanical Engineers, Part K:

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This article discusses the use of generalized eigenanalysis to extract reduced order models from the linearization of structural and aeroelastic problems written in differential-algebraic form. These problems may arise from multi-body analysis and in general from mixed approaches, where a high degree of generality and modelling flexibility are sought. A method based on a shift technique is proposed, that allows to exploit the regularity of the matrix pencil resulting from the linearization of differential-algebraic problems. Alternatively, the generalized Schur decomposition, or QZ decomposition, is directly used to select a cluster of eigenvalues related to the dynamic states. The two approaches are used to reduce the model to ordinary differential in state-space form. The two methods are applied to simple numerical problems, highlighting their robustness and versatility compared to other techniques. They are also applied to numerical models of a high-altitude long endurance aircraft obtained using a free general-purpose multi-body solver and a dedicated mixed variational solver

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A Practical Approach for the Linearization of the Constrained Multibody Dynamics Equations

Abstract: The paper presents an approach to linearize the set of index 3 nonlinear Differential Algebraic Equations (DAE)

Cited by 54 publications

References 16 publications

Derivation of Rigid Body Analysis Models From Vehicle Architecture Abstractions

Derivation of Rigid Body Analysis Models From Vehicle Architecture Abstractions

Vibration Calculation of Spatial Multibody Systems Based on Constraint-Topology Transformation

Reduced Order Models Using Generalized Eigenanalysis

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