A contribution on modeling methodologies for multibody systems.

Orsino, Renato Maia Matarazzo

doi:10.11606/t.3.2016.tde-22062016-160724

Cited by 8 publications

(23 citation statements)

References 26 publications

(31 reference statements)

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“…This approach allows to better explore the modularity of the systems if, for instance, it is possible to conceive them as a set of constrained subsystems whose mathematical models are already known. This was the context for which previous developments of similar methodologies for the modelling of multibody systems, by Orsino [1] and Orsino & Hess-Coelho [2], were proposed. They can be understood as particular cases of the general approach discussed in this text.…”

Section: Resultsmentioning

confidence: 99%

“…A remarkable result that came along with the development of this new methodology is the equivalence between the formulations by Orsino [1] and Orsino & Hess-Coelho [2] and the formulation by Udwadia & Phohomsiri [4]. The investigation concerning the derivation of a recursive algorithm based on the Udwadia-Kalaba equation, under the same conditions adopted for the general methodology, revealed an even more relevant result: the algorithm is equivalent to the one of a Kalman filter for the estimation of the state of a static process in which the constraint equations play the role of the observation ones, and the associated orthogonal projectors play the role of the covariance matrices.…”

Section: Resultsmentioning

confidence: 99%

“…Therefore, a modular methodology might not be understood simply as another alternative for the already extensive framework of existing ones, but rather as a methodology that aims to conciliate the use of others from which the models of the modules may have been obtained. Some examples of modular modelling methodologies originally developed for multibody systems can be found on works by Orsino [1], Orsino & Hess-Coelho [2] and Udwadia et al [3][4][5][6][7][8]. The latter works are typically referred to in the literature as the Udwadia-Kalaba equation.…”

Section: Introductionmentioning

confidence: 99%

“…(i) the formalisms used in the derivation of the models at the inferior level of a hierarchy (the models may either follow from the application of physical principles using some analytical formalism or can be phenomenological); (ii) the order of the differential equations involved, which can be higher than two; 2 (iii) the criteria for selecting variables, which allows exploration of the advantages of formulations based on the use of redundant variables and on reparameterizations of time rates [1,2]; (iv) the nature of the constraints and the techniques adopted for their description; and (v) how the user chooses to conceive the system modularly and how many levels there are in a given hierarchical representation.…”

Section: Introductionmentioning

confidence: 99%

“…There is a unique generalized inverse matrix that satisfies the four properties simultaneously: it is called the Moore-Penrose pseudoinverse of A and is specially denoted by A + [3,18]. Finally, it is worth commenting that the notation adopted in this text is not only compatible with the desired generality for the methodology proposed, but also tries to resemble as much as possible the notations from previous works from the author [1,2] and from texts on the Udwadia-Kalaba equation and on the Kalman filter. Once all the variables in the presented equations are matrices, no distinctive boldface notation is adopted.…”

Section: Introductionmentioning

confidence: 99%

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Recursive modular modelling methodology for lumped-parameter dynamic systems

Orsino

2017

Proc. R. Soc. A.

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This paper proposes a novel approach to the modelling of lumped-parameter dynamic systems, based on representing them by hierarchies of mathematical models of increasing complexity instead of a single (complex) model. Exploring the multilevel modularity that these systems typically exhibit, a general recursive modelling methodology is proposed, in order to conciliate the use of the already existing modelling techniques. The general algorithm is based on a fundamental theorem that states the conditions for computing projection operators recursively. Three procedures for these computations are discussed: orthonormalization, use of orthogonal complements and use of generalized inverses. The novel methodology is also applied for the development of a recursive algorithm based on the Udwadia-Kalaba equation, which proves to be identical to the one of a Kalman filter for estimating the state of a static process, given a sequence of noiseless measurements representing the constraints that must be satisfied by the system.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Recursive modular modelling methodology for lumped-parameter dynamic systems

Orsino

2017

Proc. R. Soc. A.

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Modular methodology applied to the nonlinear modeling of a pipe conveying fluid

Orsino

Pesce

2018

J Braz. Soc. Mech. Sci. Eng.

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This paper proposes an extension of a modular modeling approach, originally developed for lumped parameter systems, to the derivation of FEM-discretized equations of motion of one-dimensional distributed parameter systems. This methodology is characterized by the use of a recursive algorithm based on projection operators that allows any constraint condition to be enforced a posteriori. This leads to a modular approach in which a system can be conceived as the top member of a hierarchy in which the increase of complexity from one level to the parent one is associated to the enforcement of constraints. For lumped parameter systems this allows the implementation of modeling procedures starting from already known mathematical models of subsystems. In the case of distributed parameter systems, such a novel methodology not only allows to explore subsystembased modeling strategies, but also makes it possible to propose formulations in which compatibility and boundary conditions can be enforced a posteriori. The benchmark chosen to explore these further possibilities is the classical problem of a cantilevered pipe conveying fluid. Taking a pipe made of a linear-elastic material, allowing geometric nonlinearities and assuming an internal plug-flow, a Hamiltonian derivation of FEM-discretized equations of motion is performed according to this novel approach. Numerical simulations are carried out to address the nonlinear model obtained.

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Estudo numérico da dinâmica de um conjunto de tubos ejetando fluido sob instabilidade paramétrica.

Lourenço¹

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Risers are structures commonly found in the offshore engineering scenario. These structures are responsible, among other functions, for conveying fluid. Risers are subjected to several dynamic phenomena, particularly those related to parametric instability and to internal flow. In this study, parametric instability occurs when the stiffness parameter of the equation of motion explicitly depends on time. In the risers' scenario, such a variation is associated with the normal forces modulation caused by the motions of the floating units on the vertical plane. The focus of this research is to analyze a simplified model of riser composed of two rigid pipes, connected by rotational springs and ejecting fluid from its free end. Parametric instability arises from vertical and harmonic motions applied to the support. Herein, the study of the linearized problem is carried out by means of the Floquet Theory. This approach allowed identifying, in the plane of parameters that govern the problem, stability and instability regions of the trivial solution. In addition to this linear analysis, maps showing the post-critical response as a function of some control parameters are obtained using the non-linear mathematical model. Among other findings, the present dissertation shows that the presence of internal flow significantly affects the stability of the trivial solution. Furthermore, the concomitant parametric excitation and internal flow effects led to maps of post-critical response with a marked erosion.

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A contribution on modeling methodologies for multibody systems.

Cited by 8 publications

References 26 publications

Recursive modular modelling methodology for lumped-parameter dynamic systems

Recursive modular modelling methodology for lumped-parameter dynamic systems

Modular methodology applied to the nonlinear modeling of a pipe conveying fluid

Estudo numérico da dinâmica de um conjunto de tubos ejetando fluido sob instabilidade paramétrica.

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