Dynamics of flexible bodies in tree topology - A computer-oriented approach

Singh, Ramendra; Vandervoort, R. J.; Likins, Peter W.

doi:10.2514/3.20026

Cited by 130 publications

(20 citation statements)

References 19 publications

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“…This representation may include closed loops of bodies, prescribed motion, or other constraints that may be represented as in equation (2). The equations of motion appropriate for a set of flexible bodies in an open loop configuration appear in [2,11]. A computer program (TREETOPS) developed to simulate the dynamic response of flexible structures in a topological tree configuration is described in [10].…”

Section: Application To Complex Dynamical Systemsmentioning

confidence: 99%

Singular Value Decomposition for Constrained Dynamical Systems

Singh

Likins

1985

Journal of Applied Mechanics

149

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The method of singular value decomposition is shown to have useful application to the problem of reducing the equations of motion for a class of constrained dynamical systems to their minimum dimension. This method is shown to be superior to classical Gaussian elimination for several reasons: {i) The resulting equations of motion are assured to be of full rank, (ii) The process is more amenable to automation, as may be appropriate in the development of a computer program for application to a generic class of systems. (Hi) The analyst is spared the responsibility for the selection of specific coordinates to be eliminated by substitution in each individual case, a selection that has no physical justification but presents abundant risk of mathematical contradiction. This approach is shown to be very efficient when the governing dynamical equations are derived via Kane's method.

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Section: Application To Complex Dynamical Systemsmentioning

confidence: 99%

Singular Value Decomposition for Constrained Dynamical Systems

Singh

Likins

1985

Journal of Applied Mechanics

149

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“…Then the discrete mathematical model is established using the multi-body dynamics method [4][5][6][7][8][9]. In 1987, Kane [6] investigated a rotating flexible cantilever beam using the ZOAC model, and showed that the ZOAC model failed to describe the dynamic behavior of the beam when the beam is in high rotation speed.…”

Section: Introductionmentioning

confidence: 99%

“…In 1987, Kane [6] investigated a rotating flexible cantilever beam using the ZOAC model, and showed that the ZOAC model failed to describe the dynamic behavior of the beam when the beam is in high rotation speed. In addition, in the existing works by using the ZOAC model [4][5][6][7][8][9], the large motion of the system is usually assumed to be known, i.e., only the effect of the large motion of the system on the flexible beam is considered while ignoring the coupling effect between the large motion of the system and the elastic motion of the flexible beam. However, in practice the law for large motion of rigid-flexible coupling systems is unknown and needs to be solved, i.e., the law of external forces acted on the systems is known but the law of large motion of the systems should be solved using the theories of kinematics and dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…There are many studies on modelling of the hub-beam system, which can be classified into three categories: the Kineto-Elasto Dynamics (KED) uncoupled model [1][2][3], the zeroth-order approximation coupling (ZOAC) model (namely the traditional hybrid coordinate model) [4][5][6][7][8][9] and the first-order approximation coupling (FOAC) model [10][11][12]. In the KED uncoupled model, only the effect of large motion on the elastic deformation of the flexible beam is considered while the effect of elastic deformation on the large motion is ignored, i.e., the flexible beam is assumed to be a rigid body in solving the large motion of the system using the multi-body theory.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Analysis of a Hub‐Beam System by a First‐Order Approximation Coupling Model

Cai

Hong

2006

Multidiscipline Modeling in Materials and Structures

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In this paper, a first-order approximation coupling (FOAC) model is investigated to analyze the dynamics of the hub-beam system, which is based on the Hamilton theory and the finite element discretization method. The FOAC model for the hub-beam system considers the second-order coupling quantity of the axial displacement caused by the transverse displacement of the beam. The dynamic characteristics of the system are studied through numerical simulations under twos cases: the rotary inertia of the hub is much larger than, and is close to, that of the flexible beam. Simulation and comparison studies using both the traditional zeroth-order approximation coupling (ZOAC) model and the FOAC model shows that when large motion of the system is unknown, possible failure exists by using the ZOAC model, whereas the FOAC model is valid. When the rotary inertia of the hub is much larger than that of the beam, the result using the ZOAC model is similar to that using the FOAC model. But when the rotary inertia of the hub is close to that of the beam, the ZOAC model may lead to a large error, while the FOAC model can still accurately describe the dynamic hub-beam system.

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“…The dynamic model established based on this small deformation assumption is referred as the zeroth-order approximation coupling model (ZOAC model). This model is widely used in dynamic analysis of rigid-flexible coupling dynamic systems in the past several decades [1][2][3][4][5][6][7][8][9]. In 1987, Kane [3] investigated a rotating flexible cantilever beam using the classical ZOAC model, and showed that this model failed to describe the dynamic behaviour of beam when the beam is in high rotational speed.…”

Section: Introductionmentioning

confidence: 99%