On the Transient Dynamics of Flexible Orbiting Structures

Modi, V. J.; Ibrahim, A. M.

doi:10.1007/978-3-642-83376-2_4

Cited by 4 publications

(3 citation statements)

References 6 publications

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“…(13) and (15) are already linear in the generalized speeds u 6 + i (i = 1,...,^) associated with the modal coordinates, and this leads to error. However flawed as these equations are, they are the only ones available to an analyst wishing to describe the deformation of an arbitrary, general structure via modes.…”

Section: Generalized Inertia Forcesmentioning

confidence: 97%

“…Wu and Haug 13 accomplish this by dividing a single flexible body into substructures and constraining the relative motion between the substructures at common nodes, much like Hopkins and Likins 14 had done earlier for rotating structures, except that they represent the substructure with modes rather than as finite elements; their formulation thus requires the solution for modal coordinates of each substructure and the constraint forces and moments at the interface nodes. Representation of dynamic stiffening through direct use of geometric stiffness has been made for general structures by Modi and Ibrahim 15 and Zeiler and Buttrill, 16 and for beams by Amirouche and Ider. 17 However, the implementation of geometric stiffness in these formulations, based on the instantaneous nodal displacements, seems to be computationally intensive, even with the use of modes.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of an arbitrary flexible body in large rotation and translation

Banerjee

Dickens

1990

Journal of Guidance, Control, and Dynamics

113

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Conventional theories underlying many multibody codes used for simulating the behavior of elastic structures undergoing large rotation and translation with small vibrations fail to predict dynamic stiffening of the structures. This can lead to significantly incorrect simulations in many practical situations. A theory that does not suffer from this defect and is valid for an arbitrary structure is given here. The formulation is based on Kane's equations and consists of two steps: First, generalized inertia forces are written for an arbitrary structure for which one is forced to linearize prematurely in the modal coordinates; next, this defect in linearization is compensated for by the introduction of contributions to the generalized active forces from the "motion stiffness" of the structure. The stress associated with the motion stiffness is identified as due to 12 sets of inertia forces and 9 sets of inertia couples distributed throughout the body during the most general motion of its flying reference frame. An algorithm is set for a reader wishing to implement the theory* and illustrative examples are given to demonstrate the validity and generality of the formulation.

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Section: Generalized Inertia Forcesmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Dynamics of an arbitrary flexible body in large rotation and translation

Banerjee

Dickens

1990

Journal of Guidance, Control, and Dynamics

113

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“…Equations (9), (14), and (15) are computed in a forward pass going from body 1 to body N for use in a backward pass for generating the dynamical equations described in the next section.…”

Section: Recursive Equations Of Kinematicsmentioning

confidence: 99%

Block-diagonal equations for multibody elastodynamics with geometric stiffness and constraints

Banerjee

1993

Journal of Guidance, Control, and Dynamics

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This paper presents a comprehensive, block-diagonal matrix formulation of the equations of motion of a system of hinge-connected flexible bodies undergoing large rotation and translation together with small elastic vibration. The formulation compensates for premature linearization of equations, associated with the customary treatment of small elastic displacement, by accounting for geometric stiffness due to inertia as well as interbody forces. The algorithm is first developed for a tree configuration and is then extended to the case of closed structural loops by cutting the loops and expressing all of the kinematical variables into terms dependent and free of constraint forces/torques. A solution procedure satisfying constraints is given.

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Spacecraft attitude dynamics: Evolution and current challenges

Modi

1990

Acta Astronautica

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On the Transient Dynamics of Flexible Orbiting Structures

Cited by 4 publications

References 6 publications

Dynamics of an arbitrary flexible body in large rotation and translation

Dynamics of an arbitrary flexible body in large rotation and translation

Block-diagonal equations for multibody elastodynamics with geometric stiffness and constraints

Spacecraft attitude dynamics: Evolution and current challenges

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