Non-Linear Constraints and Stiffness Representations in Simple Flexible-Body Dynamic Beam Formulations

Abstract

Abstract: A simple discrete four-degree-of-freedom (lumped parameter) model representing a flexible beam undergoing large overall planar prescribed motion has been developed. It serves as a simple tool to investigate two previously studied problems involving flexible-body beam dynamics, namely those involving bending and membrane stiffness dominated behavior. The tool is used to investigate the requirements to accurately solve these problems using non-linear constraints and a non-linear spring representation. The validity of this model is demonstrated by comparing results to those previously published for continuous flexible-body beam formulations. One of these continuous representations is modified to include a non-linear tether spring representation. This allows additional model verification as well as insight into the non-linear constraint and stiffness representations. Taken in its entirety, this investigation demonstrates the utility of these simple lumped parameter models, by showing their ability to provide rapid insight into the behavior of the more complicated continuous models, as well as the system in general.

Get full access to this article

View all access options for this article.

References

Banerjee, A. K. and Dickens, J. M., 1990, “Dynamics of an arbitrary flexible body in large rotation and translation,” Journal of Guidance, Control and Dynamics 13(2), 221-227 .

Baumgarte, J. W., 1972, “Stabilization of constraints and integrals of motion in dynamical systems,” Computer Methods in Applied Mechanics and Engineering 1(1), 1-16 .

Christensen, E. R. and Lee, S. W., 1986, “Nonlinear finite element modeling of the dynamics of unrestrained flexible structures,” Computers and Structures 23(6), 819-829 .

Haering, W. J., 1992, A New Flexible Body Dynamic Formulation for Beam Structures Undergoing Large Overall Motion, PhD Thesis, University of Michigan.

Haering, W. J., Ryan, R. R., and Scott, R. A., 1994, “New formulation for flexible beams undergoing large overall motion,” Journal of Guidance, Control, and Dynamics 17(1), 76-83 .

Kane, T. R. and Levinson, D. A., 1983, Dynamics, Theory and Applications, McGraw-Hill, New York .

Kane, T. R. and Levinson, D. A., 1996, AutoLev User's Manual, OnLine Dynamics, Sunnyvale, CA .

Kane, T. R., Ryan, R. R., and Banerjee A. K., 1987, “Dynamics of a cantilever beam attached to a moving base,” Journal of Guidance, Control, and Dynamics 10(2), 139-151 .

Simo, J. C., 1985, “A finite strain beam formulation. The three-dimensional dynamics problem. Part I.,” Computer Methods in Applied Mechanics and Engineering 49(1), 55-70 .

10.

Yoo, H. H., 1989, Dynamic Modeling of Flexible Bodies in Multibody Systems, PhD Thesis, University of Michigan.

11.

Yoo, H. H., Ryan, R. R., and Scott, R. A., 1995, “Dynamics of flexible beams undergoing overall motions,” Journal of Sound and Vibration, 181(2), 261-278 .