Type of Document Dissertation Author Stemple, Timothy J. Author's Email Address timothys@vt.edu URN etd-3198-18655 Title Dynamics and Control of Flexible Multibody Structures Degree PhD Department Engineering Science and Mechanics Advisory Committee

Advisor Name Title Meirovitch, Leonard Committee Chair Baumann, William T. Committee Member Cramer, Mark S. Committee Member Hendricks, Scott L. Committee Member Rogers, Robert C. Committee Member Keywords

- multibody dynamics
- flexible multibody structures
- control
Date of Defense 1998-03-19 Availability unrestricted AbstractThe goal of this study is to present a method for derivingequations of motion capable of modeling the controlled

motion of an open loop multibody structure comprised of an

arbitrary number of rigid bodies and slender beams. The

procedure presented here for deriving equations of motion

for flexible multibody systems is carried out by means of

the Principle of Virtual Work (often referred to in the

dynamics literature as d'Alembert's Principle). We first

consider the motion of a general flexible body relative to

the inertial space, and then derive specific formulas for

both rigid bodies and slender beams. Next, we make a small

motions assumption, with the end result being equations for

a Rayleigh beam, which include terms which account for the

axial motion, due to bending, of points on the beam central

axis. This process includes a novel application of the

exponential form of an orthogonal matrix, which is ideally

suited for truncation. Then, the generalized coordinates and

quasi-velocities used in the mathematical model, including

those needed in the spatial discretization process of the

beam equations are discussed. Furthermore, we develop a new

set of recursive relations used to compute the inertial

motion of a body in terms of the generalized coordinates and

quasi-velocities. This research was motivated by the desire

to model the controlled motion of a flexible space robot,

and consequently, we use the multibody dynamics equations to

simulate the motion of such a structure, providing a

demonstration of the computer program. For this particular

example we make use of a new sequence of shape functions,

first used by Meirovitch and Stemple to model a two

dimensional building frame subjected to earthquake

excitations.

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