Large Static and Dynamic Deformation of Beams: The Inverse Problem.

The primary objective of this study is to establish a methodology for validating a dynamical model of a flexible two beam system undergoing large deformations. This dissertation presents a systematic approach for using a series of experiments to estimate mathematical model parameters and correct them to match the measured response. The study of any dynamical system has a natural partition between the kinetic energy terms and the potential energy terms. By using this natural partition to design a sequence of experiments, it is shown that the number of unknown parameters affecting the system response for any given experiment is greatly reduced. First, a set of static deformations are used to determine beam parameters such as the stiffness coefficients and allow modeling of nonlinear effects. Then, free response experiments are used to determine some motion parameters such as the mass per unit length of each beam and the parameters associated with natural environmental forces such as friction effects. This separation of static and free response measurements allows the recovery of model parameters without being corrupted by other forced system model errors such as joint dynamics and motor modeling which are present in a full dynamic response. A set of dynamic forced response experiments are used to determine motor parameters which model the inputs to the structure. Appropriate statistical estimation methods are utilized to forward propagate a priori and measurement covariance estimates through the sequence of nonlinear estimation processes.