Date of Award

Summer 8-16-2018

Document Type


Degree Name

Doctor of Philosophy (PhD)

First Advisor

Katie Evans


Unmanned aerial vehicles have been an area of interest in both research and industry for the past several decades. Advancements in technology have allowed such aircraft to decrease in size. UAVs are less expensive than traditional aircraft and are less restricted in where they can fly due to their compact size, leading to shifts in the way infrastructure, agriculture, and transportation surveillance and operations are handled.

However, small aerial vehicles and flexible, composite ones are more susceptible to crashes. This has led to an increased interest in methods to control such aircraft. In order to accurately model for a composite, flexible-wing aircraft, there is need for a more complex framework which takes into account the non-linear, spatially varying components associated with the frame. Throughout this project, the application under consideration is the internal damping coefficients.

In order to compare damping mechanisms, experiments were conducted in which a time history of the displacement at the tip of a cantilevered beam was measured. The optimal parameters were found for each model using a least squares cost equation for comparison with the measured data. These damping parameters were then incorporated into the generalized beam equation so that performance could be evaluated. This process was repeated for a variety of models.

This project builds upon previous studies on spatial hysteresis, a non-local internal form of damping. Spatial hysteresis damping was proposed as a damping model for large, flexible, composite space structures. This method was first proposed by H.T. Banks and D.J. Inman for large space structures constructed of graphite epoxy composite materials (see, for example, [2], [9], [10]). These structures, due to their use in spacecraft, were much more rigid than the materials in which we are primarily interested.

Spatial hysteresis was not adopted on a large scale because it is computationally expensive. In the 1980s, when the model was proposed, it was extremely time consuming to incorporate spatial hysteresis using the current technology. Spatial hysteresis involves a kernel function and additional integration variable [8], [11], [15]. However, as computer processing power has increased, so has the potential to incorporate spatial hysteresis into the partial differential equation for a cantilevered beam. Due to this, recent research has proposed that such a damping model could also be used for composite, flexible wing UAVs ([16], [18], [19], [3]). These projects found that, by incorporating spatial hysteresis damping into an Euler Bernoulli beam model for a micro aerial vehicle (MAV), the aircraft was controlled more effectively in flight than by using Kelvin Voigt damping alone.

This work expands the field in that it merges two research areas: the experimental work done on space structures and theoretical work on applying spatial hysteresis to UAV models. It allows a theoretical form of internal damping to be experimentally validated for use in mathematical models of MAVs. This is significant because, by having a more complete understanding of composite, flexible wing materials, UAV development is more able to address control issues accurately and efficiently. With the boom of the UAV industry, there is a clear need for a mathematical model which accurately describes the materials used. This project aims to address that need.