This study presents analytical and experimental procedures and design tools for the control of flexible structure vibrations using a cantilevered adaptive truss. A specific six-actuator, octahedral-octahedral truss effects the control of different flexible structures. These structures could represent space structures or robotic manipulators or a variety of other flexible structures where unwanted structural vibration could reduce the performance of the system. Three of these structures; a slender beam, a single curved beam, and two curved beams are controlled both in simulation and with an experimental test article. The test article, comprised of the flexible structure, the adaptive truss, and the actuators shows excellent agreement between simulated and experimental responses to initial conditions in both open-loop and (LQR) closed-loop control. As a example of the ability of the truss to control the slender beam, a first mode simulated frequency of 3.11Hz (3.09Hz experimental) and damping ratio of 0.0044 (0.0044) are controlled to produce a 3.20Hz (3.14Hz) frequency and a damping ratio of 0.2876 (0.2746). This 6000% increase in damping without a significant change in the modal frequency shows the potential of the adaptive truss in vibration control. The agreement between simulated and experimental data shows the validity of the modeling and experimental procedures. From the information gained, conclusions are drawn about the uses of an adaptive truss in the control of flexible structure vibrations. / Ph. D.