The pursuit of faster and more precise mechatronic systems necessitates the use of inventive mechanical designs and advanced control schemes. In recent years, flexible elements have seen increased use as they enable the development of high-precision motion systems in a wide variety of applications ranging from semiconductor fabrication to precision surgery. Although these flexures provide ample benefits for systems that require lightweight elements and predictable behavior, structural vibrations can restrict their effectiveness in achieving precise positioning. This motivates the need for vibration suppression in motion systems, particularly those with flexible components. To that end, smart structures with embedded transducers and a suitable control algorithm can be used to actively damp the underlying structure’s resonance modes, although time-varying parameters and uncertainties from various sources can degrade the performance of the vibration controller. In this thesis, an adaptive control scheme is developed to maintain the desired damping performance regardless of system variations. The method employs adaptive notch filters in a cascade arrangement to track multiple modal frequencies of a smart flexible structure, then tunes a positive position feedback controller for multimodal damping with a straightforward adjustment rule. The adaptation is shown to be fast, accurate, and efficient, with clear advantages in suppressing the vibrations of time-varying and uncertain systems. The method also provides key features absent from other adaptive damping implementations, including the ability to effectively estimate modal frequencies using brief transient signals typical of damped structures, as well as signals buried in noise. Finally, the adaptive scheme is validated experimentally with a flexible beam, showcasing its strong potential for practical applications.