In this dissertation, analytical and experimental investigations conducted into active control of longitudinal and flexural vibrations transmitted through a hollow cylindrical strut are presented. The research consists of two principal components. In one component, a mechanics based approach is used to develop partial-differential equations (PDEs) based analytical models of an active integrated strut system for control of uncoupled longitudinal and flexural waves transmitted through finite-length structural members. For attenuating longitudinal and flexural displacements at the strut end attached to a host structure, piezoelectric or magnetostrictive actuators are mounted on the strut along axial and transverse directions, respectively. Linear models of the actuators are developed, and the respective electrical or magnetic boundary constraints as well as the mechanical boundary constraints are taken into account. These models are then integrated with the mechanics model of the strut.; In the second component, experimental studies of open-loop and closed-loop longitudinal wave transmission control are conducted with strut-actuator systems. The acceleration at the end of the strut attached to the host structure is measured, when steady harmonic disturbances are transmitted in the frequency range of 0 Hz to 1 kHz. In open-loop investigations, a reduction of up to 17 dB in the vibration transmission was attained, when piezoelectric and magnetostrictive inertial actuators were used to provide the boundary control input. For closed-loop control, a feedforward control algorithm is developed; this algorithm is based on the integrated PDE model of the strut-actuator system. In this scheme, a combination of strain and acceleration measurements are used to determine the solution for the boundary-value problem governing the system. The effectiveness of the controller was investigated over a broad frequency range and vibration attenuations up to 16 dB were observed. The control algorithm is seen to be predictive of the necessary voltage amplitude and phase parameters, when a magnetostrictive actuator is used for control. The studies, which are presented in this dissertation, contribute to a fundamental understanding required for active control of wave transmission in one-dimensional finite-length structural systems. In particular, the contributions provide a novel integrated framework for modeling structures with active elements and controlling them.
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