Simultaneous active control of flexural and extension power flow in thin beams
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The primary goal of this dissertation consisted of two related parts. The first was to develop an analytical basis for predicting the active control of flexural and extensional power flow in thin semi-infinite and finite beams using piezoelectric actuators and sensors. The second part was to experimentally demonstrate these techniques applied to actual beam systems. In order to maintain total control authority over the system, the control actuators must be able to adequately excite both flexural and extensional motion in the beam. Accurate sensing or estimation of the actual power flow (or variables that can be related to the power flow) in the finite beam in real time is also a requirement. This dictated the development of advanced, new sensing techniques. In order that these overall goals were achieved several tasks were carried out as discussed below.
A theoretical model for the excitation of a thin beam by a single piezoelectric actuator mounted on the surface was developed. The model predicts the simultaneous excitation of flexural and extensional motion by a single actuator whose relative amplitudes are functions of beam and actuator parameters. Further, a single pair of axially co-located, symmetrically bonded, and independently driven piezoelectric actuators can excite flexural and extensional motion of variable complex amplitudes.
A method for the real time filtering of net positive and negative traveling flexural and extensional waves was developed. The theoretical actuator and sensor models were used to study the control of flexural and extensional power.flow in both finite and semi-infinite beams subjected to point force excitation at the free end. These actuator and sensing techniques when combined with an multiple input/output adaptive controller can simultaneously control flexural and extensional power flow in regions of a beam system over a band of frequencies.
The control of flexural and extensional power flow in thin beams was also experimentally investigated for both finite and semi-infinite beams. Power flow attenuations of 30 dB or more downstream of the control actuator location were demonstrated using a single pair of piezoelectric actuators for both resonant and damped beam systems. The experimental and theoretical results demonstrate the effectiveness of piezoelectric actuators and piezoelectric wave vector filters in the control of flexural and extensional power flow in thin beams.
- Doctoral Dissertations