Vibration Analysis, Control and Optimal Placement of MFC Actuators and sensors on Rotating Thin-Walled Composite cantilever Beams

Abstract

In the present thesis, equations of motion are derived using dynamic modelling method for rotating thin-walled composite beams. Coupled equations of motion are derived for arbitrary beam configuration using HamiltonDs principle for higher order shear deformable beam. A non-Cartesian deformation variable representing axial stretch, along with two Cartesian variables representing bending motions are used. Due to this transformation, centrifugal stiffening and gyroscopic coupling effects can be captured in linear potential and kinetic energy equations. This makes the formulation less cumbersome compared to geometrically nonlinear modelling method. Moreover, this method provides the advantage of inclusion of gyroscopic coupling. The effect of gyroscopic coupling makes the structural model more realistic and it has been demonstrated that the gyroscopic coupling cannot be neglected. The mathematical model also includes non-classical effects generally exhibited by rotating composite beams such as anisotropy, heterogeneity, warping and transverse shear. The approximate solutions of equations of motion are obtained using the extended GalerkinDs method. To validate the developed code, the results from the present method are compared with the experimental and theoretical results available in the literature. The predicted results are in good agreement with the results available in the literature. Numerical solutions for rotating composite cantilever beams are illustrated for a composite box beam configuration. Effects of taper, pretwist, presetting and gyroscopic coupling on free and forced vibration of rotating beams are studied. Numerical results reveal that gyroscopic coupling between lagging-extension modes has considerable effect on the system natural frequency, mode shape, forced response and hence cannot be neglected. The structural modelling of rotating composite thin walled beams is extended to include embedded MFC actuators and sensors. The actuators and sensors are considered as distributed over the top and bottom surface of the beam, respectively. The governing coupled equations of motion are derived from the HamiltonDs principle and approximate solution is obtained using extended GalerkinDs method.The reduced order model is formulated with the assumption that the lower order modes have lower energy associated and consequently are the most easily excitable ones. The number of modes in a reduced order model are selected by analyzing convergence of tip displacement and actuator voltage. Thereafter the reduced order model is converted to a state space form for the purpose of controller design. Optimal control algorithms such as linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) are used to estimate feedback gain. Comparison between bending vibration control performance of monolithic piezoelectric and fibre based piezoelectric actuators/sensors are studied. Distributed piezoelectric model available in the literature is used for monolithic piezoelectric actuators and sensors. It is observed that control effort by using MFC actuators and sensors is significantly less compared to that of monolithic piezoelectric actuators and sensors. Passive effect of monolithic and fibre based piezoelectric actuators on system natural frequencies are studied in numerical experiments. Optimal co...