Piezoelectric Control of Structures Prone to Instabilities.

Thin-walled structures such as stiffened panels fabricated out of high strength materials are ubiquitous in aerospace structures. These are prone to buckle in a variety of modes with strong possibility of adverse interaction under axial compression and/or bending. Optimally designed stiffened panels, at an appropriate combination of axial compression and suddenly applied lateral pressure undergo large amplitude oscillations and may experience divergence. Under aerodynamic loading, they can experience flutter instability with the amplitudes of oscillations attaining a limit (LCO) or escalating without any limit. Control of structures prone to these forms of instability using piezo-electric actuators is the theme of this dissertation.Issues involved in the control of stiffened panels under axial compression and liable to buckle simultaneously in local and overall modes are studied. The analytical approach employs finite elements in which are embedded periodic components of local buckling including the second order effects. It is shown that the adverse effects of mode interaction can be counteracted by simply controlling the overall bending of the stiffener by piezo-electric actuators attached its tips. Control is exercised by self-sensing actuators by direct negative feedback voltages proportional to the bending strains of the stiffener. In a dynamic loading environment, where vibrations are triggered by suddenly applied lateral pressure, negative velocity feedback is employed with voltages proportional to the bending strain-rate. The local plate oscillations are effectively controlled by a piezo-electric actuators placed along the longitudinal center line of the panel.The problem of flutter under aerodynamic pressure of stiffened panels in the linear and post-critical regimes is studied using modal analysis and finite strips. The analysis, control and interpretation of the response are facilitated by identification of two families of characteristic modes of vibration, viz. local and overall modes and by a classification of the local modes into two distinct categories, viz., symmetric and anti-symmetric modes respectively. The symmetric local modes interact with overall modes from the outset, i.e. in the linear flutter problem whereas both the sets of local modes interact with overall modes in the post-critical range via cubic terms in the elastic potential. However the effects of interaction in the flutter problem are far less dramatic in comparison to the interactive buckling problem unless the overall modes are activated, say by dynamic pressure on the plate. Control of the panel is exercised by piezo-electric patches placed on the plate at regions of maximum curvature as well as on the stiffener.Two types of control strategies were investigated for the panel subject to fluttering instability. The first is the direct negative velocity feedback control using a single gain factor for each of the sets of plate patches and stiffener patches respectively. A systematic method of determining the gains for the patches has been developed. This is based on the application of LQR algorithm in conjunction with a linearized stiffness matrix of the uncontrolled structure computed at a set of pre-selected times. This type of control was successful till the aerodynamic pressure coefficient reaches up to about six times its critical value, where after it simply failed. The second type of control is the multi-input and multi-output full state feedback control. The LQR algorithm and the linearized stiffness matrix are invoked again, but the gain matrix is computed at the beginning of every time step in the analysis and immediately implemented to control the structure. This type of control pr