Control Application of Piezoelectric Materials to Aeroelastic Self-excited Vibrations

A method for application of piezoelectric materials to aeroelasticity of turbomachinery blades is presented. The governing differential equations of an overhung beam are established. The induced voltage in attached piezoelectric sensors due to the strain of the beam is calculated. In aeroelastic self-excited vibrations, the aerodynamic generalized force of a specified mode can be described as a linear function of the generalized coordinate and their derivatives. This simplifies the closed loop system designed for vibration control of the corresponding structure. On the other hand, there is an industrial interest in measurement of displacement, velocity, acceleration or a contribution of them for machinery condition monitoring. Considering this criteria in quadratic optimal control systems, a special style of performance index is configured. Utilizing the current relations in an aeroelastic case with proper attachment of piezoelectric elements can provide higher margin of instability and lead to lower vibration magnitude.