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 its 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 criterion 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. 1. Introduction The dependence of mechanical and electrical properties of piezoelectric materials on their application in various materials as patches or layers makes them an appropriate sensor or actuator for vibration control of structures. In sensing situation, the mechanical and creep deformations of structures can be determined by measuring the electrical potential produced in piezoelectric materials. This property is termed the direct property of the piezoelectric material. Then an effective feedback mechanism sends an electric signal to an actuator to keep the vibration of the mechanical system to a minimum. In actuator applications, the inverse piezoelectric effect is used. Recently, this technique is widely used in the active control of vibrations, deformation control of structures, and aerospace industries. This technique has been investigated by research in solid and aeroelastic areas. In solid, Gaudenzi et al. [1] investigated the vibration control of an overhung beam by means of finite element approach based on Euler-Bernoulli beams. They studied state feedback and velocity feedback control of vibration. Moreover, Q. Wang and C. M. Wang [2] implemented vibration control of a beam with piezoelectric patches by taking finite element method into account. They determined an optimized position for an appropriate actuator and the subsequent vibration amplitude of a hinged-hinged beam by applying a feedback control procedure and converting the finite element model into its state space form. Narayanan and Balamurugan [3] studied