Vibration Reduction of a Plate Using Active Control

4. ULUSLARARASI MÜHENDİSLİK MİMARLIK VE TASARIM KONGRESİ , İstanbul, Türkiye, 23 Nisan - 24 Ekim 2019, ss.121

Abstract: Vibration reduction of a simply supported beam using H-infinity control is performed in this study.

The plate is rectangular, elastic and simply supported from all sides. Disturber force is continuous and effecting

perpendicular on the arbitrary point of the upper surface. Firstly nine different mode shapes are inspected.

The behavior of the plate is modeled as the Biharmonic Equation and has three independent (x,y,t) variable.

The fourth-order partial differential equation is used with Love Plate Theory. Kirchhoff-Love plate theory is

thin shell theory. It assumes that shear deformations and high order terms are neglectable. According to the

boundary conditions double trigonometric series of Navier Method is used for the solution of the biharmonic

equation. The solution of the biharmonic equation is assumed separable to variables which spatial location and

time for the controller to be applied. The biharmonic equation is converted to State-Space form. Each mode behavior

is accepted as a new state. The equation of motion should be in State-Space form for the using H-infinity

controller. State Feedback H-infinity Method is used for vibration reduction. Velocity and displacement values

are decreased with actuators which is piezoelectric. All mode values are summed for finding total displacement

and velocity. The all situation has been simulated and solved in Matlab Simulink application.