4. ULUSLARARASI MÜHENDİSLİK MİMARLIK VE TASARIM KONGRESİ , İstanbul, Turkey, 23 April - 24 October 2019, pp.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.