Electromechanical control of the dynamics of a thin elasticplate: Analytical method and finite differences simulation

• The electromechanical control of the dynamics of thin plate is considered.
• The boundaries for the control of vibration and snap through instability are obtained.
• Horseshoes and dissipative chaos are eliminated leading to sinusoidal vibrations.

The electromechanical control of the dynamics of thin elastic plate is analysed using both the modal approach and the direct numerical simulation of partial differential equation. The electromechanical controller is constituted of a RL circuit with some stings connected through a magnet to the plate. The direct numerical simulation reveals the existence of different vibration modes. The boundary limits of the control parameters leading to the reduction of vibration amplitude, snap through instability and Melnikov chaos are determined and plotted in terms of the system parameters. It is seen that electromechanical control can eliminate the chaotic domain leading to periodic oscillations.