Dynamical Modeling and Distributed Vibration Control for the Multi-Plate Jointed by Hinges

The dynamical characteristics and vibration control for the multi-plate jointed by hinges are investigated in this paper. The connection for the multi-plate fixed on the external component is the discontinuous interval constraint, which is different the traditional point constraint. A novel power series multiplier method is proposed to describe the local fixed support constraint boundary. This method not only overcomes the dependency of the deformation function’s leading term but also addresses the limitation of traditional Lagrange multiplier methods, which are confined to point constraints. Subsequently, the Lagrange multiplier method is utilized to establish the constraints imposed by the hinges on the inter-plate connections. The natural frequencies and modes of the structure are obtained by using the Rayleigh-Ritz method. A comparison with finite element results validates the effectiveness of the proposed method. The impact of hinge stiffness on the structure’s natural characteristics is also examined. Furthermore, the electro-mechanical coupling dynamic equations for hinged multi-plate structure with piezoelectric actuators are established, and the control effects on the structural response under nonlinear excitation are examined. A proportional-derivative control law is adopted to adjust the voltages of piezoelectric sensors and actuators, optimize control parameters, and achieve optimal control effects. The results indicate that the power series multiplier constraint method can accurately characterize interval constraints and is well-suited for constructing dynamic models of plates with non-classical boundary conditions. The distributed control method based on piezoelectric actuators enables targeted vibration suppression for specific modal shapes.