Active vibration reduction by optimally placed sensors and actuators with application to stiffened plates by beams

This study concerns new investigation of active vibration reduction of a stiffened plate bonded with discrete sensor/actuator pairs located optimally using genetic algorithms based on a developed finite element modeling. An isotropic plate element stiffened by a number of beam elements on its edges and having a piezoelectric sensor and actuator pair bonded to its surfaces is modeled using the finite element method and Hamilton's principle, taking into account the effects of piezoelectric mass, stiffness and electromechanical coupling. The modeling is based on the first order shear deformation theory taking into account the effects of bending, membrane and shear deformation for the plate, the stiffening beam and the piezoelectric patches. A Matlab finite element program has been built for the stiffened plate model and verified with ANSYS and also experimentally. Optimal placement of ten piezoelectric sensor/actuator pairs and optimal feedback gain for active vibration reduction are investigated for a plate stiffened by two beams arranged in the form of a cross. The genetic algorithm was set up for optimization of sensor/actuator placement and feedback gain based on the minimization of the optimal linear quadratic index as an objective function to suppress the first six modes of vibration. Comparison study is presented for active vibration reduction of a square cantilever plate stiffened by crossed beams with two sensor/actuator configurations: firstly, ten piezoelectric sensor/actuator pairs are located in optimal positions; secondly, a piezoelectric layer of single sensor/actuator pair covering the whole of the stiffened plate as a SISO system.