Active vibration reduction of a flexible structure bonded with optimised piezoelectric pairs using half and quarter chromosomes in genetic algorithms

The optimal placement of sensors and actuators in active vibration control is limited by the number of candidates in the search space. The search space of a small structure discretized to one hundred elements for optimising the location of ten actuators gives 1.73 × 10 ¹³ possible solutions, one of which is the global optimum. In this work, a new quarter and half chromosome technique based on symmetry is developed, by which the search space for optimisation of sensor/actuator locations in active vibration control of flexible structures may be greatly reduced. The technique is applied to the optimisation for eight and ten actuators located on a 500×500mm square plate, in which the search space is reduced by up to 99.99%. This technique helps for updating genetic algorithm program by updating natural frequencies and mode shapes in each generation to find the global optimal solution in a greatly reduced number of generations. An isotropic plate with piezoelectric sensor/actuator pairs bonded to its surface was investigated using the finite element method and Hamilton's principle based on first order shear deformation theory. The placement and feedback gain of ten and eight sensor/actuator pairs was optimised for a cantilever and clamped-clamped plate to attenuate the first six modes of vibration, using minimization of linear quadratic index as an objective function.