Optimal vibration attenuation of an adhesively-bonded cantilevered single-lap joint

Abstract

In this study the three-dimensional transient vibration attenuation of an adhesively-bonded cantilevered single-lap joint was controlled using actuators. First, the vibration attenuation of the adhesive joint, which was disturbed by applying a concentrated load to the free edge of the lower adherend, was determined without a control force. In order to reduce displacement level and vibration attenuation time, a variable transverse control force was applied to a point on the lower adherend surface using an actuator. The transient variation of the control force was expressed by a periodic function so that the damped vibration of the adhesive joint was decreased. The optimal transient variation of the control force applied by the actuator is an optimization problem requiring the minimization of the objective function including the total elastic strain and kinetic energies, and the actuator work. In addition, the optimum placement of the actuator on the surface of the lower adherend is the second optimization problem. Optimal transient control force history and optimal actuator position were determined using the Open Loop Control Approach and Genetic Algorithm. The peak displacement reduced by 69.6% and the attenuation time decreased by 33%. In addition, the control performance of two actuators was investigated. Thus, the first actuator was located at the optimal position of a single actuator case, and then the optimal transient variations of the control forces applied by both actuators and the optimal position of the second actuator were determined. An additional decrease of 30% in the total energy of the adhesive joint and in the total work of both actuators in comparison to the single actuator case was found, whereas the difference in the vibration attenuation time of the adhesive joint was minor.