Optimal piezo-actuator locations/lengths and applied voltage for shape control of beams

Shape control of beams under general loading conditions is implemented using piezoceramic actuators to provide the control forces. The objective of the shape-control is to minimize the maximum deflection of the beam to obtain a min-max deflection configuration with respect to loading and piezo-actuators. In practice, the loading on a beam is a variable quantity with respect to its magnitude, and this aspect can be handled easily by optimizing the magnitude of the applied voltage to achieve the min-max deflection. This property of the smart materials technology overcomes the problem of one-off conventional optimal designs which become suboptimal when the loading magnitude changes. In addition to the magnitude of the applied voltage, the optimal values for the locations and the lengths of the piezo-actuators are determined to achieve the min-max deflection. Due to the complexity of the governing equations involving finite length piezo patches, the numerical results are obtained by the finite-difference method. The analysis of the problem shows the effect of the actuator locations, lengths and the applied voltage on the maximum deflection. The optimal Values for the actuator locations and the voltage are determined as functions of the load locations and load magnitudes, respectively. The effect of the actuator length on the min-max deflection is investigated and it is observed that the optimal length depends on the applied voltage. Finally, it is shown that using multiple actuators are more effective than a single actuator in the cases of complicated loading.