Optimal placement of piezo actuators on a beam: a dynamic problem from stochastic to deterministic

In order to deal with uncertainties in optimization problems, this paper addresses a novel methodology which consists of the nonlinear interval number programming (NINP), particle swarm optimization (PSO) and finite element method (FEM). The placement of piezo actuators on a beam is optimized to obtain the dynamic maximum tip deflection when it is subjected to applied voltages varying in time by the use of the methodology; in the meantime, two constraints are considered, i.e. the deflection of midpoint of the beam should change in a specific range and the maximum bond shear stress should be below a specific value (interval number). To provide a valuable guide to designers, the influence degree of every stochastic parameter is studied, e.g. the dielectric permittivity and thickness of patches. In the optimization process, all stochastic parameters are eliminated through a NINP theory, and so a determined design result is finally obtained.