Simultaneous Design of Structural Topology and Control for Vibration Reduction Using Piezoelectric Material

Abstract

This article presents a research on the optimal design of actively controlled structures, aiming to suppress vibrations induced by external disturbances. Design is conducted simultaneously for the structural topology and actuator locations. A topology optimization problem is formulated for three material phases (two solid materials and void) with two design variables groups. A nonpiezoelectric elastic isotropic material forms the structural only part of the design, while a piezoelectric material composes the active part. Since treating structural and control design variables in the same optimization framework is inconvenient, this work proposes a nested solution approach, where the actuator locations and controller syntheses are considered as sub processes included in the main optimization process dealing with the structural topology. The main optimization loop designs the structural variables, i.e., it is decided where there should be solid material and where there should be voids. The actuators are placed by an inner design loop within the structural problem, by a control law optimization that defines where the material should have piezoelectric properties. Numerical examples show that the approach used in this paper can produce a clear structural topology with a good actuators placement.