Alves da Silveira, Otávio Augusto3; Ono Fonseca, Jun Sérgio4; Santos, Ilmar1
1 Department of Mechanical Engineering, Technical University of Denmark2 Solid Mechanics, Department of Mechanical Engineering, Technical University of Denmark3 Federal University of Santa Catarina4 Universidade Federal do Rio Grande do Sul
This work develops a methodology for the optimal design of actuators for the vibration control of flexible structures. The objective is the maximization of a measure of the controllability Gramian. The test case is the embedding of piezoelectric inserts in elastic structures for vibration control in modal space. A topology optimization was formulated to distribute two material phases in the domain: a passive linear elastic material and an active linear piezoelectric material, with a volume constraint in the latter. The objective function is the trace of the controllability Gramian of a LQR control system. Analytical sensitivities for the finite element model are derived for the objective function and constraints. Results are shown for two dimensional vibration control of a short beam with varying number of electrodes (control inputs) and vibration modes.
Structural and Multidisciplinary Optimization, 2015, Vol 51, p. 145-157
Actuator placement; Controllability Gramian; Topology optimization; Piezoelectric; Vibration control