A controllability-based formulation for the topology optimization of smart structures

Juliano F. Gonçalves , Jun S.O. Fonseca , Otávio A.A. Silveira

Abstract

This work presents a methodology to distribute piezoelectric material for structural vibration active control. The objective is to design controlled structures with actuators which maximizes the system controllability. A topology optimization was formulated in order to distribute two material phases in the domain: a passive linear elastic material and an active linear piezoelectric material. The objective is the maximization of the smallest eigenvalue of the system controllability Gramian. Analytical sensitivities for the finite element model are derived for the objective functions and constraints. Results and comparisons with previous works are presented for the vibration control of a two-dimensional short beam.

Key Words

piezoelectric actuators; controllability Gramian; topology optimization

Address

Juliano F. Gonçalves and Jun S.O. Fonseca — Department of Mechanical Engineering, Federal University of Rio Grande do Sul, R: Sarmento Leite 425, CEP 90050-170, Porto Alegre, Brazil
Otávio A.A. Silveira — Department of Civil Engineering, Federal University of Santa Catarina, R: João Pio Duarte da Silva 205, CEP 88040-970, Florianópolis, Brazil

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