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Simultaneous optimization of piezoelectric actuator topology and polarization

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Abstract

This article addresses the problem of piezoelectric actuator design for active structural vibration control. The topology optimization method using the Piezoelectric Material with Penalization and Polarization (PEMAP-P) model is employed in this work to find the optimum actuator layout and polarization profile simultaneously. A coupled finite element model of the structure is derived assuming a two-phase material, and this structural model is written into the state-space representation. The proposed optimization formulation aims to determine the distribution of piezoelectric material which maximizes the controllability for a given vibration mode. The optimization of the layout and poling direction of embedded in-plane piezoelectric actuators are carried out using a Sequential Linear Programming (SLP) algorithm. Numerical examples are presented considering the control of the bending vibration modes for a cantilever and a fixed beam. A Linear-Quadratic Regulator (LQR) is synthesized for each case of controlled structure in order to compare the influence of the polarization profile.

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Acknowledgments

The authors acknowledge the financial support of the Brazilian agencies CNPq and CAPES.

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Authors and Affiliations

  1. Laboratory of Mechatronics and Control (LAMECC), Department of Mechanical Engineering, Federal University of Rio Grande do Sul, Sarmento Leite, 425, 90050-170, Porto Alegre, RS, Brazil

    Juliano F. Gonçalves & Eduardo A. Perondi

  2. Applied Mechanics Group (GMAp), Department of Mechanical Engineering, Federal University of Rio Grande do Sul, Sarmento Leite, 425, 90050-170, Porto Alegre, RS, Brazil

    Daniel M. De Leon

Authors
  1. Juliano F. Gonçalves
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  2. Daniel M. De Leon
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  3. Eduardo A. Perondi
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Correspondence to Juliano F. Gonçalves.

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Responsible Editor: Seonho Cho

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Gonçalves, J.F., De Leon, D.M. & Perondi, E.A. Simultaneous optimization of piezoelectric actuator topology and polarization. Struct Multidisc Optim 58, 1139–1154 (2018). https://doi.org/10.1007/s00158-018-1957-8

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  • DOI: https://doi.org/10.1007/s00158-018-1957-8

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