Optimal configuration of piezoelectric transducers for active control of mechanical vibrations using topological optimization method
DOI:
https://doi.org/10.33131/24222208.319Keywords:
Active vibration control, Piezoelectric material, Topological optimizationAbstract
The topological optimization method is used to find an optimal distribution of piezoelectric transducers (sensor and actuator) on an elastic structure from a finite element model in state space variables. With two objective functions in parallel, we aim to maximize the traces of both the observability and controllability Gramian. In the solution of the optimization problem, the SIMP material interpolation model and the Sequential Linear Programming (PLS) method are used; therefore, the sensitivity analysis of both objective functions is presented. Finally, an LQG controller is implemented to verify the structural performance obtained after the optimization process for a case study of a Cantilever beam subjected to vibration, equipped with an actuator and a piezoelectric sensor. The optimization results are verified with the energy analysis of the control effort, the sensitivity of the sensor, and the damping coefficient of the plant-controller system.
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References
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[2] A. Preumont and K. Seto, Active control of structures. John Wiley & Sons, 2008.
[3] D. J. Inman, Vibration with control. John Wiley & Sons, 2006.
[4] A. Preumont, Vibration Control of Active Structures, 3th ed., vol. 179. Bruxelles: Springer, 2011.
[5] S. O. R. Moheimani and A. J. Fleming, Piezoelectric transducers for vibration control and damping. Springer, 2006.
[6] A. Hać and L. Liu, “Sensor and actuator location in motion control of flexible structures,” J. Sound Vib., vol. 167, no. 2, pp. 239–261, 1993.
[7] R. Alkhatib and M. F. Golnaraghi, “Active structural vibration control: a review,” Shock Vib. Dig., vol. 35, no. 5, p. 367, 2003.
[8] K. Hiramoto, H. Doki, and G. Obinata, “Optimal Sensor/Actuator Placement for Active Vibration Control Using Explicit Solution of Algebraic Riccati Equation,” J. Sound Vib., vol. 229, no. 5, pp. 1057–1075, 2000.
[9] M. Güney and E. E\cskinat, “Optimal actuator and sensor placement in flexible structures using closed-loop criteria,” J. Sound Vib., vol. 312, no. 1–2, pp. 210–233, 2008.
[10] K. D. Dhuri and P. Seshu, “Multi-objective optimization of piezo actuator placement and sizing using genetic algorithm,” J. Sound Vib., vol. 323, no. 3–5, pp. 495–514, 2009.
[11] X. Zhang and Z. Kang, “Dynamic topology optimization of piezoelectric structures with active control for reducing transient response,” Comput. Methods Appl. Mech. Eng., vol. 281, no. 1, pp. 200–219, 2014.
[12] J. Hu, X. Zhang, and Z. Kang, “Layout design of piezoelectric patches in structural linear quadratic regulator optimal control using topology optimization,” J. Intell. Mater. Syst. Struct., p. 1045389X18758178, 2018.
[13] O. A. A. da Silveira, “Projeto simultâneo de otimização topológica e controle para redução de vibrações utilizando material piezelétrico,” Universidade Federal do Rio Grande do Sul, 2012.
[14] O. Menuzzi, J. S. O. Fonseca, E. A. Perondi, J. F. Gonçalves, E. Padoin, and O. A. A. Silveira, “Piezoelectric sensor location by the observability Gramian maximization using topology optimization,” Comput. Appl. Math., pp. 1–16, 2017.
[15] V. Piefort, “Finite Element Modelling of Piezoelectric Active Structures,” Université Libre de Bruxelles, 2001.
[16] A. Meitzler, H. F. Tiersten, A. W. Warner, D. Berlincourt, G. A. Couqin, and F. S. Welsh III, “IEEE standard on piezoelectricity.” Society, 1988.
[17] G. Nader, “Desenvolvimento de técnicas de caracterização de transdutores piezelétricos,” Universidade de São Paulo, 2002.
[18] D. E. Kirk, Optimal control theory: an introduction. Courier Corporation, 2012.
[19] H. A. Eschenauer and N. Olhoff, “Topology optimization of continuum structures: a review,” Appl. Mech. Rev., vol. 54, no. 4, pp. 331–390, 2001.
[20] W. Montealegre, “Projeto de" MEMS" eletrotermomecânicos usando o método de otimização topológica,” Universidade de São Paulo (USP). Escola Politécnica, 2005.
[21] M. P. Bendsøe and O. Sigmund, “Material interpolation schemes in topology optimization,” Arch. Appl. Mech., vol. 69, no. 9–10, pp. 635–654, 1999.
[22] J. K. Guest, J. H. Prévost, and T. Belytschko, “Achieving minimum length scale in topology optimization using nodal design variables and projection functions,” Int. J. Numer. Methods Eng., vol. 61, no. 2, pp. 238–254, 2004.
[23] D. Berrío, “Optimización topológica de un instrumento musical idiófono tipo metalófono,” Universidad Nacional de Colombia, 2017.
[24] S. Xu, Y. Cai, and G. Cheng, “Volume preserving nonlinear density filter based on heaviside functions,” Struct. Multidiscip. Optim., vol. 41, no. 4, pp. 495–505, 2010.
[25] S. S. Rao, Engineering optimization: theory and practice. John Wiley & Sons, 2009.
[26] R. T. Haftka and Z. Gürdal, Elements of structural optimization, vol. 11. Springer Science & Business Media, 2012.
[27] H. S. Tzou and C. I. Tseng, “Distributed vibration control and identification of coupled elastic/piezoelectric systems: finite element formulation and applications,” Mech. Syst. Signal Process., vol. 5, no. 3, pp. 215–231, 1991.
[28] V. Piefort, “Finite Element Modelling of Piezoelectric Active Structures,” Université Libre de Bruxelles, 2001.
[29] W. S. Hwang and H. C. Park, “Finite element modeling of piezoelectric sensors and actuators,” AIAA J., vol. 5, no. 31, pp. 930–937, 1993.
[30] Z. Lašová and R. Zemčík, “Comparison of finite element models for piezoelectric materials,” Procedia Eng., vol. 48, pp. 375–380, 2012.
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Published
2018-12-31
How to Cite
Giraldo, D., & Montealegre Rubio, W. (2018). Optimal configuration of piezoelectric transducers for active control of mechanical vibrations using topological optimization method. Revista CINTEX, 23(2), 86–94. https://doi.org/10.33131/24222208.319
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RESEARCH PAPERS
