Abstract
A topology optimization method is proposed for the design of piezocomposite resonator with the aim of maximizing excitation strength and synthesizing desired eigenmodes. The objective function consists of maximizing the electromechanical coupling strength at the mode of interest. The topology layout of a structure with desired eigenmodes is obtained by adding the modal assurance criterion as additional constraint in the topology optimization model. Numerical examples are presented and the results illustrate that aside from maximizing the electromechanical coupling strength, the existing eigenmode of the piezocomposite resonator can be modified to be the desired one at the mode of interest.
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References
E.C.N. Silva, N. Kikuchi, Design of piezoelectric transducers using topology optimization, Smart Mater. Struct. 8 (1999) 350–364.
S.W. Or, H.L.W. Chan, P.C.K. Liu, Piezocomposite ultrasonic transducer for high-frequency wire-bonding of microelectronics devices, Sensors Actuator A Phys. 133 (2007) 195–199.
V. Ruiz-Díez, T. Manzaneque, J. Hernando-García, A. Ababneh, M. Kucera, U. Schmid, et al., Design and characterization of AIN-based in-plane microplate resonators, J. Micromech. Microeng. 23 (2013) 074003.
J.L. Sanchez-Rojas, J. Hernando, A. Donoso, J.C. Bellido, T. Manzaneque, A. Ababneh, et al., Modal optimization and filtering in piezoelectric microplate resonators, J. Micromech. Microeng 20 (2010) 055027.
Y. Ha, S. Cho, Design sensitivity analysis and topology optimization of eigenvalue problems for piezoelectric resonators, Smart Mater. Struct. 15 (2006) 1513.
E.C.N. Silva, J.S. Ono Fonseca, F.M. de Espinosa, A.T. Crumm, G.A. Brady, J.W. Halloran, et al., Design of piezocomposite materials and piezoelectric transducers using topology optimization – Part I, Arch. Comput. Method E. 6 (1999) 117–182.
M.P. Bendsøe, N. Kikuchi, Generating optimal topologies in structural design using a homogenization method, Comput. Methods Appl. Mech. Eng. 71 (1988) 197–224.
M.P. Bendsøe, Optimal shape design as a material distribution problem, Struct. Optim. 1 (1989) 193–202.
Y.M. Xie, G.P. Steven, A simple evolutionary procedure for structural optimization, Comput. Struct. 49 (1993) 885–896.
M.Y. Wang, X. Wang, D. Guo, A level set method for structural topology optimization, Comput. Methods Appl. Mech. Eng. 192 (2003) 227–246.
X. Guo, W. Zhang, J. Zhang, J. Yuan, Explicit structural topology optimization based on moving morphable components (MMC) with curved skeletons, Comput. Methods Appl. Mech. Eng. 310 (2016) 711–748.
X. Guo, W. Zhang, W. Zhong, Doing topology optimization explicitly and geometrically – a new moving morphable components based framework, J. Appl. Mech. 81 (2014) 081009.
W. Zhang, W. Yang, J. Zhou, D. Li, X. Guo, Structural topology optimization through explicit boundary evolution, J. Appl. Mech. 84 (2016) 011011.
W. Zhang, J. Yuan, J. Zhang, X. Guo, A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model, Struct. Multidisc. Optim. 53 (2016) 1243–1260.
J. Deaton, R. Grandhi, A survey of structural and multidisciplinary continuum topology optimization: post 2000, Struct. Multidisc. Optim. 49 (2014) 1–38.
M. Kögl, E.C.N. Silva, Topology optimization of smart structures: design of piezoelectric plate and shell actuators, Smart Mater. Struct. 14 (2005) 387–399.
F. Wein, M. Kaltenbacher, E. Bänsch, G. Leugering, F. Schury, Topology optimization of a piezoelectric-mechanical actuator with single- and multiple-frequency excitation, Int. J. Appl. Electromagn. Mech. 30 (2009) 201–221.
X. Zhang, Z. Kang, Dynamic topology optimization of piezoelectric structures with active control for reducing transient response, Comput. Methods Appl. Mech. and Eng. 281 (2014) 200–219.
B. Zheng, C.J. Chang, H. Gea, Topology optimization of energy harvesting devices using piezoelectric materials, Struct. Multidisc. Optim. 38 (2009) 17–23.
S. Chen, S. Gonella, W. Chen, W.K. Liu, A level set approach for optimal design of smart energy harvesters, Comput. Methods Appl. Mech. Eng. 199 (2010) 2532–2543.
C.J. Rupp, A. Evgrafov, K. Maute, M.L. Dunn, Design of piezoelectric energy harvesting systems: a topology optimization approach based on multilayer plates and shells, J. Intell. Mater. Syst. Struct. 20 (2009) 1923–1939.
Z.Q. Lin, H. Gea, S.T. Liu, Design of piezoelectric energy harvesting devices subjected to broadband random vibrations by applying topology optimization, Acta Mech. Sinica 27 (2011) 730–737.
P.H. Nakasone, E.C.N. Silva, Dynamic design of piezoelectric laminated sensors and actuators using topology optimization, J. Intell. Mater. Syst. Struct. 21 (2010) 1627–1652.
W.M. Rubio, H.P. Glaucio, S. Emilio Carlos Nelli, Tailoring vibration mode shapes using topology optimization and functionally graded material concepts, Smart Mater. Struct. 20 (2011) 025009.
R. Lerch, Simulation of piezoelectric devices by two- and three-dimensional finite elements, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37 (1990) 233–247.
Z. Kang, L. Tong, Topology optimization-based distribution design of actuation voltage in static shape control of plates, Comput. Struct. 86 (2008) 1885–1893.
Z. Kang, L. Tong, Integrated optimization of material layout and control voltage for piezoelectric laminated plates, J. Intell. Mater. Syst. Struct. 19 (2008) 889–904.
J. Zelenka, Piezoelectric Resonators and Their Applications, Elsevier Science Publishers B. V., 1986.
D. Ewins, Modal Testing: Theory, Practice and Application, second ed., Research Studies Press Ltd, England, 2000.
R.L. Fox, M.P. Kapoor, Rates of change of eigenvalues and eigenvectors, AIAA J. 6 (1968) 2426–2429.
R.B. Nelson, Simplified calculation of eigenvector derivatives, AIAA J. 14 (1976) 1201–1205.
I.W. Lee, G.H. Jung, An efficient algebraic method for the computation of natural frequency and mode shape sensitivities – Part I. Distinct natural frequencies, Comput. Struct. 62 (1997) 429–435.
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Project supported by the Shenzhen Basic Research Program (JCYJ20170307141601162) and the National Natural Science Foundation of China (11601347, 11402011).
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Wang, X., Lin, Z. & Ren, Y. Topology optimization of piezocomposite resonator for maximizing excitation strength and synthesizing desired eigenmodes. Acta Mech. Solida Sin. 30, 531–539 (2017). https://doi.org/10.1016/j.camss.2017.10.001
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DOI: https://doi.org/10.1016/j.camss.2017.10.001