A velocity field level set method for topology optimization of piezoelectric layer on the plate with active vibration control

References

• R. Alkhatib, and M.F. Golnaraghi, Active structural vibration control: A review, Shock Vib. Dig., vol. 35, no. 5, pp. 367–383, 2003. DOI: 10.1177/05831024030355002.
   Google Scholar
• R. Stanway, J.L. Sproston, and A.K. El-Wahed, Applications of electro-rheological fluids in vibration control: a survey, Smart Mater. Struct., vol. 5, no. 4, pp. 464–482, 1996. DOI: 10.1088/0964-1726/5/4/011.
   Web of Science ®Google Scholar
• M.A. Karkoub, and M. Zribi, Active/semi-active suspension control using magnetorheological actuators, Int. J. Syst. Sci., vol. 37, no. 1, pp. 35–44, 2006. DOI: 10.1080/00207720500436344.
   Web of Science ®Google Scholar
• C.-C. Lan, and C.-H. Fan, An accurate self-sensing method for the control of shape memory alloy actuated flexures, Sens. Actuators A Phys., vol. 163, no. 1, pp. 323–332, 2010. DOI: 10.1016/j.sna.2010.07.018.
   Web of Science ®Google Scholar
• S.O. Moheimani, and A.J. Fleming, Piezoelectric Transducers for Vibration Control and Damping, Springer-Verlag, London, 2006. DOI: 10.1007/1-84628-332-9.
   Google Scholar
• J.A.B. Gripp, and D.A. Rade, Vibration and noise control using shunted piezoelectric transducers: A review, Mech. Syst. Signal Process., vol. 112, pp. 359–383, 2018. DOI: 10.1016/j.ymssp.2018.04.041.
   Web of Science ®Google Scholar
• J. Onoda, and R.T. Haftka, An approach to structure/control simultaneous optimization for largeflexible spacecraft, Aiaa J., vol. 25, no. 8, pp. 1133–1138, 1987. DOI: 10.2514/3.9754.
   Google Scholar
• S. Devasia, T. Meressi, B. Paden, and E. Bayo, Piezoelectric actuator design for vibration suppression - placement and sizing, J. Guid. Control. Dyn., vol. 16, no. 5, pp. 859–864, 1993. DOI: 10.2514/3.21093.
   Web of Science ®Google Scholar
• D. Sun, and L. Tong, Design optimization of piezoelectric actuator patterns for static shape control of smart plates, Smart Mater. Struct., vol. 14, no. 6, pp. 1353–1362, 2005. DOI: 10.1088/0964-1726/14/6/027.
   Web of Science ®Google Scholar
• S.Y. Wang, K. Tai, and S.T. Quek, Topology optimization of piezoelectric sensors/actuators for torsional vibration control of composite plates, Smart Mater. Struct., vol. 15, no. 2, pp. 253–269, 2006. DOI: 10.1088/0964-1726/15/2/004.
   Web of Science ®Google Scholar
• I. Bruant, L. Gallimard, and S. Nikoukar, Optimal piezoelectric actuator and sensor location for active vibration control, using genetic algorithm, J. Sound Vib., vol. 329, no. 10, pp. 1615–1635, 2010. DOI: 10.1016/j.jsv.2009.12.001.
   Web of Science ®Google Scholar
• A. Takezawa, K. Makihara, N. Kogiso, and M. Kitamura, Layout optimization methodology of piezoelectric transducers in energy-recycling semi-active vibration control systems, J. Sound Vib., vol. 333, no. 2, pp. 327–344, 2014. DOI: 10.1016/j.jsv.2013.09.017.
   Web of Science ®Google Scholar
• G.I.N. Rozvany, M. Zhou, and T. Birker, Generalized shape optimization without homogenization, Struct. Optim., vol. 4, no. 3–4, pp. 250–252, 1992. DOI: 10.1007/BF01742754.
   Google Scholar
• M.P. Bendsøe, and O. Sigmund, Material interpolation schemes in topology optimization, Arch. Appl. Mech., vol. 69, no. 9–10, pp. 635–654, 1999. DOI: 10.1007/s004190050248.
   Web of Science ®Google Scholar
• Y.M. Xie, and G.P. Steven, A simple evolutionary procedure for structural optimization, Comput. Struct., vol. 49, no. 5, pp. 885–896, 1993. DOI: 10.10160/045-7949(93)90035-C.
   Web of Science ®Google Scholar
• L. Xia, Q. Xia, X. Huang, and Y.M. Xie, Bi-directional evolutionary structural optimization on advanced structures and materials: A comprehensive review, Arch. Comput. Methods Eng., vol. 25, pp. 437–478, 2018. DOI: 10.1007/s11831-016-9203-2.
   Google Scholar
• M.Y. Wang, X. Wang, and D. Guo, A level set method for structural topology optimization, Comput. Methods Appl. Mech. Eng., vol. 192, no. 1–2, pp. 227–246, 2003. DOI: 10.1016/S0045-7825(02)00559-5.
   Web of Science ®Google Scholar
• G. Allaire, F. Jouve, and A.M. Toader, Structural optimization using sensitivity analysis and a level-set method, J. Comput. Phys., vol. 194, no. 1, pp. 363–393, 2004. DOI: 10.1016/j.jcp.2003.09.032.
   Web of Science ®Google Scholar
• A. Takezawa, S. Nishiwaki, and M. Kitamura, Shape and topology optimization based on the phase field method and sensitivity analysis, J. Comput. Phys., vol. 229, no. 7, pp. 2697–2718, 2010. DOI: 10.1016/j.jcp.2009.12.017.
   Web of Science ®Google Scholar
• Y. Luo, and J. Bao, A material-field series-expansion method for topology optimization of continuum structures, Comput. Struct., vol. 225, pp. 106122, 2019. DOI: 10.1016/j.compstruc.2019.106122.
   Web of Science ®Google Scholar
• J. Du, and N. Olhoff, Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps, Struct. Multidisc. Optim., vol. 34, no. 2, pp. 91–110, 2007. DOI: 10.1007/s00158-007-0101-y.
   Web of Science ®Google Scholar
• S.Y. Kim, C.K. Mechefske, and I.Y. Kim, Optimal damping layout in a shell structure using topology optimization, J. Sound Vib., vol. 332, no. 12, pp. 2873–2883, 2013. DOI: 10.1016/j.jsv.2013.01.029.
   Web of Science ®Google Scholar
• H. Li, Z. Luo, M. Xiao, L. Gao, and J. Gao, A new multiscale topology optimization method for multiphase composite structures of frequency response with level sets, Comput. Methods Appl. Mech. Eng., vol. 356, pp. 116–144, 2019. DOI: 10.1016/j.cma.2019.07.020.
   Web of Science ®Google Scholar
• Z. Li, T. Shi, L. Xia, and Q. Xia, Maximizing the first eigenfrequency of structures subjected to uniform boundary erosion through the level set method, Eng. Comput., vol. 35, no. 1, pp. 21–33, 2019. DOI: 10.1007/s00366-018-0580-z.
   Web of Science ®Google Scholar
• J.-H. Zhu, T. Liu, W.-H. Zhang, Y.-L. Wang, and J.-T. Wang, Concurrent optimization of sandwich structures lattice core and viscoelastic layers for suppressing resonance response, Struct. Multidiscip. Optim., vol. 64, pp. 1801–1824, 2021. DOI: 10.1007/s00158-021-02943-x.
   Google Scholar
• E.C.N. Silva, and N. Kikuchi, Design of piezoelectric transducers using topology optimization, Smart Mater. Struct., vol. 8, no. 3, pp. 350–364, 1999. DOI: 10.1088/0964-1726/8/3/307.
   Google Scholar
• M. Kögl, and E.C.N. Silva, Topology optimization of smart structures: design of piezoelectric plate and shell actuators, Smart Mater. Struct., vol. 14, no. 2, pp. 387–399, 2005. DOI: 10.1088/0964-1726/14/2/013.
   Web of Science ®Google Scholar
• S. Zhang, R. Schmidt, and X. Qin, Active vibration control of piezoelectric bonded smart structures using PID algorithm, Chinese J. Aeronaut., vol. 28, no. 1, pp. 305–313, 2015. DOI: 10.1016/j.cja.2014.12.005.
   Web of Science ®Google Scholar
• D. Ruiz, A. Díaz-Molina, O. Sigmund, A. Donoso, J.C. Bellido, and J.L. Sánchez-Rojas, Optimal design of robust piezoelectric unimorph microgrippers, Appl. Math. Model., vol. 55, pp. 1–12, 2018. DOI: 10.1016/j.apm.2017.10.024.
   Web of Science ®Google Scholar
• M. He, X. Zhang, L. dos Santos Fernandez, A. Molter, L. Xia, and T. Shi, Multi-material topology optimization of piezoelectric composite structures for energy harvesting, Compos. Struct., vol. 265, pp. 113783, 2021. DOI: 10.1016/j.compstruct.2021.113783.
   Web of Science ®Google Scholar
• C.J. Rupp, A. Evgrafov, K. Maute, and M.L. Dunn, Design of piezoelectric energy harvesting systems: A topology optimization approach based on multilayer plates and shells, J. Intell. Mater. Syst. Struct., vol. 20, no. 16, pp. 1923–1939, 2009. DOI: 10.1177/1045389X09341200.
   Web of Science ®Google Scholar
• J.Y. Noh, and G.H. Yoon, Topology optimization of piezoelectric energy harvesting devices considering static and harmonic dynamic loads, Adv. Eng. Softw., vol. 53, pp. 45–60, 2012. DOI: 10.1016/j.advengsoft.2012.07.008.
   Web of Science ®Google Scholar
• J. Drenckhan, A. Lumsdaine, and M. Parsons, Topology Optimization of a Piezoelectric Actuator on an Elastic Beam, J. Intell. Mater. Syst. Struct., vol. 19, no. 4, pp. 445–455, 2008. DOI: 10.1177/1045389X06075522.
   Web of Science ®Google Scholar
• A. Donoso, and O. Sigmund, Optimization of piezoelectric bimorph actuators with active damping for static and dynamic loads, Struct. Multidisc. Optim., vol. 38, no. 2, pp. 171–183, 2009. DOI: 10.1007/s00158-008-0273-0.
   Web of Science ®Google Scholar
• L.A.M. Mello, A. Takezawa, and E.C.N. Silva, Designing piezoresistive plate-based sensors with distribution of piezoresistive material using topology optimization, Smart Mater. Struct., vol. 21, no. 8, pp. 085029, 2012. DOI: 10.1088/0964-1726/21/8/085029.
   Web of Science ®Google Scholar
• X. Zhang, and Z. Kang, Topology optimization of piezoelectric layers in plates with active vibration control, J. Intell. Mater. Syst. Struct., vol. 25, no. 6, pp. 697–712, 2014. DOI: 10.1177/1045389X13500577.
   Web of Science ®Google Scholar
• 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, pp. 200–219, 2014. DOI: 10.1016/j.cma.2014.08.011.
   Web of Science ®Google Scholar
• 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., vol. 29, no. 10, pp. 2277–2294, 2018. DOI: 10.1177/1045389X18758178.
   Web of Science ®Google Scholar
• D. Ruiz, J.C. Bellido, and A. Donoso, Design of piezoelectric modal filters by simultaneously optimizing the structure layout and the electrode profile, Struct. Multidisc. Optim., vol. 53, no. 4, pp. 715–730, 2016. DOI: 10.1007/s00158-015-1354-5.
   Web of Science ®Google Scholar
• D. Ruiz, and S. Horta Muñoz, Optimal design of electrode polarization in piezoelectric unimorph beams to induce traveling waves, Appl. Math. Model., vol. 99, pp. 1–13, 2021. DOI: 10.1016/j.apm.2021.06.007.
   Web of Science ®Google Scholar
• M. Moretti, E.C.N. Silva, and J.N. Reddy, Topology optimization of flextensional piezoelectric actuators with active control law, Smart Mater. Struct., vol. 28, no. 3, pp. 035015, 2019. DOI: 10.1088/1361-665X/aafd56.
   Web of Science ®Google Scholar
• M. Moretti, and E.C.N. Silva, Topology optimization of piezoelectric bi-material actuators with velocity feedback control, Front. Mech. Eng., vol. 14, no. 2, pp. 190–200, 2019. DOI: 10.1007/s11465-019-0537-y.
   Web of Science ®Google Scholar
• B. Niu, Y. Shan, and E. Lund, Discrete material optimization of vibrating composite plate and attached piezoelectric fiber composite patch, Struct. Multidisc. Optim., vol. 60, no. 5, pp. 1759–1782, 2019. DOI: 10.1007/s00158-019-02359-8.
   Web of Science ®Google Scholar
• J. Zhai, L. Shang, and G. Zhao, Topology optimization of piezoelectric curved shell structures with active control for reducing random vibration, Struct. Multidisc. Optim., vol. 61, no. 4, pp. 1439–1452, 2020. DOI: 10.1007/s00158-019-02423-3.
   Web of Science ®Google Scholar
• J.F. Gonçalves, D.M. De Leon, and E.A. Perondi, Topology optimization of embedded piezoelectric actuators considering control spillover effects, J. Sound Vib., vol. 388, pp. 20–41, 2017. DOI: 10.1016/j.jsv.2016.11.001.
   Web of Science ®Google Scholar
• D.G. Guzmán, E.C.N. Silva, and W.M. Rubio, Topology optimization of piezoelectric sensor and actuator layers for active vibration control, Smart Mater. Struct., vol. 29, no. 8, pp. 085009, 2020. DOI: 10.1088/1361-665X/ab9061.
   Web of Science ®Google Scholar
• Y. Liu, X. Wang, and Y. Li, Distributed piezoelectric actuator layout-design for active vibration control of thin-walled smart structures, Thin-Walled Struct., vol. 147, pp. 106530, 2020. DOI: 10.1016/j.tws.2019.106530.
   Web of Science ®Google Scholar
• H. Ding, and B. Xu, Material microstructure topology optimization of piezoelectric composite beam under initial disturbance for vibration suppression, J. Vib. Control., pp. 1-15 2021. DOI: 10.1177/1077546321993331.
   Google Scholar
• Z. Luo, A short survey: Topological shape optimization of structures using level set methods, J. Appl. Mech. Eng., vol. 02, pp. 123–128, 2013. DOI: 10.4172/2168-9873.1000123.
   Google Scholar
• N.P. Van Dijk, K. Maute, M. Langelaar, and F. Van Keulen, Level-set methods for structural topology optimization: A review, Struct. Multidisc. Optim., vol. 48, no. 3, pp. 437–472, 2013. DOI: 10.1007/s00158-013-0912-y.
   Web of Science ®Google Scholar
• Y. Wang, and Z. Kang, A velocity field level set method for shape and topology optimization, Int. J. Numer. Methods Eng., vol. 115, no. 11, pp. 1315–1336, 2018. DOI: 10.1002/nme.5845.
   Web of Science ®Google Scholar
• Y. Wang, Z. Kang, and P. Liu, Velocity field level‐set method for topological shape optimization using freely distributed design variables, Int. J. Numer. Methods Eng., vol. 120, no. 13, pp. 1411–1427, 2019. DOI: 10.1002/nme.6185.
   Web of Science ®Google Scholar
• S.Y. Wang, S.T. Quek, and K.K. Ang, Vibration control of smart piezoelectric composite plates, Smart Mater. Struct., vol. 10, no. 4, pp. 637–644, 2001. DOI: 10.1088/0964-1726/10/4/306.
   Web of Science ®Google Scholar
• H. Liu, W. Zhang, and T. Gao, A comparative study of dynamic analysis methods for structural topology optimization under harmonic force excitations, Struct. Multidisc. Optim., vol. 51, no. 6, pp. 1321–1333, 2015. DOI: 10.1007/s00158-014-1218-4.
   Web of Science ®Google Scholar
• K. Svanberg, The method of moving asymptotes-a new method for structural optimization, Int. J. Numer. Meth. Eng., vol. 24, no. 2, pp. 359–373, 1987. DOI: 10.1002/nme.1620240207.
   Web of Science ®Google Scholar
• K. Zhao, et al., Fabrication of piezoelectric thick-film stator using electrohydrodynamic jet printing for micro rotary ultrasonic motors, Ceram. Int., vol. 46, no. 16, pp. 26129–26135, 2020. DOI: 10.1016/j.ceramint.2020.07.108.
   Web of Science ®Google Scholar