Topology optimization of piezoelectric bi-material actuators with velocity feedback control

doi:10.1007/s11465-019-0537-y

Frontiers of Mechanical Engineering

2019, Vol. 14

Issue (2): 190-200 https://doi.org/10.1007/s11465-019-0537-y

本期目录

Topology optimization of piezoelectric bi-material actuators with velocity feedback control

Mariana MORETTI, Emílio C. N. SILVA(

)

School of Engineering, University of São Paulo, São Paulo, SP 05508-030, Brazil

全文: PDF(1515 KB) HTML

Abstract：

In recent years, the new technologies and discoveries on manufacturing materials have encouraged researchers to investigate the appearance of material properties that are not naturally available. Materials featuring a specific stiffness, or structures that combine non-structural and structural functions are applied in the aerospace, electronics and medical industry fields. Particularly, structures designed for dynamic actuation with reduced vibration response are the focus of this work. The bi-material and multifunctional concepts are considered for the design of a controlled piezoelectric actuator with vibration suppression by means of the topology optimization method (TOM). The bi-material piezoelectric actuator (BPEA) has its metallic host layer designed by the TOM, which defines the structural function, and the electric function is given by two piezo-ceramic layers that act as a sensor and an actuator coupled with a constant gain active velocity feedback control (AVFC). The AVFC, provided by the piezoelectric layers, affects the structural damping of the system through the velocity state variables readings in time domain. The dynamic equation analyzed throughout the optimization procedure is fully elaborated and implemented. The dynamic response for the rectangular four-noded finite element analysis is obtained by the Newmark’s time-integration method, which is applied to the physical and the adjoint systems, given that the adjoint formulation is needed for the sensitivity analysis. A gradient-based optimization method is applied to minimize the displacement energy output measured at a predefined degree-of-freedom of the BPEA when a transient mechanical load is applied. Results are obtained for different control gain values to evaluate their influence on the final topology.

Key words： topology optimization method bi-material piezoactuator active velocity feedback control time-domain transient analysis host structure design vibration suppression

收稿日期: 2018-10-09 出版日期: 2019-04-22

Corresponding Author(s): Emílio C. N. SILVA

引用本文:

. [J]. Frontiers of Mechanical Engineering, 2019, 14(2): 190-200.
Mariana MORETTI, Emílio C. N. SILVA. Topology optimization of piezoelectric bi-material actuators with velocity feedback control. Front. Mech. Eng., 2019, 14(2): 190-200.

链接本文:

https://academic.hep.com.cn/fme/CN/10.1007/s11465-019-0537-y
https://academic.hep.com.cn/fme/CN/Y2019/V14/I2/190

Fig.1

Fig.2

Fig.3

Parameter	Symbol	Value	Unit
Domain size (width, heigh, depth)	$(w d, h d, d d)$	(20,4,0.2)	cm
Substrate size (width, heigh, depth)	$(w s, h s, d s)$	(20,2.67,0.2)	cm
Piezoceramic size (width, heigh, depth)	$(w p, h p, d p)$	(20,0.67,0.2)	cm
Substrate mesh size	( $x s$ , $y s$ )	(120,16)	?
Piezo ceramic mesh size	( $x p$ , $y p$ )	(120,4)	?
Mechanical load amplitude	$‖ F ‖$	1	N
Initial material volume	$V ini$	30%	?
Material volume constraint	$V max$	70%	?
Proportional damping	(α,β)	(0,1×10^?⁵)	?

Tab.1

Material	$E$ /GPa	$ζ$ /(kg?m⁻³)	$ν$
Fictitious (mat1)	300	1	0.24
Alumina (mat2)	392	4000	0.24

Tab.2

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

K				Post-processed
K	$f (ρ)$	$V mat1$	$ω n 1$ /Hz	$f (ρ)$	$V mat1$	$ω n 1$ /Hz
0.00	3.6508×10⁻¹⁵	60.02%	1217.7312	3.6638×10⁻¹⁵	53.96%	1220.31
9.00×10⁴	3.4135×10⁻¹⁵	60.95%	1217.7312	3.4270×10⁻¹⁵	55.05%	1222.25
3.60×10⁵	3.0654×10⁻¹⁵	60.17%	1214.3580	3.0773×10⁻¹⁵	54.01%	1218.80
7.20×10⁵	2.8837×10⁻¹⁵	58.15%	1214.3580	2.8947×10⁻¹⁵	51.67%	1210.43

Tab.3

Fig.9

Fig.10

Fig.11

1	J SOu, N Kikuchi. Integrated optimal structural and vibration control design. Structural Optimization, 1996, 12(4): 209–216 https://doi.org/10.1007/BF01197358
2	R FGibson. A review of recent research on mechanics of multifunctional composite materials and structures. Composite Structures, 2010, 92(12): 2793–2810 https://doi.org/10.1016/j.compstruct.2010.05.003
3	XYang, Y Li. Topology optimization to minimize the dynamic compliance of a bi-material plate in a thermal environment. Structural and Multidisciplinary Optimization, 2013, 47(3): 399–408 https://doi.org/10.1007/s00158-012-0831-3
4	XZhang, Z Kang. Topology optimization of piezoelectric layers in plates with active vibration control. Journal of Intelligent Material Systems and Structures, 2014, 25(6): 697–712 https://doi.org/10.1177/1045389X13500577
5	J FGonçalves, D MDe Leon, E APerondi. Topology optimization of embedded piezoelectric actuators considering control spillover effects. Journal of Sound and Vibration, 2017, 388: 20–41 https://doi.org/10.1016/j.jsv.2016.11.001
6	XZhang, Z Kang, MLi. Topology optimization of electrode coverage of piezoelectric thin-walled structures with CGVF control for minimizing sound radiation. Structural and Multidisciplinary Optimization, 2014, 50(5): 799–814 https://doi.org/10.1007/s00158-014-1082-2
7	JZhao, C Wang. Dynamic response topology optimization in the time domain using model reduction method. Structural and Multidisciplinary Optimization, 2016, 53(1): 101–114 https://doi.org/10.1007/s00158-015-1328-7
8	XZhang, Z Kang. Dynamic topology optimization of piezoelectric structures with active control for reducing transient response. Computer Methods in Applied Mechanics and Engineering, 2014, 281: 200–219 https://doi.org/10.1016/j.cma.2014.08.011
9	ATakezawa, K Makihara, NKogiso, et al. Layout optimization methodology of piezoelectric transducers in energy-recycling semi-active vibration control systems. Journal of Sound and Vibration, 2014, 333(2): 327–344 https://doi.org/10.1016/j.jsv.2013.09.017
10	HTzou, C Tseng. Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: A piezoelectric finite element approach. Journal of Sound and Vibration, 1990, 138(1): 17–34 https://doi.org/10.1016/0022-460X(90)90701-Z
11	SWang, S Quek, KAng. Vibration control of smart piezoelectric composite plates. Smart Materials and Structures, 2001, 10(4): 637–644 https://doi.org/10.1088/0964-1726/10/4/306
12	GCaruso, S Galeani, LMenini. Active vibration control of an elastic plate using multiple piezoelectric sensors and actuators. Simulation Modelling Practice and Theory, 2003, 11(5‒6): 403–419 https://doi.org/10.1016/S1569-190X(03)00056-X
13	MRay, J Reddy. Optimal control of thin circular cylindrical laminated composite shells using active constrained layer damping treatment. Smart Materials and Structures, 2004, 13(1): 64–72 https://doi.org/10.1088/0964-1726/13/1/008
14	C M AVasques, JDias Rodrigues. Active vibration control of smart piezoelectric beams: Comparison of classical and optimal feedback control strategies. Computers & Structures, 2006, 84(22‒23): 1402–1414 https://doi.org/10.1016/j.compstruc.2006.01.026
15	S MKim, S Wang, M JBrennan. Comparison of negative and positive position feedback control of a exible structure. Smart Materials and Structures, 2011, 20(1): 015011 https://doi.org/10.1088/0964-1726/20/1/015011
16	S BChoi, H S Kim, J S Park. Multi-mode vibration reduction of a CD-ROM drive base using a piezoelectric shunt circuit. Journal of Sound and Vibration, 2007, 300(1–2): 160–175 https://doi.org/10.1016/j.jsv.2006.07.041
17	K WChan, W H Liao. Precision positioning of hard disk drives using piezoelectric actuators with passive damping. In: Proceedings of 2006 IEEE International Conference on Mechatronics and Automation. Luoyang: IEEE, 2006, 1269–1274 https://doi.org/10.1109/ICMA.2006.257809
18	SZhang, R Schmidt, XQin. Active vibration control of piezoelectric bonded smart structures using PID algorithm. Chinese Journal of Aeronautics, 2015, 28(1): 305–313 https://doi.org/10.1016/j.cja.2014.12.005
19	T EBruns, D A Tortorelli. Topology optimization of non-linear elastic structures and compliant mechanisms. Computer Methods in Applied Mechanics and Engineering, 2001, 190(26–27): 3443–3459 https://doi.org/10.1016/S0045-7825(00)00278-4
20	J SJensen, P B Nakshatrala, D A Tortorelli. On the consistency of adjoint sensitivity analysis for structural optimization of linear dynamic problems. Structural and Multidisciplinary Optimization, 2014, 49(5): 831–837 https://doi.org/10.1007/s00158-013-1024-4
21	M AMoetakef, K L Lawrence, S P Joshi, et al.Closed-form expressions for higher order electroelastic tetrahedral elements. AIAA Journal, 1995, 33(1): 136–142 https://doi.org/10.2514/3.12343
22	J NReddy. An Introduction to the Finite Element Method. Vol. 2. New York: McGraw-Hill, 1993
23	XDong, L Ye, ZPeng, et al.A study on controller structure interaction of piezoelectric smart structures based on finite element method. Journal of Intelligent Material Systems and Structures, 2014, 25(12): 1401–1413 https://doi.org/10.1177/1045389X13507353
24	DTcherniak. Topology optimization of resonating structures using simp method. International Journal for Numerical Methods in Engineering, 2002, 54(11): 1605–1622 https://doi.org/10.1002/nme.484
25	JZhao, C Wang. Topology optimization for minimizing the maximum dynamic response in the time domain using aggregation functional method. Computers & Structures, 2017, 190: 41–60 https://doi.org/10.1016/j.compstruc.2017.05.002
26	GRozvany. Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics. Structural and Multidisciplinary Optimization, 2001, 21(2): 90–108 https://doi.org/10.1007/s001580050174
27	M PBendsøe, OSigmund. Topology optimization: Theory, Methods and Applications. Berlin: Springer, 2003
28	SZargham, T A Ward, R Ramli, et al.Topology optimization: A review for structural designs under vibration problems. Structural and Multidisciplinary Optimization, 2016, 53(6): 1157–1177 https://doi.org/10.1007/s00158-015-1370-5
29	G IRozvany. A critical review of established methods of structural topology optimization. Structural and Multidisciplinary Optimization, 2009, 37(3): 217–237 https://doi.org/10.1007/s00158-007-0217-0
30	LYin, G Ananthasuresh. Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme. Structural and Multidisciplinary Optimization, 2001, 23(1): 49–62 https://doi.org/10.1007/s00158-001-0165-z
31	VBalamurugan, S Narayanan. A piezolaminated composite degenerated shell finite element for active control of structures with distributed piezosensors and actuators. Smart Materials and Structures, 2008, 17(3): 035031 https://doi.org/10.1088/0964-1726/17/3/035031

Viewed

Full text

Abstract

Cited

Shared

Discussed