This article investigates the modeling of macro fiber composite-actuated laminate plates with distributed actuator patches. The investigation details an analytical and finite element modeling, with experimental validation of the bending strain and deflection of an epoxy E-glass fiber composite laminate. An analytical approach is also developed to estimate the plate deflection from the experimental strain measurements. The analytical method uses direct integration of single dimensional plate bending moments obtained by strain-induced shear moments from the macro fiber composite actuators. Finite element analysis software was used with the composite laminate modeled in ANSYS ACP. The results from both analytical and numerical models show good agreement with the experimental results, with strain values agreeing within 20 ppm and the maximum difference in deflection not exceeding 0.1 mm between models. Finally, an application of the analytical model for developing morphing aerofoil designs is demonstrated.
ANSI/IEEE Std 176-1987 (1987) IEEE standard on piezoelectricity.
2.
BilgenO (2010) Aerodynamic and electromechanical design, modeling and implementation of piezocomposite airfoils. PhD Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA.
3.
BilgenOFriswellMI (2012) Piezoceramic composite actuators for a solid-state variable-camber wing. In: 23rd international conference on adaptive structures and technologies (ICAST2012), Nanjing, China, 11–13 October.
4.
BilgenOFriswellMI (2013) Implementation of a continuous-inextensible-surface piezocomposite airfoil. Journal of Aircraft50(4): 508–518.
5.
BilgenOKaramiMAInmanDJ, et al. (2011) The actuation characterization of cantilevered unimorph beams with single crystal piezoelectric materials. Smart Materials and Structures20: 1–9.
6.
BilgenOKochersbergerKBInmanDJ (2009) Macro-fiber composite actuators for a swept wing unmanned aircraft. The Aeronautical Journal113(1144): 385–395.
7.
BilgenOKochersbergerKBInmanDJ, et al. (2010) Novel, bidirectional, variable-camber airfoil via macro-fiber composite actuators. Journal of Aircraft47(1): 303–314.
8.
BowenCRButlerRJervisR, et al. (2006) Morphing and shape control using unsymmetrical composites. Journal of Intelligent Material Systems and Structures18(1): 89–98.
9.
BowenCRGiddingsPFSaloAIT, et al. (2011) Modeling and characterization of piezoelectrically actuated bistable composites. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control58(9): 1737–1750.
10.
BowenCRKimHASaloAIT (2014) Active composites based on bistable laminates. Procedia Engineering75: 140–144.
11.
BryantRG (2007) Overview of NASA Langley’s piezoelectric ceramic packaging technology and applications. In: 10th Japan international SAMPE symposium and exhibition, Tokyo, Japan, 27–30 November.
12.
BuMMelvinTEnsellG, et al. (2003) Design and theoretical evaluation of a novel microfluidic device to be used for PCR. Journal of Micromechanics and Microengineering13: S125–S130.
13.
ButlerSF (1973) Aircraft drag prediction for project appraisal and performance estimation (AGARD CP-124).
14.
CheeCYKTongLStevenGP (1998) A review on the modelling of piezoelectric sensors and actuators incorporated in intelligent structures. Journal of Intelligent Material Systems and Structures9(1): 3–19.
15.
CookTA (1971) The effects of ridge excrescences and trailing-edge control gaps on two dimensional aerofoil characteristics (ARC-RM-3698).
16.
CôtéFMassonPMradN, et al. (2004) Dynamic and static modelling of piezoelectric composite structures using a thermal analogy with MSC/NASTRAN. Composite Structures65(3–4): 4710–4484.
17.
CrawleyEAndersonE (1990) Detailed models of piezoceramic actuation of beams. Journal of Intelligent Material Systems and Structures1(1): 4–25.
18.
CrawleyEDeLuisJ (1987) Use of piezoelectric actuators as elements of intelligent structures. AIAA Journal25(10): 1373–1385.
19.
DebiasiMBouremelYLuZ, et al. (2013a) Deformation of the upper and lower surfaces of an airfoil by macro fiber composite actuators. In: 31st AIAA applied aerodynamics conference, San Diego, CA, 24–27 June.
20.
DebiasiMLeongCWBouremelY (2013b) Application of macro-fiber-composite materials on UAV wings. In: Proceedings of the aerospace technology seminar (ATS 2013), Singapore, March.
21.
DeraemaekerANasserH (2010) Numerical evaluation of the equivalent properties of macro fiber composite (MFC) transducers using periodic homogenization. International Journal of Solids and Structures47(24): 3272–3285.
22.
DeVoeDLPisanoAP (1997) Modeling and optimal design of piezoelectric cantilever microactuators. Journal of Microelectromechanical Systems6(3): 266–270.
23.
DwarakanathanDRamkumarRRajaS, et al. (2015) Design, development and ground testing of hingeless elevons for MAV using piezoelectric composite actuators. Advances in Aircraft and Spacecraft Science2(3): 303–328.
24.
FicheraSIsnardiIMottersheadJE (2019) High-bandwidth morphing actuator for aeroelastic model control. Aerospace6(2): 1–13.
25.
FreedBDBabuskaV (1997) Finite element modeling of composite piezoelectric structures with MSC/NASTRAN. In: Proceedings of the SPIE, smart structures and materials 1997: Smart structures and integrated systems, vol. 3041, San Diego, CA, 3–6 March.
26.
GaoXShihWHShihY (2009) Induced voltage of piezoelectric unimorph cantilevers of different nonpiezoelectric/piezoelectric length ratios. Smart Materials and Structures18: 125018.
GiddingsPBowenCRButlerR, et al. (2008) Characterisation of actuation properties of piezoelectric bi-stable carbon-fibre laminates. Composites Part A: Applied Science and Manufacturing39(4): 697–703.
29.
GustafsonEA (2011) Design, simulation, and wind tunnel verification of a morphing airfoil. MS Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA.
30.
IHS ESDU 92039 (1992) Drag due to gaps round undeflected trailing-edge controls and flaps at subsonic speeds.
31.
LaCroixBWIfjuPG (2012) Finite element modeling of macro fiber composite piezoelectric actuators on micro air vehicles. In: 53rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Honolulu, HI, 23–26 April.
32.
LaCroixBWIfjuPG (2015) Investigating potential substrates to maximize out-of-plane deflection of piezoelectric macro-fiber composite actuators. Journal of Intelligent Material Systems and Structures26(7): 781–795.
33.
LatalskiJ (2011) Modelling of MFC piezoelectric active elements in abaqus system. Eksploatacja I Niezawodnosc/Maintenance and Reliability4: 72–78.
34.
LeeAJMoosavianAInmanDJ (2017) Control and characterization of a bistable laminate generated with piezoelectricity. Smart Materials and Structures26(8): 085007.
35.
LiLXueZLiC (2016) A modified pin force model for beams with active material bonded. Materials and Design97: 249–256.
36.
LiXShihWYAksayIA, et al. (1999) Electromechanical behavior of PZT-brass unimorphs. Journal of American Ceramics Society82(7): 1733–1740.
37.
LloydJM (2004) Electrical properties of macro-fiber composite actuators and sensors. MS Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA.
38.
MaJLiuYHeT, et al. (2011) Double drive modes unimorph deformable mirror for low-cost adaptive optics. Applied Optics50(29): 5647–5654.
39.
MolinariGQuackMArrietaAF, et al. (2014) Design and realization of a compliant adaptable wing. In: ASME 2014 conference on smart materials, adaptive structures and intelligent systems: Volume 2: Mechanics and behavior of active materials; integrated system design and implementation; bioinspired smart materials and systems; energy harvesting, Newport, RI, 8–10 September.
40.
MolinariGQuackMArrietaAF, et al. (2015) Design, realization and structural testing of a compliant adaptable wing. Smart Materials and Structures24(10): 105027.
41.
NelsonLJBowenCRStevensR, et al. (2003) High-field behavior of piezoelectric fiber composites. In: Proceedings of the SPIE, smart structures and materials: Active materials: Behavior and mechanics, vol. 5053, San Diego, CA, 2–6 March.
42.
NguyenMHouwmanERijndersG (2017) Large piezoelectric strain with ultra-low strain hysteresis in highly c-axis oriented Pb(Zr0.52Ti0.48)O3 films with columnar growth on amorphous glass substrates. Scientific Reports7(1): 1–9.
43.
OhanianOJIIIDavidBTaylorSL, et al. (2013) Piezoelectric morphing versus servo-actuated MAV control surfaces, part II: flight testing. In: 51st AIAA aerosapce sciecnes meeting including the new horizons forum and aerospace exposition, Grapevine (Dallas/Ft. Worth Region), TX, 7–10 January, p. 2013-0767. Reston, VA: AIAA.
44.
OhanianOJIIIHicklingCStiltnerB, et al. (2012) Piezoelectric morphing versus servo-actuated MAV control surfaces. In: 53rd AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Honolulu, HI, 23–26 April.
45.
PandeyAArockiarajanA (2017) Fatigue study on the sensor performance of macro fiber composite (MFC): theoretical and experimental approach. Composite Structures174: 301–318.
46.
ParadiesRCiresaP (2009) Active wing design with integrated flight control using piezoelectric macro fiber composites. Smart Materials Structures18: 1–9.
47.
ParkJSKimJH (2007) Coefficients of thermal expansion for single crystal piezoelectric fiber composites. Composites Part B: Engineering38(7–8): 795–799.
48.
PortelaPCamanhoPWeaverP, et al. (2008) Analysis of morphing, multi stable structures actuated by piezoelectric patches. Computers & Structures86: 3–5:347–356.
49.
PrasathSSArockiarajanA (2013) Effective electromechanical response of macro-fiber composite (MFC): analytical and numerical models. International Journal of Mechanical Sciences77: 98–106.
50.
ProbstTA (2012) Evaluating the aerodynamic performance of MFC-actuated morphing wings to control a small UAV. PhD Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA.
51.
ReavesMCHortaLG (2001) Test cases for modeling and validation of structures with piezoelectric actuators. In: 42nd AIAA/ASME/ASCE/AHS/ASC structure and structural dynamics conference, Seattle, WA, 16–19 April.
52.
SchrockJMeurerTKugiA (2010) Control of a flexible beam actuated by macro-fiber composite patches: II: hysteresis and creep compensation, experimental results. Smart Materials and Structures20(1): 015016.
53.
SchultzMR (2003) Use of piezoelectric actuators to effect snap-through behaviour of unsymmetric composite laminates. PhD Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA.
54.
SchultzMRHyerMW (2004) A morphing concept based on unsymmetric composite laminates and piezoceramic MFC actuators. In: 45th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics & materials conference, Palm Springs, CA, 19–22 April.
55.
SenbaAIkedaTUedaT (2010) A two-way morphing actuation of bi-stable composites with piezoelectric fibers. In: 51st AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Orlando, FL, 12–15 April.
56.
SteigerKMokrýP (2015) Finite element analysis of the macro fiber composite actuator: macroscopic elastic and piezoelectric properties and active control thereof by means of negative capacitance shunt circuit. Smart Materials and Structures24: 025026.
57.
StoneyGG (1909) The tension of metallic films deposited by electrolysis. Proceedings of the Royal Society London Series A82: 172–175.
58.
StuebnerMSmithRCHaysM, et al. (2009) Modeling the nonlinear behavior of macro fiber composite actuators. In: Proceedings of the SPIE, behavior and mechanics of multifunctional materials and composites, vol. 7289, San Diego, CA, 8–12 March, pp. 728913–728918. Bellingham, WA: SPIE.
59.
TanDYavarowPErturkA (2017) Nonlinear structural dynamics of macro-fiber composite cantilevers for resonant actuation. In: ASME 2017 Conference on smart materials, adaptive structures and intelligent systems, volume 2: Modeling, simulation and control of adaptive systems; integrated system design and implementation, Snowbird, UT, 18–20 September.
60.
TanDYavarowPErturkA (2018) Nonlinear elastodynamics of piezoelectric macro-fiber composites with interdigitated electrodes for resonant actuation. Composite Structures187: 137–143.
61.
TawfikSAStefan DancilaDArmaniosE (2011) Unsymmetric composite laminates morphing via piezoelectric actuators. Composites Part A: Applied Science and Manufacturing42(7): 748–756.
62.
TimoshenkoS (1925) Analysis of bi-metal thermostats. Journal of the Optical Society of America11: 233–255.
63.
TimoshenkoSWoinowsky-KreigerS (1959) Theory of Plates and Shells. New York: McGraw Hill.
64.
WeinbergM (1999) Working equations for piezoelectric actuators and sensors. Journal of Microelectromechanical Systems8(4): 529–533.
65.
WilkieWInmanDHighJ, et al. (2004) Recent developments in NASA piezocomposite actuator technology. In: 9th international conference on new actuators, Bremen, 14–16 June.
66.
WilliamsBRParkGInmanDJ, et al. (2002) An overview of composite actuators with piezoceramic fibers. In: Proceedings of 20th international modal analysis conference, vol. 4753, Los Angeles, CA, 4–7 February, pp. 421–427. Bethel, CT: Society for Experimental Mechanics.
67.
WilliamsRB (2004) Nonlinear mechanical and actuation characterization of piezoceramic fiber composites. PhD Thesis, Virginia Polytechnic Institute and State University, Blacksburg, VA.
68.
WilliamsRBInmanDJWilkieWK (2006) Nonlinear response of the macro fiber composite actuator to monotonically increasing excitation voltage. Journal of Intelligent Material Systems and Structures17(7): 601–608.
69.
WilliamsRBSchultzMRHyerMW, et al. (2004) Nonlinear tensile and shear behavior of macro fiber composite actuators. Journal of Composite Materials38(10): 855–869.
70.
XuXLiBFengY, et al. (2007) Design, fabrication and characterization of a bulk-PZT-actuated MEMS deformable mirror. Journal of Micromechanics and Microengineering17: 2439–2446.
71.
ZhangSQLiYXSchmidtR (2015) Modeling and simulation of macro-fiber composite layered smart structures. Composite Structures126: 89–100.
72.
ZhengXLinLIchchouMN, et al. (2017) Hysteresis and the nonlinear equivalent piezoelectric coefficient of MFCs for actuation. Chinese Journal of Aeronautics30(1): 88–98.
