Aeroelastic Modeling of Smart Composite Wings Using Geometric Stiffness
Publication: Journal of Aerospace Engineering
Volume 32, Issue 2
Abstract
This paper presents a novel model for the aeroelastic analysis of composite wings with attached piezoelectric actuators, using the concept of geometric stiffness. The mathematical model is introduced and validated against numerical and experimental results, and good agreement is obtained. It is consequently used to investigate the effect of piezoelectric forces on the aeroelastic behavior of composite wings. In the present analyses, the piezoelectric effect is studied for a voltage range from 0 to 100 V. Two wing configurations are considered: one with the piezoelectric sheets attached at the wing root (root configuration), and the second with the piezoelectric patches distributed along the wing span (staggered configuration). The present numerical examples show that both piezoelectric configurations significantly increase the divergence and flutter speeds, and hence improve the aeroelastic stability of composite wings. In general, the piezoelectric effect is more significant in the staggered configuration. In case of a straight wing, for instance, the divergence speed increases by 26.9%, and the flutter speed increases by 34.3% because of the change of the flutter mode. The staggered configuration is more effective than the root configuration for all other cases. It is concluded that the way piezoelectric patches are distributed on the wing and the magnitude of the applied voltage can considerably improve aeroelastic performance of the wings.
Get full access to this article
View all available purchase options and get full access to this article.
References
Albano, E., and P. Rodden. 1969. “A doublet-lattice method for calculating lift distributions on oscillating surfaces in subsonic flows.” AIAA J. 7 (2): 279–285. https://doi.org/10.2514/3.55530.
Balakrishnan, A. 2012. Aeroelasticity. New York: Springer.
Balamurugan, V., and S. Narayanan. 2001. “Shell finite element for smart piezoelectric composite plate/shell structures and its application to the study of active vibration control.” Finite Elements Anal. Des. 37 (9): 713–738. https://doi.org/10.1016/S0168-874X(00)00070-6.
Beheshti-Aval, S. B., and M. Lezgy-Nazargah. 2010. “A finite element model for composite beams with piezoelectric layers using a sinus model.” J. Mech. 26 (3): 335–344. https://doi.org/10.1017/S1727719100003890.
Bisplinghoff, R. L., H. Ashley, and R. L. Halfman. 1996. Aeroelasticity. Mineola, NY: Courier.
Cinefra, M., E. Carrera, and S. Valvano. 2015. “Variable kinematic shell elements for the analysis of electro-mechanical problems.” Mech. Adv. Mater. Struct. 22 (1–2): 77–106. https://doi.org/10.1080/15376494.2014.908042.
Cook, A. C., and S. S. Vel. 2012. “Multiscale analysis of laminated plates with integrated piezoelectric fiber composite actuators.” Compos. Struct. 94 (2): 322–336. https://doi.org/10.1016/j.compstruct.2011.06.027.
Correia, V. M. F., M. A. A. Gomes, A. Suleman, C. M. M. Soares, and C. A. M. Soares. 2000. “Modelling and design of adaptive composite structures.” Comput. Methods Appl. Mech. Eng. 185 (2–4): 325–346. https://doi.org/10.1016/S0045-7825(99)00265-0.
Correia, V. M. F., J. F. A. Madeira, A. L. Araújo, and C. M. M. Soares. 2017. “Multiobjective design optimization of laminated composite plates with piezoelectric layers.” Compos. Struct. 169 (1): 10–20. https://doi.org/10.1016/j.compstruct.2016.09.052.
Crawley, E. F., and J. De Luis. 1987. “Use of piezoelectric actuators as elements of intelligent structures.” AIAA J. 25 (10): 1373–1385. https://doi.org/10.2514/3.9792.
de Abreu, G., J. F. Ribeiro, and V. Steffen Jr. 2004. “Finite element modeling of a plate with localized piezoelectric sensors and actuators.” J. Braz. Soc. Mech. Sci. Eng. 26 (2): 117–128. https://doi.org/10.1590/S1678-58782004000200002.
de Medeiros, R., R. Rodriguez-Ramos, R. Guinovart-Diaz, J. Bravo-Castillero, J. A. Otero, and V. Tita. 2015. “Numerical and analytical analyses for active fiber composite piezoelectric composite materials.” J. Intell. Mater. Syst. Struct. 26 (1): 101–118. https://doi.org/10.1177/1045389X14521881.
Donadon, M. V., S. F. M. Almeida, and A. R. de Faria. 2002. “Stiffening effects on the natural frequencies of laminated plates with piezoelectric actuators.” Compos. Part B: Eng. 33 (5): 335–342. https://doi.org/10.1016/S1359-8368(02)00026-4.
Dowell, E. H. 2015. Vol. 217 of A modern course in aeroelasticity: Solid mechanics and its applications. Cham, Switzerland: Springer.
Fung, Y. C. 2002. An introduction to the theory of aeroelasticity. Mineola, NY: Courier.
Gupta, V. K., P. Seshu, and K. K. Issac. 2004. “Finite element and experimental investigation of piezoelectric actuated smart shells.” AIAA J. 42 (10): 2112–2123. https://doi.org/10.2514/1.2902.
Ha, S. K., C. Keilers, and F.-K. Chang. 1992. “Finite element analysis of composite structures containing distributed piezoceramic sensors and actuators.” AIAA J. 30 (3): 772–780. https://doi.org/10.2514/3.10984.
Haddadpour, H., M. A. Kouchakzadeh, and F. Shadmehri. 2008. “Aeroelastic instability of aircraft composite wings in an incompressible flow.” Compos. Struct. 83 (1): 93–99. https://doi.org/10.1016/j.compstruct.2007.04.012.
Hernandes, J. A., S. F. M. Almeida, and A. Nabarrete. 2000. “Stiffening effects on the free vibration behavior of composite plates with PZT actuators.” Compos. Struct. 49 (1): 55–63. https://doi.org/10.1016/S0263-8223(99)00125-7.
Hollowell, S. J., and J. Dugundji. 1984. “Aeroelastic flutter and divergence of stiffness coupled, graphite/epoxy cantilevered plates.” J. Aircraft 21 (1): 69–76. https://doi.org/10.2514/3.48224.
Hwang, W.-S., and H. C. Park. 1993. “Finite element modeling of piezoelectric sensors and actuators.” AIAA J. 31 (5): 930–937. https://doi.org/10.2514/3.11707.
Kameyama, M., and H. Fukunaga. 2007. “Optimum design of composite plate wings for aeroelastic characteristics using lamination parameters.” Comput. Struct. 85 (3–4): 213–224. https://doi.org/10.1016/j.compstruc.2006.08.051.
Koo, K.-N. 2001. “Aeroelastic characteristics of double-swept isotropic and composite wings.” J. Aircraft 38 (2): 343–348. https://doi.org/10.2514/2.2767.
Lam, K. Y., X. Q. Peng, G. R. Liu, and J. N. Reddy. 1997. “A finite-element model for piezoelectric composite laminates.” Smart Mater. Struct. 6 (5): 583–591. https://doi.org/10.1088/0964-1726/6/5/009.
Leo, D. J. 2007. Engineering analysis of smart material systems. Hoboken, NJ: Wiley.
Liu, G. R., and S. S. Quek. 2003. The finite element method: A practical course. Oxford, UK: Butterworth-Heinemann.
Mahran, M., A. ELsabbagh, and H. Negm. 2017. “A comparison between different finite elements for elastic and aero-elastic analyses.” J. Adv. Res. 8 (6): 635–648. https://doi.org/10.1016/j.jare.2017.06.009.
Mahran, M., H. Negm, and A. Elsabbagh. 2015a. Aero-elastic analysis of plate wings using the finite element method. Germany: Lambert Academic Publishing.
Mahran, M., H. Negm, and A. El-Sabbagh. 2015b. “Aero-elastic characteristics of tapered plate wings.” Finite Elements Anal. Des. 94 (Feb): 24–32. https://doi.org/10.1016/j.finel.2014.09.009.
Mahran, M., H. Negm, K. Maalawi, and A. El-Sabbagh. 2015c. “Aero-elastic analysis of composite plate swept wings using the finite element method.” Accessed 18 June 2015. https://www.researchgate.net/profile/Karam_Maalawi/publication/280875922_Aero-elastic_analysis_of_composite_plate_swept_wings_using_the_finite_element_method/links/55c9a53708aea2d9bdc93ee7.pdf.
Marinkovic, D., H. Koppe, and U. Gabbert. 2006. “Accurate modeling of the electric field within piezoelectric layers for active composite structures.” J. Intell. Mater. Syst. Struct. 18 (5): 503–513. https://doi.org/10.1177/1045389X06067139.
Mieszczak, Z., M. Krawczuk, and W. Ostachowicz. 2002. “Static and dynamic analysis of multilayer composite plate with piezoelectric elements.” J. Theor. Appl. Mech. 40 (3): 649–665.
Neto, M. A., R. P. Leal, and W. Yu. 2012. “A triangular finite element with drilling degrees of freedom for static and dynamic analysis of smart laminated structures.” Comput. Struct. 108–109: 61–74. https://doi.org/10.1016/j.compstruc.2012.02.014.
Nguyen, D., N. Nguyen, and K. Trinh. 2013. “Finite element modeling and vibration analysis of aeroelastic wing structures.” In Proc., 51st AIAA Aerospace Sciences Meeting: Including the New Horizons Forum and Aerospace Exposition. Reston, VA: American Institute of Aeronautics and Astronautics.
Nikbay, M., and P. Acar. 2012. “Flutter based aeroelastic optimization of an aircraft wing with analytical approach.” In Proc., 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf. Reston, VA: American Institute of Aeronautics and Astronautics.
Otiefy, R. A. H., and H. M. Negm. 2010. “Wing box transonic-flutter suppression using piezoelectric self-sensing actuators attached to skin.” Smart Mater. Struct. 19 (12): 125001. https://doi.org/10.1088/0964-1726/19/12/125001.
Phung-Van, P., L. De Lorenzis, C. H. Thai, M. Abdel-Wahab, and H. Nguyen-Xuan. 2015. “Analysis of laminated composite plates integrated with piezoelectric sensors and actuators using higher-order shear deformation theory and isogeometric finite elements.” Comput. Mater. Sci. 96: 495–505. https://doi.org/10.1016/j.commatsci.2014.04.068.
Piefort, V. 2001. “Finite element modelling of piezoelectric active structures.” Ph.D. thesis, Active Structures Laboratory, Dept. of Mechanical Engineering and Robotics, Université Libre de Bruxelles.
Qian, W., R. Huang, H. Hu, and Z. Yonghui. 2014. “Active flutter suppression of a multiple-actuated-wing wind tunnel model.” Chin. J. Aeronaut. 27 (6): 1451–1460. https://doi.org/10.1016/j.cja.2014.10.011.
Reddy, J. N. 1999. “On laminated composite plates with integrated sensors and actuators.” Eng. Struct. 21 (7): 568–593. https://doi.org/10.1016/S0141-0296(97)00212-5.
Reddy, J. N. 2004. Mechanics of laminated composite plates and shells: Theory and analysis. Boca Raton, FL: CRC Press.
Reddy, J. N. 2005. An introduction to the finite element method. New York: McGraw-Hill.
Rezaiee-Pajand, M., and Y. Sadeghi. 2013. “A bending element for isotropic, multilayered and piezoelectric plates.” Latin Am. J. Solids Struct. 10 (2): 323–348. https://doi.org/10.1590/S1679-78252013000200006.
Sapkal, K. S., and P. J. Attar. 2012. “Aeroelastic analysis of a composite material delta wing in low subsonic flow.” AIAA J. 50 (1): 162–175. https://doi.org/10.2514/1.J051212.
Sartorato, M., R. de Medeiros, and V. Tita. 2015. “A finite element formulation for smart piezoelectric composite shells: Mathematical formulation, computational analysis and experimental evaluation.” Compos. Struct. 127: 185–198. https://doi.org/10.1016/j.compstruct.2015.03.009.
Soares, C. M. M., C. A. M. Soares, and V. M. F. Correia. 1997. “Optimization of multilaminated structures using higher-order deformation models.” Comput. Methods Appl. Mech. Eng. 149 (1–4): 133–152. https://doi.org/10.1016/S0045-7825(97)00066-2.
Song, Z.-G., and F.-M. Li. 2012. “Active aeroelastic flutter analysis and vibration control of supersonic composite laminated plate.” Compos. Struct. 94 (2): 702–713. https://doi.org/10.1016/j.compstruct.2011.09.005.
Subramanian, K., A. Elangovan, and R. Rajkumar. 1993. “Elastic stability of varying thickness plates using the finite element method.” Comput. Struct. 48 (4): 733–738. https://doi.org/10.1016/0045-7949(93)90267-H.
Sulbhewar, L. N., P. Raveendranath, L. N. Sulbhewar, and P. Raveendranath. 2015. “An efficient coupled polynomial interpolation scheme to eliminate material-locking in the Euler-Bernoulli piezoelectric beam finite element.” Latin Am. J. Solids Struct. 12 (1): 153–172. https://doi.org/10.1590/1679-78251401.
Suleman, A., F. Afonso, and C. Spada. 2016. “Aeroelastic analysis of high aspect ratio wings.” In Proc., 54th AIAA Aerospace Sciences Meeting. Reston, VA: American Institute of Aeronautics and Astronautics.
Tzou, H. S. 1993. “Piezoelectric shells.” Vol. 19 of Solid mechanics and its applications. Dordrecht, Netherlands: Springer.
Wright, J. R., and J. E. Cooper. 2007. Introduction to aircraft aeroelasticity and loads: Aerospace series. Chichester, UK: Wiley.
Zienkiewicz, O. C., and R. L. Taylor. 2005. The finite element method for solid and structural mechanics. 6th ed. Amsterdam, Netherlands: Elsevier.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 32 • Issue 2 • March 2019
Copyright
©2018 American Society of Civil Engineers.
History
Received: Dec 19, 2017
Accepted: Jun 22, 2018
Published online: Nov 26, 2018
Published in print: Mar 1, 2019
Discussion open until: Apr 26, 2019
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.