The active aeroelastic flutter characteristics of supersonic beams are investigated. The main contribution of this research is that the piezoelectric material is used to increase the flutter velocities of the supersonic beams. A modeling approach based on the conventional theory of structural dynamics is employed. The process of deriving equations is not complicated and easy to understand. This methodology is verified to be accurate and effective. Hamilton’s principle with the assumed mode method is used to develop the equation of motion of the structural systems. The supersonic piston theory is adopted to evaluate the aerodynamic pressure. Using the standard eigenvalue methodology, the solutions for complex eigenvalue problem are obtained. A displacement and acceleration feedback control strategy is used to obtain the active stiffness and active mass. The aeroelastic flutter bounds are obtained by calculating the natural frequencies and damping ratios. The effects of the active stiffness and mass on the flutter properties of the supersonic beams are analyzed. From the numerical results, it is seen that by adding the active stiffness and mass to the supersonic beams, the aeroelastic flutter properties can be effectively improved. Especially, if the acceleration and displacement feedback gains are increased to proper values, the flutter can even be eliminated for the supersonic cantilevered beams.
Abbas, L.K., Qian, C., Marzocca, P., Zafer, G. and Mostafa, A.2008. ‘‘Active Aerothermoelastic Control of Hypersonic Double-Wedge Lifting Surface,’’ Chinese Journal of Aeronautics, 21:8-18.
2.
Ashley, H. and Zartarian, G.1956. ‘‘Piston Theory - A New Aerodynamic Tool for the Aeroelastician,’’ Journal of the Aeronautical Sciences, 23:1109-1118.
3.
Bae, J.S., Inman, D.J. and Lee, I.2004. ‘‘Effects of Structural Nonlinearity on Subsonic Aeroelastic Characteristics of an Aircraft Wing with Control Surface , ’’ Journal of Fluids and Structures, 19:747-763.
4.
Balakrishnan, A.V.2008. ‘‘Nonlinear Aeroelasticity: The Steady-State Theory,’’ AIAA Journal, 46:177-184.
5.
Balamurugan, V. and Narayanan, S.2001. ‘‘Active Vibration Control of Piezolaminated Smart Beams,’’ Defence Science Journal, 51:103-114.
6.
Balamurugan, V. and Narayanan, S.2008. ‘‘A Piezolaminated Composite Degenerated Shell Finite Element for Active Control of Structures With Distributed Piezosensors and Actuators,’’Smart Materials and Structures , 17:035031.
7.
Baz, A. and Ro, J.1996. ‘‘Vibration Control of Plates With Active Constrained Layer Damping,’’ Smart Materials and Structures, 5:272-280.
8.
Cai, C., Zheng, H., Hung, K.C. and Zhang, Z.J.2006. ‘‘Vibration Analysis of a Beam With an Active Constraining Layer Damping Patch,’’ Smart Materials and Structures, 15:147-156.
9.
Chen, L.W., Lin, C.Y. and Wang, C.C.2002. ‘‘Dynamic Stability Analysis and Control of a Composite Beam with Piezoelectric Layers,’’ Composite Structures, 56:97-109.
10.
Fazelzadeh, S.A. and Hosseini, M.2007. ‘‘Aerothermoelastic Behavior of Supersonic Rotating Thin-Walled Beams Made of Functionally Graded Materials, ’’ Journal of Fluids and Structures, 23:1251-1264.
11.
Friedmann, P.P., McNamara, J.J., Thuruthimattam, B.J. and Nydick, I.2004. ‘‘Aeroelastic Analysis of Hypersonic Vehicles ,’’ Journal of Fluids and Structures , 19:681-712.
12.
Gao, J.X. and Liao, W.H.2005. ‘‘Vibration Analysis of Simply Supported Beams with Enhanced Self-sensing Active Constrained Layer Damping Treatments , ’’ Journal of Sound and Vibration, 280:329-357.
Han, J.H., Tani, J. and Qiu, J.2006. ‘‘Active Flutter Suppression of a Lifting Surface Using Piezoelectric Actuation and Modern Control Theory, ’’ Journal of Sound and Vibration, 291:706-722.
15.
Hedgepeth, I.E. and Widmayer, E.1963. ‘‘Dynamic and Aeroelastic Problems of Lifting Re-entry Bodies,’’ Aerospace Engineering , 22:148-153.
16.
Jegarkandi, M.F., Nobari, A.S., Sabzehparvar, M. and Haddadpour, H.2009. ‘‘Aeroelastic Stability Consideration of Supersonic Flight Vehicle Using Nonlinear Aerodynamic Response Surfaces,’’Journal of Fluids and Structures, 25:1079-1101.
17.
Kim, H.W. and Kim, J.H.2005. ‘‘Effect of Piezoelectric Damping Layers on the Dynamic Stability of Plate Under a Thrust,’’ Journal of Sound and Vibration, 284:597-612.
18.
Kim, D.H. and Lee, I.2000. ‘‘Transonic and Low-Supersonic Aeroelastic Analysis of a Two-Degree-of-Freedom Airfoil With a Freeplay Non-linearity ,’’ Journal of Sound and Vibration, 234:859-880.
19.
Koo, K.N. and Hwang, W.S.2004. ‘‘Effects of Hysteretic and Aerodynamic Damping on Supersonic Panel Flutter of Composite Plates,’’ Journal of Sound and Vibration, 273:569-583.
20.
Kumar, N. and Singh, S.P.2009. ‘‘Vibration and Damping Characteristics of Beams with Active Constrained Layer Treatments Under Parametric Variations,’’Materials and Design, 30:4162-4174.
21.
Kwon, H.J., Kim, D.H. and Lee, I.2004. ‘‘Frequency and Time Domain Flutter Computations of a Wing With Oscillating Control Surface Including Shock Interference Effects ,’’ Aerospace Science and Technology , 8:519-532.
22.
Li, D., Guo, S. and Xiang, J.2010. ‘‘Aeroelastic Dynamic Response and Control of an Airfoil Section With Control Surface Nonlinearities,’’Journal of Sound and Vibration, 329:4756-4771.
23.
Li, F.M., Kishimoto, K., Wang, Y.S., Chen, Z.B. and Huang, W.H.2008. ‘‘Vibration Control of Beams With Active Constrained Layer Damping,’’Smart Materials and Structures , 17:065036.
24.
Li, Q., Mei, C. and Huang, J.K.2007. ‘‘Suppression of Thermal Postbuckling and Nonlinear Panel Flutter Motions Using Piezoelectric Actuators, ’’ AIAA Journal, 45:1861-1873.
25.
Librescu, L. and Na, S.2001. ‘‘Active Vibration Control of Doubly Tapered Thin-Walled Beams Using Piezoelectric Actuation,’’ Thin-Walled Structures, 39:65-82.
26.
Librescu, L., Na, S., Marzocca, P., Chung, C. and Kwak, M.K.2005. ‘‘Active Aeroelastic Control of 2-D Wing-Flap Systems Operating in an Incompressible Flowfield and Impacted by a Blast Pulse ,’’ Journal of Sound and Vibration , 283:685-706.
27.
Librescu, L., Na, S., Qin, Z. and Lee, B.2008. ‘‘Active Aeroelastic Control of Aircraft Composite Wings Impacted by Explosive Blasts,’’ Journal of Sound and Vibration, 318:74-92.
28.
Moita, J.M.S., Correia, I.F.P., Mota Soares, C.M. and Mota Soares, C.A.2004. ‘‘Active Control of Adaptive Laminated Structures with Bonded Piezoelectric Sensors and Actuators, ’’ Computers and Structures, 82:1349-1358.
29.
Moon, S.H.2006. ‘‘Finite Element Analysis and Design of Control System With Feedback Output Using Piezoelectric Sensor/ Actuator for Panel Flutter Suppression,’’ Finite Elements in Analysis and Design, 42:1071-1078.
30.
Moon, S.H. and Hwang, J.S.2005. ‘‘Panel Flutter Suppression With an Optimal Controller Based on the Nonlinear Model Using Piezoelectric Materials , ’’ Composite Structures, 68:371-379.
31.
Moon, S.H. and Kim, S.J.2003. ‘‘Suppression of Nonlinear Composite Panel Flutter With Active/Passive Hybrid Piezoelectric Networks Using Finite Element Method,’’ Composite Structures, 59:525-533.
32.
Na, S., Librescu, L. and Shim, J.K.2003. ‘‘Modeling and Bending Vibration Control of Nonuniform Thin-Walled Rotating Beams Incorporating Adaptive Capabilities ,’’ International Journal of Mechanical Sciences , 45:1347-1367.
33.
Oh, I.K. and Kim, D.H.2009. ‘‘Vibration Characteristics and Supersonic Flutter of Cylindrical Composite Panels With Large Thermoelastic Deflections,’’Composite Structures, 90:208-216.
34.
Oh, I.K. and Lee, I.2006. ‘‘Supersonic Flutter Suppression of Piezolaminated Cylindrical Panels Based on Multifield Layerwise Theory, ’’ Journal of Sound and Vibration, 291:1186-1201.
35.
Prakash, T. and Ganapathi, M.2006. ‘‘Supersonic Flutter Characteristics of Functionally Graded Flat Panels Including Thermal Effects, ’’ Composite Structures, 72:10-18.
36.
Qiu, Z.C., Han, J.D., Zhang, X.M., Wang, Y.C. and Wu, Z.W.2009. ‘‘Active Vibration Control of a Flexible Beam Using a Non-collocated Acceleration Sensor and Piezoelectric Patch Actuator,’’Journal of Sound and Vibration, 326:438-455.
37.
Qin, Z., Marzocca, P. and Librescu, L.2002. ‘‘Aeroelastic Instability and Response of Advanced Aircraft Wings at Subsonic Flight Speeds,’’ Aerospace Science and Technology, 6:195-208.
38.
Raja, S., Pashilkar, A.A., Sreedeep, R. and Kamesh, J.V.2006. ‘‘Flutter Control of a Composite Plate With Piezoelectric Multilayered Actuators,’’ Aerospace Science and Technology, 10:435-441.
39.
Ramesh Kumar, K. and Narayanan, S.2008. ‘‘Active Vibration Control of Beams with Optimal Placement of Piezoelectric Sensor/Actuator Pairs,’’Smart Materials and Structures, 17:055008 (15pp).
40.
Rao, V.M., Behal, A., Marzocca, P. and Rubillo, C.M.2006. ‘‘Adaptive Aeroelastic Vibration Suppression of a Supersonic Airfoil with Flap,’’ Aerospace Science and Technology, 10:309-315.
41.
Ray, M.C. and Batra, R.C.2007. ‘‘Vertically Reinforced 1-3 Piezoelectric Composites for Active Damping of Functionally Graded Plates, ’’ AIAA Journal, 45:1779-1783.
42.
Ray, M.C. and Batra, R.C.2008. ‘‘Smart Constrained Layer Damping of Functionally Graded Shells Using Vertically/Obliquely Reinforced 1-3 Piezocomposite Under a Thermal Environment,’’Smart Materials and Structures , 17:055007.
43.
Reddy, K.K., Chen, J., Behal, A. and Marzocca, P.2007. ‘‘Multiinput/Multi-output Adaptive Output Feedback Control Design for Aeroelastic Vibration Suppression, ’’ Journal of Guidance, Control, and Dynamics, 30:1040-1048.
44.
Sharnappa, Ganesan, N. and Sethuraman, R.2007. ‘‘Dynamic Modeling of Active Constrained Layer Damping of Composite Beam Under Thermal Environment,’’Journal of Sound and Vibration, 305:728-749.
45.
Shin, W.H., Oh, I.K., Han, J.H. and Lee, I.2006. ‘‘Aeroelastic Characteristics of Cylindrical Hybrid Composite Panels With Viscoelastic Damping Treatments, ’’ Journal of Sound and Vibration, 296:99-116.
46.
Sun, D. and Tong, L.2004. ‘‘A Compressional-Shear Model for Vibration Control of Beams With Active Constrained Layer Damping,’’ International Journal of Mechanical Sciences, 46:1307-1325.
47.
Thibert, J.J. and Arnal, D.2000. ‘‘A Review of ONERA Aerodynamic Research in Support of a Future Supersonic Transport Aircraft,’’ Progress in Aerospace Sciences, 36:581-627.
48.
To, C.W.S. and Chen, T.2007. ‘‘Optimal Control of Random Vibration in Plate and Shell Structures With Distributed Piezoelectric Components,’’International Journal of Mechanical Sciences, 49:1389-1398.
49.
Vasques, C.M.A., Mace, B.R., Gardonio, P. and Rodrigues, J.D.2006. ‘‘Arbitrary Active Constrained Layer Damping Treatments on Beams: Finite Element Modelling and Experimental Validation ,’’ Computers and Structures, 84:1384-1401.
50.
Vasques, C.M.A. and Rodrigues, J.D.2008. ‘‘Combined Feedback/ Feedforward Active Control of Vibration of Beams with ACLD Treatments: Numerical Simulation, ’’ Computers and Structures, 86:292-306.
51.
Yang, S. and Lee, I.1996. ‘‘Aeroelastic Analysis for Flap of Airfoil in Transonic Flow,’’ Computers and Structures , 61:421-430.
52.
Yu, P., Chen, Z., Librescu, L. and Marzocca, P.2007. ‘‘Implications of Time-Delayed Feedback Control on Limit Cycle Oscillation of a Two-Dimensional Supersonic Lifting Surface ,’’ Journal of Sound and Vibration, 304:974-986.
53.
Yun, H. and Han, J.2009. ‘‘Robust Flutter Analysis of a Nonlinear Aeroelastic System With Parametric Uncertainties,’’Aerospace Science and Technology, 13:139-149.
54.
Zhang, Y., Niu, H., Xie, S. and Zhang, X.2008. ‘‘Numerical and Experimental Investigation of Active Vibration Control in a Cylindrical Shell Partially Covered by a Laminated PVDF Actuator,’’Smart Materials and Structures, 17:035024.
