×

zbMATH — the first resource for mathematics

Active control of geometrically nonlinear transient vibrations of laminated composite cylindrical panels using piezoelectric fiber reinforced composite. (English) Zbl 1401.74139
Summary: This paper addresses the analysis of active constrained layer damping \((\mathbf{ACLD})\) of geometrically nonlinear transient vibrations of laminated thin composite cylindrical panels using piezoelectric-fiber- reinforced composite \((\mathbf{PFRC})\) materials. The constraining layer of the \((\mathbf{ACLD})\) treatment is considered to be made of the \(\mathbf{PFRC}\) materials. The Golla-Hughes-McTavish \((\mathbf{GHM})\) method has been implemented to model the constrained viscoelastic layer of the ACLD treatment in time domain. The Von Kármán type-nonlinear strain-displacement relations and a simple first-order shear deformation theory are used for deriving this electromechanical coupled problem. A three-dimensional finite element \((\mathbf{FE})\) model of smart composite panels integrated with the patches of such \((\mathbf{ACLD})\) treatment has been developed to demonstrate the performance of these patches on enhancing the damping characteristics of thin symmetric and antisymmetric laminated cylindrical panels in controlling the geometrically nonlinear transient vibrations. The numerical results indicate that the \((\mathbf{ACLD})\) patches significantly improve the damping characteristics of both symmetric and antisymmetric panels for suppressing the geometrically nonlinear transient vibrations of the panels. The effect of the shallowness angle of the panels on the control authority of the patches has also been investigated.

MSC:
74H45 Vibrations in dynamical problems in solid mechanics
74E30 Composite and mixture properties
74F15 Electromagnetic effects in solid mechanics
74K20 Plates
74S05 Finite element methods applied to problems in solid mechanics
74M05 Control, switches and devices (“smart materials”) in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bailey T., Hubbard J.E.: Distributed piezoelectric polymer active vibration control of a cantilever beam. J. Guid. Control Dyn. 8, 605–611 (1985) · Zbl 0633.93047 · doi:10.2514/3.20029
[2] Baz A., Poh S.: Performance of an active control system with piezoelectric actuators. J. Sound Vib. 126, 327–343 (1988) · doi:10.1016/0022-460X(88)90245-3
[3] Lee C.K., Chiang W.W., Sulivan O.: Piezoelectric modal sensor/actuator pairs for critical active damping vibration control. J. Acoust. Soc. Am. 90(1), 374–384 (1991) · doi:10.1121/1.401260
[4] Hanagud S., Obal M.W., Calise A.J.: Optimal vibration control by the use of piezoceramic sensors and actuators. J. Guid. Control Dyn. 15(5), 1199–1206 (1992) · doi:10.2514/3.20969
[5] Devasia S., Tesfay M., Padu B., Bayo E.A.J.: Piezoelectric actuator design for vibration suppression: placement and sizing. J. Guid. Control Dyn. 16, 859–864 (1993) · doi:10.2514/3.21093
[6] Gu Y., Clark R.L., Fuller C.R.: Experiments on active control of plate vibration using piezoelectric actuators and polyvinylidene fluoride modal sensors. J. Vib. Acoust. 116, 303–308 (1994) · doi:10.1115/1.2930429
[7] Kim J., Varadan V.V., V. K., Bao X.Q.: Finite element modeling of a smart cantilever plate and comparison with experiments. Smart Mater. Struct. 5(2), 165–170 (1996) · doi:10.1088/0964-1726/5/2/005
[8] Heyliger P.: Exact solutions for simply supported laminated piezoelectric plates. ASME J. Appl. Mech. 64, 299–306 (1997) · Zbl 0890.73052 · doi:10.1115/1.2787307
[9] He L.H.: Axisymmetric response of circular plates with piezoelectric layers: an exact solution. Int. J. Mech. Sci. 40(12), 1265–1279 (1998) · Zbl 0963.74536 · doi:10.1016/S0020-7403(98)00017-4
[10] Vel S.S., Batra R.C.: Exact solution for rectangular sandwich plates with embedded piezoelectric hear actuators. AIAA J. 39(7), 1363–1373 (2001) · doi:10.2514/2.1455
[11] Irschick H.: A review on static and dynamic shape control of structures by piezoelectric and actuators. Eng. Struct. 24(1), 5–11 (2002) · doi:10.1016/S0141-0296(01)00081-5
[12] Ray M.C.: Optimal control of laminated shells with piezoelectric sensor and actuator layers. AIAA J. 41, 1151–1157 (2003) · doi:10.2514/2.2058
[13] Xu S.X., Koko T.S.: Finite element analysis and design of actively controlled piezoelectric smart structures. Finite Elements Anal. Des. 40(3), 241–262 (2004) · doi:10.1016/S0168-874X(02)00225-1
[14] Peng F., Ng A., Hu Y.R.: Actuator placement optimization and adaptive vibration control of plate smart structures. J. Intell. Mater. Syst. Struct. 16, 263–271 (2005) · doi:10.1177/1045389X05050105
[15] Meng G., Ye L., Dong X.J., Wei K.X.: Closed loop finite element modeling of piezoelectric smart structures. Shock Vib. 13(1), 1–12 (2006)
[16] Kumari P., Nath J.K., Dumir P.C., Kapuria S.: 2D exact solutions for flat hybrid piezoelectric and magnetoelastic angle-ply panels under harmonic load. Smart Mater. Struct. 16(5), 1651–1661 (2007) · doi:10.1088/0964-1726/16/5/018
[17] Kwak M.K., Heo S., Jeong M.: Dynamic modeling and active vibration controller design for a cylindrical shell equipped with piezoelectric sensors and actuators. J. Sound Vib. 321, 510–524 (2009) · doi:10.1016/j.jsv.2008.09.051
[18] Balamurugan V., Narayanan S.: Finite element modeling of stiffened piezolaminated plates and shells with piezoelectric layers for active vibration control. Smart Mater. Struct. 19, 105003 (2010) · doi:10.1088/0964-1726/19/10/105003
[19] Baz, A.: Active constrained layer damping. U.S. patent 5,485,053 (1996)
[20] Baz A., Ro J.: Vibration control of plates with active constrained layer damping. Smart Mater. Struct. 5, 135–144 (1996)
[21] Ray M.C., Baz A.: Optimization of energy dissipation of active constrained layer damping treatment of plates. J. Sound Vib. 208, 391–406 (1997) · doi:10.1006/jsvi.1997.1171
[22] Ray M.C., Baz A.: Control of nonlinear vibration of beams using active constrained layer damping treatment. J. Vib. Control 7, 539–549 (2001) · Zbl 1045.74036 · doi:10.1177/107754630100700404
[23] Ray M.C., Oh J., Baz A.: Active constrained layer damping of thin cylindrical shells. J. Sound Vib. 240(5), 921–935 (2001) · doi:10.1006/jsvi.2000.3287
[24] Chantalakhana C., Stanway R.: Active constrained layer damping of clamped-clamped plate vibrations. J. Sound Vib. 241(5), 755–777 (2001) · doi:10.1006/jsvi.2000.3317
[25] Ro J, Baz A.: Optimum placement and control of active constrained layer damping using modal strain energy approach. J. Vib. Control 8, 861–876 (2002) · Zbl 1049.74717 · doi:10.1177/107754602029204
[26] Ray M.C., Pradhan A.K.: Active damping of laminated thin cylindrical composite panels using vertically/obliquely reinforced 1-3 piezoelectric composites. Acta Mech. 209(3–4), 201–218 (2010). doi: 10.1007/s00707-009-0149-4 · Zbl 1381.74090 · doi:10.1007/s00707-009-0149-4
[27] Mallik N., Ray M.C.: Effective coefficients of piezoelectric fiber reinforced composites. AIAA J. 41(4), 704–710 (2003) · doi:10.2514/2.2001
[28] Ray M.C., Mallik N.: Performance of smart damping treatment using piezoelectric fiber reinforced composites. AIAA J. 43(1), 184–193 (2005) · doi:10.2514/1.7552
[29] Ray M.C., Shivakumar J.: Active constrained layer damping of geometrically nonlinear transient vibrations of composite plates using piezoelectric fiber-reinforced composite. Thin-Walled Struct. 47, 178–189 (2009) · doi:10.1016/j.tws.2008.05.011
[30] Panda S., Ray M.C.: Active constrained layer damping of geometrically nonlinear vibrations of functionally graded plates using piezoelectric fiber reinforced composites. Smart Mater. Struct. 17(2), 1–15 (2008) · doi:10.1088/0964-1726/17/2/025012
[31] Sarangi S.K., Ray M.C.: Smart damping of geometrically nonlinear vibrations of laminated composite beams using vertically reinforced 1-3 piezoelectric composites. Smart Mater. Struct. 19, 075020 (2010) · Zbl 1277.74032 · doi:10.1088/0964-1726/19/7/075020
[32] Sarangi S.K., Ray M.C.: Active damping of geometrically nonlinear vibrations of laminated composite plates using vertically/obliquely reinforced 1-3 piezoelectric composites. Acta Mech. 222(3–4), 363–380 (2011). doi: 10.1007/s00707-011-0531-x · Zbl 1277.74032 · doi:10.1007/s00707-011-0531-x
[33] Sarangi S.K., Ray M.C.: Active damping of geometrically nonlinear vibrations of laminated composite shallow shells using vertically/obliquely reinforced 1-3 piezoelectric composites. Int. J. Mech. Mater. Des. 7(1), 29–44 (2011) · Zbl 1277.74032 · doi:10.1007/s10999-010-9147-x
[34] Reddy J.N., Chandrashekara K.: Nonlinear analysis of laminated shells including transverse shear strains. AIAA J. 23, 40–41 (1985)
[35] Kundu C.K., Han J.H.: Nonlinear buckling analysis of hygrothermoelastic composite shell panels using finite element method. Composites B 40, 313–328 (2009) · doi:10.1016/j.compositesb.2008.12.001
[36] Lam M.J., Inman D.J., Saunders W.R.: Hybrid damping models using the Golla_hughes-McTavish method with internally balanced model reduction and output feedback. Smart Mater. Struct. 9, 362–371 (2000) · doi:10.1088/0964-1726/9/3/318
[37] Mc Tavish D.J., Hughes P.C.: Modeling of linear viscoelastic space structures. J. Vib. Acoust. 115, 103–113 (1993) · doi:10.1115/1.2930302
[38] Lim Y.-H., Varadan V.V., Varadan K.K.: Closed loop finite element modeling of active constrained layer damping in the time domain analysis. Smart Mater. Struct. 11, 89–97 (2002) · doi:10.1088/0964-1726/11/1/310
[39] Reddy J.N.: Geometrically nonlinear transient analysis of laminated composite plates. AIAA J. 21(4), 621–629 (1983) · Zbl 0506.73074 · doi:10.2514/3.8122
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.