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Nonlinear active vibration control of piezoelastic laminated plates considering interfacial damage effects. (English) Zbl 1269.74176

Summary: In this paper, the coupling of the direct and converse piezoelectric effects of the piezoelectric layers treated as sensor and actuator is considered, and a nonlinear active vibration control model for cross-ply piezoelastic laminated plates containing the damage effect of the intra-layer materials and inter-laminar interfaces is presented. The model is based on the general six-degrees-of-freedom plate theory and Von Karman-type of nonlinear strains. For the interfacial conditions, interfacial shear slip modeling between layers is introduced, which is depicted by three shape functions and interfacial damage variables. By using the Hamilton variation principle and the simple negative velocity feedback control algorithm, the active control of damping is derived to the nonlinear dynamic equations and used to actively control the vibration response of the plate. In numerical examples for simply supported laminated plates, this model is validated by comparison with existing results documented in the literature; the effects of feedback control gain and the location of piezoelectric layers on the vibration control is discussed, and different damage models on the nonlinear vibration response of piezoelectric laminated plate with interfacial imperfections are investigated.

MSC:

74M05 Control, switches and devices (“smart materials”) in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
74K20 Plates
74F15 Electromagnetic effects in solid mechanics
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[1] Benjeddou, A., Thin-Walled Structures 40 (7) pp 573– (2002) · doi:10.1016/S0263-8231(02)00013-7
[2] Cheng, Z.Q., Journal of Applied Mechanics 63 pp 1019– (1996) · Zbl 0882.73034 · doi:10.1115/1.2787221
[3] Doebling, S.W., The Shock and Vibration Digest 30 (2) pp 91– (1998) · doi:10.1177/058310249803000201
[4] Dosch, J.J., Journal of Intelligent Material Systems and Structures 3 pp 166– (1992) · doi:10.1177/1045389X9200300109
[5] Fu, Y., Nonlinear Dynamics 55 (3) pp 203– (2008)
[6] Gao, J.X., Journal of Sound and Vibration 264 pp 911– (2003) · Zbl 1236.74283 · doi:10.1016/S0022-460X(02)01189-6
[7] Heyliger, P., Journal of Applied Mechanics 64 pp 299– (1997) · Zbl 0890.73052 · doi:10.1115/1.2787307
[8] Ishak, S.I., Composite Part B 32 (4) pp 287– (2001) · doi:10.1016/S1359-8368(01)00019-1
[9] Kachanov, L.M., Introduction to Continuum Damage Mechanics, Maritinus (1986) · Zbl 0596.73091 · doi:10.1007/978-94-017-1957-5
[10] Ladeveze, P., Composite Science and Technology 43 pp 257– (1992) · doi:10.1016/0266-3538(92)90097-M
[11] Lee, C.K., 1992, Piezoelectric Laminates: Theory and Experiment for Distributed Sensors and Actuators. Intelligent Structure Systems. Kluwer Academic, Amsterdam, pp. 75-167. · doi:10.1007/978-94-017-1903-2_3
[12] DOI: 10.1007/978-3-642-18255-6 · Zbl 0852.73003 · doi:10.1007/978-3-642-18255-6
[13] Lin, Y., Journal of Vibration Engineering 9 (2) pp 107– (1996)
[14] Liu, G.R., ASME Journal of Applied Mechanics 62 pp 607– (1995) · Zbl 0839.73067 · doi:10.1115/1.2895989
[15] Liu, G.R., Computer Methods in Applied Mechanics and Engineering 190 (42) pp 5505– (2001) · Zbl 1014.74030 · doi:10.1016/S0045-7825(01)00173-6
[16] Liu, G.R., International Journal of Solids and Structures 31 (21) pp 2965– (1994) · Zbl 0943.74553 · doi:10.1016/0020-7683(94)90063-9
[17] Liu, G.R., Journal of Sound and Vibration 220 (5) pp 827– (1999) · doi:10.1006/jsvi.1998.1970
[18] Lu, X., AIAA Journal 30 pp 1063– (1992) · Zbl 0761.73073 · doi:10.2514/3.11028
[19] Mitchell, J.A., International Journal of Solids and Structures 199 32 (16) pp 2345– (1995) · Zbl 0869.73038 · doi:10.1016/0020-7683(94)00229-P
[20] Pagano, N.J., Journal of Composite Materials 3 pp 398– (1969) · doi:10.1177/002199836900300304
[21] Pai, P.F., International Journal of Solids and Structures 30 (12) pp 1603– (1993) · Zbl 0785.73065 · doi:10.1016/0020-7683(93)90193-B
[22] Parton, V.Z., Acta Astronautica 3 pp 671– (1976) · Zbl 0351.73115 · doi:10.1016/0094-5765(76)90105-3
[23] Peng, X.Q., Journal of Sound and Vibration 209 pp 635– (1998) · doi:10.1006/jsvi.1997.1249
[24] Rabotnov, Y.N., 1963, ”On the equation of state for creep,” In: Progress in Applied Mechanics, The Prager Anniversary Volume , MacMillan, New York, pp. 307-315. · doi:10.1243/PIME_CONF_1963_178_030_02
[25] Ray, M.C., Composite Structures 45 pp 667– (1992) · Zbl 0772.73070 · doi:10.1016/0045-7949(92)90485-I
[26] Seeley, C.E., Smart Materials Structures 7 pp 502– (1998) · doi:10.1088/0964-1726/7/4/010
[27] Shen, S., International Journal of Solids and Structures 36 pp 1925– (1999) · Zbl 0942.74051 · doi:10.1016/S0020-7683(98)00068-7
[28] Shu, X., International Journal of Solids and Structures 37 pp 4289– (2000) · Zbl 0974.74017 · doi:10.1016/S0020-7683(99)00144-4
[29] Shu, X., International Journal of Mechanical Sciences 43 pp 935– (2001) · Zbl 1169.74581 · doi:10.1016/S0020-7403(00)00053-9
[30] Shu, X., International Journal of Mechanical Sciences 41 pp 1673– (2005) · Zbl 1192.74112 · doi:10.1016/j.ijmecsci.2005.07.003
[31] Soldatos, K.P., Composite Structures 46 pp 333– (1999) · doi:10.1016/S0263-8223(99)00061-6
[32] Soldatos, K.P., Composites Science and Technology 61 pp 247– (2001) · doi:10.1016/S0266-3538(00)00207-4
[33] Soldatos, K.P., International Journal of Solids and Structures 34 (22) pp 2857– (1997) · Zbl 0939.74532 · doi:10.1016/S0020-7683(96)00170-9
[34] Sun, D., International Journal of Solid and Structures 38 pp 9033– (2001) · Zbl 1043.74033 · doi:10.1016/S0020-7683(01)00180-9
[35] Xu, K.M., Computer Methods in Applied Mechanics and Engineering 141 (1) pp 125– (1997)
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