Abstract
A recently developed coupled third-order zigzag theory for the statics of piezoelectric hybrid cross-ply plates is extended to dynamics. The theory combines a third-order zigzag approximation for the in-plane displacements and a sub-layerwise linear approximation for the electric potential, considering all components of the electric field. The nonuniform variation of the transverse displacement due to the piezoelectric field is accounted for. The conditions for the absence of shear traction at the top and bottom surfaces and continuity of transverse shear stresses in the presence of electromechanical loading are satisfied exactly, thereby reducing the number of displacement variables to five, which is the same as in a first- or third-order equivalent single-layer theory. The governing equations of motion are derived from the extended Hamilton's principle. The theory is assessed by comparing the Navier solutions for the free and forced harmonic vibration response of simply supported plates with the exact three-dimensional piezoelasticity solutions. Comparisons for hybrid test, composite and sandwich plates establish that the present theory is quite accurate for the dynamic response of moderately thick plates.
Similar content being viewed by others
References
Heyliger, P., Saravanos, D.A.: Exact free-vibration analysis of laminated plates with embedded piezoelectric layers. J Acoust Soc Am 98, 1547–1557 (1995)
Batra, R.C., Liang, X.Q.: The vibration of a rectangular laminated elastic plate with embedded piezoelectric sensors and actuators. Comput Struct 63, 203–216 (1997)
Ray, M.C., Bhattacharya, R., Samanta, B.: Exact solutions for dynamic analysis of composite plates with distributed piezoelectric layers. Comput Struct 66, 737–743 (1998)
Kapuria, S., Achary, G.G.S.: Exact 3D piezoelasticity solution of hybrid cross-ply plates with damping under harmonic electro-mechanical loads. J Sound Vib, 282, 617–634, (2005)
Ha, S.K., Keilers, C., Chang, F.K.: Finite element analysis of composite structures containing distributed piezoceramic sensors and actuators. AIAA J 30, 772–780 (1992)
Yu, Y.Y.: Some recent advances in linear and nonlinear dynamical modeling of elastic and piezoelectric plates. J Intell Mater Syst Struct 6, 237–254 (1995)
Chee, C.Y.K., Tong, L., Steven, G.P.: A review on the modeling of piezoelectric sensors and actuators incorporated in intelligent structures. J Intell Mater Syst Struct 9, 3–19 (1998)
Saravanos, D.A., Heyliger P.R.: Mechanics and computational models for laminated piezoelectric beams, plates, and shells. Appl Mech Rev 52, 305–320 (1999)
Gopinathan, S.V., Varadan, V.V., Varadan, V.K.: A review and critique of theories for piezoelectric laminates. Smart Mater Struct 9, 24–48 (2000)
Detwiler, J.C., Shen, M.H., Venkaya, V.B.: Finite element analysis of laminated composite structures containing distributed piezoelectric actuators and sensors. Finite Elem Anal Des 20, 87–100 (1995)
Yu, J.W., Kang, W.Y., Kim, S.J.: Elastic tailoring of laminated composite plate by anisotropic piezoelectric polymers-theory, computation, and experiment. J Compos Mater 29, 1201–1221 (1995)
Huang, J.H., Wu, T.L.: Analysis of hybrid multilayered piezoelectric plates. Int J Eng Sci 34, 171–181 (1996)
Saravanos, D.A.: Damped vibration of composite plates with passive piezoelectric–resistor elements. J Sound Vib 221, 867–885 (1999)
Krommer, V.M., Irschik, H.: A Reissner–Mindlin type plate theory including the direct piezoelectric and the pyroelectric effect. Acta Mech 141, 51–69 (2000)
Vel, S.S., Batra, R.C.: Analysis of piezoelectric bimorphs and plates with segmented actuators. Thin-walled Struct 39, 23–44 (2001)
Mitchell. J.A., Reddy, J.N.: A refined hybrid plate theory for composite laminates with piezoelectric laminae. Int J Solids Struct 32, 2345–2367 (1995)
Shen, S., Kuang, Z.B.: An active control model of laminated piezothermoelastic plate. Int J Solids Struct 36, 1925–1947 (1999)
Correia, V.M.F., Gomes, M.A.A., Suleman, A., Soares, C.M.M.: Modelling and design of adaptive composite structures. Comput Meth Appl Mech Eng 185, 325–346 (2000)
Zhou, X., Chattopadhyay, A., Gu, H.: Dynamic responses of smart composite using a coupled thermo-piezoelectric-mechanical model. AIAA J 38, 1939–1948 (2000)
Batra, R.C., Vidoli, S.: Higher-order piezoelectric plate theory derived from a three-dimensional variational principle. AIAA J 40, 91–104 (2002)
Kulkarni, S.A., Bajoria, K.M.: Finite element modeling of smart plates/shells using higher order shear deformation theory. Compos Struct 62, 41–50 (2003)
Saravanos, D.A., Heyliger, P.R., Hopkins, D.A.: Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates. Int J Solids Struct 34, 359–378 (1997)
Benjeddou, A., Deu, J.-F.: A two-dimensional closed-form solution for the free-vibration analysis of piezoelectric sandwich plates. Int J Solids Struct 39, 1463–1486 (2002)
Kapuria, S., Dumir, P.C., Ahmed, A.: An efficient coupled layer-wise theory for static analysis of piezoelectric sandwich beams. Arch Appl Mech 73, 147–159 (2003)
Kapuria, S., Ahmed, A., Dumir, P.C.: An efficient coupled zigzag theory for harmonic dynamic analysis of piezoelectric composite and sandwich beams with damping. J Sound Vib 279, 345–371 (2005)
Kapuria, S.: A coupled zigzag third order theory for hybrid cross-ply plates. ASME J Appl Mech 71, 604–614 (2004)
Cho, M., Oh, J.: Higher order zigzag theory for fully coupled thermo-electro-mechanical smart composite plates. Int J Solids Struct 41, 1331–1356 (2004)
Auld, B.A.: Acoustic fields and waves in solids, Vol. I Wiley, New York, pp. 373 (1973)
Tzou, H.S., Bao, Y.: A theory on anisotropic piezothermoelastic shell laminates with sensor/actuator applications. J Sound Vib 184, 453–473 (1995)
Tiersten, H.F.: Linear piezoelectric plate vibrations. Plenum, New York (1969)
Averril, R.C., Yip, Y.C. : An efficient thick beam theory and finite element model with zig-zag sublaminate approximation. AIAA J 34, 1626–1632 (1996)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kapuria, S., Achary, G. A coupled zigzag theory for the dynamics of piezoelectric hybrid cross-ply plates. Arch Appl Mech 75, 42–57 (2005). https://doi.org/10.1007/s00419-005-0386-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-005-0386-5