Analytical solution for free vibration of piezoelectric coupled moderately thick circular plates

Aldraihem, 2000, Smart beams with extension and thickness—shear piezoelectric actuators, Smart Mater. Struct., 9, 1, 10.1088/0964-1726/9/1/301 Almajid, 2001, Analysis of out-of-plane displacement and stress field in a piezocomposite plate with functionally graded microstructure, Int. J. Solids Struct., 38, 3377, 10.1016/S0020-7683(00)00264-X Bailey, 1985, Distributed piezoelectric polymer active vibration control of a cantilever beam, J. Guid. Cont. Dyn., 8, 605, 10.2514/3.20029 Bisegna, 1996, An exact three-dimensional solution for simply supported rectangular piezoelectric plates, ASME J. Appl. Mech., 63, 628, 10.1115/1.2823343 Chandrashekhara, 1993, Active vibration control of laminated composite plates using piezoelectric devices: a finite element approach, J. Intel. Mater. Syst. Struct., 4, 496, 10.1177/1045389X9300400409 Crawley, E.F., Anderson, E., 1989. Detailed model of piezoelectric actuation of beams. Proceedings of the 30th AIAA/ASMA/SAE Conference on Structures, Structural Dynamics, and Material. Washington, DC, April 1989, pp. 2000–2010 Crawley, 1987, Use of piezoelectric actuators as elements of intelligent structures, AIAA J., 25, 1373, 10.2514/3.9792 Fernandes, 2001, Two-dimensional modelling of laminated piezoelectric composites: analysis and numerical results, Thin-Walled Struct., 39, 3, 10.1016/S0263-8231(00)00051-3 Hagood, 1995, Modeling of a piezoelectric rotary ultrasonic motor, IEEE Trans. Ultrason. Ferroelectr. Freq. Cont., 44, 210, 10.1109/58.365235 Heyliger, 1997, Exact solutions for simply supported laminated piezoelectric plates, ASME J. Appl. Mech., 64, 299, 10.1115/1.2787307 Heyliger, 2000, Free vibration of laminated circular piezoelectric plates and discs, J. Sound Vib., 229, 935, 10.1006/jsvi.1999.2520 HKS Inc., 1993. ABAQUS User's Manual (verion 5.2). Hibbitt, Karlsson and Sorenson Inc., Providence, RI Huang, 1996, Analysis of hybrid multilayered piezoelectric plates, Int. J. Engng. Sci., 34, 171, 10.1016/0020-7225(95)00087-9 Hwang, 1993, Finite element modeling of piezoelectric sensors and actuators, AIAA J., 31, 930, 10.2514/3.11707 Khdeir, 1997, An exact solution for the bending of thin and thickness cross-ply laminated beams, Compos. Struct., 37, 195, 10.1016/S0263-8223(97)80012-8 Khdeir, 1999, Jordan canonical form solution for thermally induced deformations of cross-ply laminated composite beams, J. Thermal Stresses, 22, 331, 10.1080/014957399280904 Kim, 1996, Finite element modeling of a smart cantilever plate and comparison with experiments, Smart Mater. Struct., 5, 165, 10.1088/0964-1726/5/2/005 Lam, 1997, A finite element model for piezoelectric composite laminates, Smart Mater. Struct., 6, 583, 10.1088/0964-1726/6/5/009 Lebrun, 1997, Electromechanical conversion in an ultrasonic motor using a non-axisymmetric (1,1) mode, Smart Mater. Struct., 8, 47, 10.1088/0964-1726/6/1/006 Love, 1994 Mindlin, 1951, Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates, J. Appl. Mech., 18, 31, 10.1115/1.4010217 Mindlin, 1951, Thickness-shear and flexural vibrations of crystal plates, J. Appl. Phys., 22, 316, 10.1063/1.1699948 Mindlin, 1952, Forced thickness-shear and flexural vibrations of piezoelectric crystal plates, J. Appl. Phys., 23, 83, 10.1063/1.1701983 Mindlin, R.D., 1955. An introduce to the mathematical theory of vibrations of elastic plates. US Army Signal Corps engineering Laboratories, Fort Monmouth, NJ Mindlin, 1972, High frequency vibrations of piezoelectric crystal plates, Int. J. Solids Struct., 8, 895, 10.1016/0020-7683(72)90004-2 Mindlin, 1984, Frequencies of piezoelectrically forced vibrations of electroded, doubly rotated, quartz plates, Int. J. Solids Struct., 20, 141, 10.1016/0020-7683(84)90005-2 Sheikh, 2001, An appropriate FE model for through-thickness variation of displacement and potential in thin/moderately thick smart laminates, Compos. Struct., 51, 401, 10.1016/S0263-8223(00)00156-2 So, 1998, Three-dimensional vibrations of thick circular and annular plates, J. Sound Vib., 209, 15, 10.1006/jsvi.1997.1228 Speigel, 1999 Swanson Inc., 1993. ANSYS User's Manual, version 5.2. Swanson Inc., Houston, PA Tiersten, 1969 Timoshenko, 1974 Wang, 2000, A new theory for electroded piezoelectric plates and its finite element application for the forced vibrations of quartz crystal resonators, Int. J. Solids Struct., 37, 5653, 10.1016/S0020-7683(99)00241-3 Wang, 2000, Flexural vibration analysis of sandwich beam coupled with piezoelectric actuator, Smart Mater. Struct., 9, 103, 10.1088/0964-1726/9/1/311 Wang, 2001, Analysis of piezoelectric coupled circular plate, Smart Mater. Struct., 10, 229, 10.1088/0964-1726/10/2/308 Whitney, 1970, Shear deformation in heterogeneous anisotropic plates, ASME J. Appl. Mech., 37, 1031, 10.1115/1.3408654 Yu, 1995, Some recent advances in linear and nonlinear dynamical modelling of elastic and piezoelectric plates, J. Intel. Mater. Syst. Struct., 6, 237, 10.1177/1045389X9500600211