1 |
Heyliger, P. and Brooks, S. (1995), "Free vibration of piezoelectric laminates in cylindrical bending", J. Solids Struct., 32(20), 2945-2960. https://doi.org/10.1016/0020-7683(94)00270-7.
DOI
|
2 |
Cheng, Z.Q., Lim, C. and Kitipornchai, S. (1999), "Three-dimensional exact solution for inhomogeneous and laminated piezoelectric plates", J. Eng. Sci., 37(11), 1425-1439. https://doi.org/10.1016/S0020-7225(98)00125-6.
DOI
|
3 |
Heyliger, P. and Brooks, S. (1996), "Exact solutions for laminated piezoelectric plates in cylindrical bending", J. Appl. Mech., 63(4), 903-910.
DOI
|
4 |
Heyliger, P. and Saravanos, D. (1995), "Exact free-vibration analysis of laminated plates with embedded piezoelectric layers", J. Acoustical Soc. America, 98(3), 1547-1557. https://doi.org/10.1121/1.413420.
DOI
|
5 |
Hussein, M. and Heyliger, P. (1998), "Three-dimensional vibrations of layered piezoelectric cylinders", J. Eng. Mech., 124(11), 1294-1298. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:11(1294).
DOI
|
6 |
Jones, A.T. (1970), "Exact natural frequencies for cross-ply laminates", J. Compos. Mater., 4(4), 476-491. https://doi.org/10.1177/002199837000400404.
DOI
|
7 |
Jones, A.T. (1971), "Exact natural frequencies and modal functions for a thick off-axis lamina", J. Compos. Mater., 5(4), 504-520. https://doi.org/10.1177/002199837100500409.
DOI
|
8 |
Kapuria, S. and Dhanesh, N. (2017), "Free edge stress field in smart piezoelectric composite structures and its control: An accurate multiphysics solution", J. Solids Struct., 126, 196-207. https://doi.org/10.1016/j.ijsolstr.2017.08.007.
DOI
|
9 |
Kapuria, S. and Kumari, P. (2011), "Extended Kantorovich method for three-dimensional elasticity solution of laminated composite structures in cylindrical bending", J. Appl. Mech., 78(6), 061004. https://doi.org/10.1115/1.4003779.
DOI
|
10 |
Kapuria, S. and Kumari, P. (2012), "Multiterm extended Kantorovich method for three-dimensional elasticity solution of laminated plates", J. Appl. Mech., 79(6), 061018. https://doi.org/10.1115/1.4006495.
DOI
|
11 |
Kapuria, S. and Kumari, P. (2013), "Extended Kantorovich method for coupled piezoelasticity solution of piezolaminated plates showing edge effects", Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 469(2151), 20120565. https://doi.org/10.1098/rspa.2012.0565.
DOI
|
12 |
Kumari, P. and Behera, S. (2017a), "Three-dimensional free vibration analysis of levy-type laminated plates using multi-term extended Kantorovich method", Compos. Part B Eng., 116, 224-238. https://doi.org/10.1016/j.compositesb.2017.01.057.
DOI
|
13 |
Kapuria, S., Kumari, P. and Nath, J. (2010), "Efficient modeling of smart piezoelectric composite laminates: a review", Acta Mechanica, 214(1-2), 31-48. https://doi.org/10.1007/s00707-010-0310-0.
DOI
|
14 |
Kerr, A.D. (1969), "An extended Kantorovich method for the solution of eigenvalue problems", J. Solids Struct., 5(6), 559-572. https://doi.org/10.1016/0020-7683(69)90028-6.
DOI
|
15 |
Kerr, A.D. and Alexander, H. (1968), "An application of the extended Kantorovich method to the stress analysis of a clamped rectangular plate", Acta Mechanica, 6(2-3), 180-196. https://doi.org/10.1007/BF01170382.
DOI
|
16 |
Khdeir, A. (2001), "Free and forced vibration of antisymmetric angle-ply laminated plate strips in cylindrical bending", J. Vib. Control, 7(6), 781-801. https://doi.org/10.1177/107754630100700602.
DOI
|
17 |
Kim, J.S. (2007), "Free vibration of laminated and sandwich plates using enhanced plate theories", J. Sound Vib., 308(1-2), 268-286. https://doi.org/10.1016/j.jsv.2007.07.040.
DOI
|
18 |
Kumari, P. and Behera, S. (2017b), "Three-dimensional free vibration analysis of levy-type laminated plates using multi-term extended Kantorovich method", Compos. Part B Eng., 116, 224-238. https://doi.org/10.1016/j.compositesb.2017.01.057.
DOI
|
19 |
Kumari, P., Kapuria, S. and Rajapakse, R. (2014), "Three-dimensional extended Kantorovich solution for Levy-type rectangular laminated plates with edge effects", Compos. Struct., 107, 167-176. https://doi.org/10.1016/j.compstruct.2013.07.053.
DOI
|
20 |
Kumari, P., Nath, J., Dumir, P. and Kapuria, S. (2007), "2D exact solutions for flat hybrid piezoelectric and magnetoelastic angle-ply panels under harmonic load", Smart Mater. Struct., 16(5), 1651. https://doi.org/10.1088/0964-1726/16/5/018.
DOI
|
21 |
Saravanos, D.A. and Heyliger, P.R. (1999), "Mechanics and computational models for laminated piezoelectric beams, plates, and shells", Appl. Mech. Rev., 52(10), 305-320. https://doi.org/10.1115/1.3098918.
DOI
|
22 |
Kumari, P., Singh, A., Rajapakse, R. and Kapuria, S. (2017), "Three-dimensional static analysis of Levy-type functionally graded plate with in-plane stiffness variation", Compos. Struct., 168, 780-791. https://doi.org/10.1016/j.compstruct.2017.02.078.
DOI
|
23 |
Messina, A. (2001), "Two generalized higher order theories in free vibration studies of multilayered plates", J. Sound Vib., 242(1), 125-150. https://doi.org/10.1006/jsvi.2000.3364.
DOI
|
24 |
Messina, A. and Soldatos, K.P. (2002), "A general vibration model of angle-ply laminated plates that accounts for the continuity of interlaminar stresses", J. Solids Struct., 39(3), 617-635. https://doi.org/10.1016/S0020-7683(01)00169-X.
DOI
|
25 |
Pan, E. and Heyliger, P.R. (2003), "Exact solutions for magneto-electro-elastic laminates in cylindrical bending", J. Solids Struct., 40(24), 6859-6876. https://doi.org/10.1016/j.ijsolstr.2003.08.003.
DOI
|
26 |
Qing, G., Qiu, J. and Liu, Y. (2006), "A semi-analytical solution for static and dynamic analysis of plates with piezoelectric patches", J. Solids Struct., 43(6), 1388-1403. https://doi.org/10.1016/j.ijsolstr.2005.03.048.
DOI
|
27 |
Sayyad, A.S. and Ghugal, Y.M. (2015), "On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results", Compos. Struct., 129, 177-201. https://doi.org/10.1016/j.compstruct.2015.04.007.
DOI
|
28 |
Sheng, H., Wang, H. and Ye, J. (2007), "State space solution for thick laminated piezoelectric plates with clamped and electric open-circuited boundary conditions", J. Mech. Sci., 49(7), 806-818. https://doi.org/10.1016/j.ijmecsci.2006.11.012.
DOI
|
29 |
Shu, X. (2005b), "Modelling of cross-ply piezoelectric composite laminates in cylindrical bending with interfacial shear slip", J. Mech. Sci., 47(11), 1673-1692. https://doi.org/10.1016/j.ijmecsci.2005.07.003.
DOI
|
30 |
Shu, X. (2005a), "Free vibration of laminated piezoelectric composite plates based on an accurate theory", Compos. Struct., 67(4), 375-382. https://doi.org/10.1016/j.compstruct.2004.01.022.
DOI
|
31 |
Udayakumar, B. and Gopal, K.N. (2017), "A modified state space differential quadrature method for free vibration analysis of soft-core sandwich panels", J. Sandwich Struct. Mater., https://doi.org/10.1177/1099636217727801.
|
32 |
Singh, A., Kumari, P. and Hazarika, R. (2018), "Analytical Solution for Bending Analysis of Axially Functionally Graded Angle-Ply Flat Panels", Math. Problems Eng., 2018. https://doi.org/10.1155/2018/2597484.
|
33 |
Singhatanadgid, P. and Singhanart, T. (2017), "The Kantorovich method applied to bending, buckling, vibration, and 3D stress analyses of plates: A literature review", Mech. Adv. Mater. Struct., pages 1-19. https://doi.org/10.1080/15376494.2017.1365984.
|
34 |
Singhatanadgid, P. and Singhanart, T. (2019), "The Kantorovich method applied to bending, buckling, vibration, and 3D stress analyses of plates: A literature review", Mech. Adv. Mater. Struct., 26(2), 170-188. https://doi.org/10.1080/15376494.2017.1365984.
DOI
|
35 |
Vel, S.S., Mewer, R. and Batra, R. (2004), "Analytical solution for the cylindrical bending vibration of piezoelectric composite plates", J. Solids Struct., 41(5-6), 1625-1643. https://doi.org/10.1016/j.ijsolstr.2003.10.012.
DOI
|
36 |
Wu, C.P., Chiu, K.H. and Wang, Y.M. (2008), "A review on the three-dimensional analytical approaches of multilayered and functionally graded piezoelectric plates and shells", Comput. Mater. Continua, 8(2), 93- 132.
|
37 |
Yang, J., Batra, R. and Liang, X. (1994), "The cylindrical bending vibration of a laminated elastic plate due to piezoelectric actuators", Smart Mater. Struct., 3(4), 485. https://doi.org/10.1088/0964-1726/3/4/011.
DOI
|
38 |
Wu, C.P. and Liu, Y.C. (2016), "A review of semi-analytical numerical methods for laminated composite and multilayered functionally graded elastic/piezoelectric plates and shells", Compos. Struct., 147, 1-15. https://doi.org/10.1016/j.compstruct.2016.03.031.
DOI
|
39 |
Xu, K., Noor, A.K. and Tang, Y.Y. (1997), "Three-dimensional solutions for free vibrations of initially-stressed thermoelectroelastic multilayered plates", Comput. Methods Appl. Mech. Eng., 141(1-2), 125-139. https://doi.org/10.1016/S0045-7825(96)01065-1.
DOI
|
40 |
Yan, W., Lv, T., Lei, T. and Zhi, J. (2019), "Exact analysis of imperfect angle-ply laminated panels with surface-bonded piezoelectric layers", Arch. Appl. Mech., 1-12. https://doi.org/10.1007/s00419-018-01502-z.
|
41 |
Yang, J., Batra, R.C. and Liang, X. (1995), "Vibration of a simply supported rectangular elastic plate due to piezoelectric actuators", Smart Structures and Materials 1995: Mathematics and Control in Smart Structures, Volume 2442, International Society for Optics and Photonics, Bellingham, WA, USA. 168-181.
|
42 |
Zhang, Z., Feng, C. and Liew, K. (2006), "Three-dimensional vibration analysis of multilayered piezoelectric composite plates", J. Eng. Sci., 44(7), 397-408. https://doi.org/10.1016/j.ijengsci.2006.02.002.
DOI
|
43 |
Zhou, Y., Chen, W. and Lu, C. (2010), "Semi-analytical solution for orthotropic piezoelectric laminates in cylindrical bending with interfacial imperfections", Compos. Struct., 92(4), 1009-1018. https://doi.org/10.1016/j.compstruct.2009.09.048.
DOI
|
44 |
Zhou, Y., Chen, W., Lu, C. and Wang, J. (2009), "Free vibration of cross-ply piezoelectric laminates in cylindrical bending with arbitrary edges", Compos. Struct., 87(1), 93-100. https://doi.org/10.1016/j.compstruct.2008.01.002.
DOI
|
45 |
Behera, S. and Kumari, P. (2018), "Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory", Adv. Comput. Design, 3(3), 213-232. https://doi.org/10.12989/acd.2018.3.3.213.
DOI
|
46 |
Abad, F. and Rouzegar, J. (2019), "Exact wave propagation analysis of moderately thick Levytype plate with piezoelectric layers using spectral element method", Thin-Walled Struct., 141, 319-331. https://doi.org/10.1016/j.tws.2019.04.007.
DOI
|
47 |
Abaqus, A. (2013), "6.13 Analysis Users Manual", SIMULIA, Providence, IR, USA.
|
48 |
Balabaev, S. and Ivina, N. (2014), "A three-dimensional analysis of natural vibrations of rectangular piezoelectric transducers", Russian J. Nondestructive Testing, 50(10), 602-606. https://doi.org/10.1134/S1061830914100027.
DOI
|
49 |
Barati, M.R. and Zenkour, A.M. (2018), "Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions", J. Vib. Control, 24(10), 1910-1926. https://doi.org/10.1177/1077546316672788.
DOI
|
50 |
Batra, R. and Liang, X. (1997), "The vibration of a rectangular laminated elastic plate with embedded piezoelectric sensors and actuators", Comput. Struct., 63(2), 203-216. https://doi.org/10.1016/S0045-7949(96)00349-5.
DOI
|
51 |
Behera, S. and Kumari, P. (2019), "Analytical Piezoelasticity Solution for Natural Frequencies of Levy-Type Piezolaminated Plates", J. Appl. Mech., 11(03), 1950023. https://doi.org/10.1142/S1758825119500236.
|
52 |
Chen, W. and Ding, H. (2002), "On free vibration of a functionally graded piezoelectric rectangular plate", Acta Mechanica, 153(3-4), 207-216. https://doi.org/10.1007/BF01177452.
DOI
|
53 |
Chen, W. and Lee, K.Y. (2004), "On free vibration of cross-ply laminates in cylindrical bending", J. Sound Vib., 3(273), 667-676. https://doi.org/10.1016/j.jsv.2003.08.003.
DOI
|
54 |
Chen, W. and Lu, C. (2005), "3D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported", Compos. Struct., 69(1), 77-87. https://doi.org/10.1016/j.compstruct.2004.05.015.
DOI
|
55 |
Dube, G., Kapuria, S. and Dumir, P. (1996a), "Exact piezothermoelastic solution of simplysupported orthotropic circular cylindrical panel in cylindrical bending", Archive Appl. Mech., 66(8), 537-554. https://doi.org/10.1007/BF00808143.
DOI
|
56 |
Cheng, Z.Q. and Batra, R. (2000a), "Three-dimensional asymptotic analysis of multiple-electroded piezoelectric laminates", AIAA J., 38(2), 317-324. https://doi.org/10.2514/2.959.
DOI
|
57 |
Cheng, Z.Q. and Batra, R. (2000b), "Three-dimensional asymptotic scheme for piezothermoelastic laminates", J. Thermal Stresses, 23(2), 95-110. https://doi.org/10.1080/014957300280470.
DOI
|
58 |
Cheng, Z.Q., Lim, C. and Kitipornchai, S. (2000), "Three-dimensional asymptotic approach to inhomogeneous and laminated piezoelectric plates", J. Solids Struct., 37(23), 3153-3175. https://doi.org/10.1016/S0020-7683(99)00036-0.
DOI
|
59 |
Dube, G., Kapuria, S. and Dumir, P. (1996b), "Exact piezothermoelastic solution of simply supported orthotropic flat panel in cylindrical bending", J. Mech. Sci., 38(11), 1161-1177. https://doi.org/10.1016/0020-7403(96)00020-3.
DOI
|
60 |
Ebrahimi, F. and Barati, M.R. (2016), "Size-dependent thermal stability analysis of graded piezomagnetic nanoplates on elastic medium subjected to various thermal environments", Appl. Phys., 122(10), 910. https://doi.org/10.1007/s00339-016-0441-9.
DOI
|
61 |
Ebrahimi, F. and Barati, M.R. (2017a), "Damping vibration analysis of smart piezoelectric polymeric nanoplates on viscoelastic substrate based on nonlocal strain gradient theory", Smart Mater. Struct., 26(6), 065018. https://doi.org/10.1088/1361-665X/aa6eec.
DOI
|
62 |
Ebrahimi, F. and Barati, M.R. (2017b), "Magnetic field effects on dynamic behavior of inhomogeneous thermo-piezo-electrically actuated nanoplates", J. Brazilian Soc. Mech. Sci. Eng., 39(6), 2203-2223. https://doi.org/10.1007/s40430-016-0646-z.
DOI
|