References
25
37. J.N. Reddy, A refined nonlinear theory of plates with transverse shear deformation. Int. J.
Solids Struct. 20, 881–896 (1984)
38. N.F. Hanna, A.W. Leissa, A higher order shear deformation theory for the vibration of thick
plates. J. Sound Vib. 170, 545–555 (1994)
39. V.M.F. Correia, M.A.A. Gomes, A. Suleman, C.M.M. Soares, C.A.M. Soares, Modelling
and design of adaptive composite structures. Comput. Methods Appl. Mech. Eng. 185(2),
325–346 (2000)
40. I.F.P. Correia, C.M.M. Soares, C.A.M. Soares, J. Herskovits, Active control of axisymmetric
shells with piezoelectric layers: a mixed laminated theory with a high order displacement
field. Comput. Struct. 80, 2265–2275 (2002)
41. J.S. Moita, P.G. Martins, C.M.M. Soares, C.A.M. Soares, Optimal dynamic control of laminated adaptive structures using a higher order model and a genetic algorithm. Comput. Struct.
86, 198–206 (2008)
42. B.A. Selim, L.W. Zhang, K.M. Liew, Active vibration control of fgm plates with piezoelectric
layers based on reddy’s higher-order shear deformation theory. Compos. Struct. 155, 118–134
(2016)
43. M.A.R. Loja, C.M.M. Soares, C.A.M. Soares, Higher-order B-spline finite strip model for
laminated adaptive structures. Compos. Struct. 52, 419–427 (2001)
44. C.M.M. Soares, C.A.M. Soares, V.M.F. Correia, M.A.R. Loja, Higher-order B-spline strip
models for laminated composite structures with integrated sensors and actuators. Compos.
Struct. 54, 267–274 (2001)
45. M.C. Ray, J.N. Reddy, Active control of laminated cylindrical shells using piezoelectric fiber
reinforced composites. Compos. Sci. Technol. 65, 1226–1236 (2005)
46. C.M.A. Vasques, J.D. Rodrigues, Coupled three-layered analysis of smart piezoelectric beams
with different electric boundary conditions. Int. J. Numer. Methods Eng. 62, 1488–1518 (2005)
47. S. Kapuria, An efficient coupled theory for multilayered beams with embedded piezoelectric
sensory and active layers. Int. J. Solids Struct. 38, 9179–9199 (2001)
48. S. Kapuria, P.C. Dumir, A. Ahmed, An efficient coupled layerwise theory for dynamic analysis
of piezoelectric composite beams. J. Sound Vib. 261, 927–944 (2003)
49. O. Polit, M. D’Ottavio, P. Vidal, High-order plate finite elements for smart structure analysis.
Compos. Struct. 151, 81–90 (2016)
50. E. Carrera, L. Demasi, Classical and advanced multilayered plate elements based upon PVD
and RMVT. Part 2: numerical implementations. Int. J. Numer. Methods Eng. 55, 253–291
(2002)
51. E.F. Crawley, J. Luis, Use of piezoelectric actuators as elements of intelligent structures.
AIAA J. 25(10), 1373–1385 (1987)
52. H.S. Tzou, W.K. Chai, Design and testing of a hybrid polymeric electrostrictive/piezoelectric
beam with bang-bang control. Mech. Syst. Signal Process. 21, 417–429 (2007)
53. I. Kucuk, I.S. Sadek, E. Zeihi, S. Adali, Optimal vibration control of piezolaminated smart
beams by the maximum principle. Comput. Struct. 89, 744–749 (2011)
54. S. Narayanan, V. Balamurugan, Finite element modeling of piezolaminated smart structures
for active vibration control with distributed sensors and actuators. J. Sound Vib. 262, 529–562
(2003)
55. M. Marinaki, Y. Marinakis, G.E. Stavroulakis, Vibration control of beams with piezoelectric
sensors and actuators using partical swarm optimization. Expert Syst. Appl. 38, 6872–6883
(2011)
56. Y. Zhu, J.W. Zu, Modeling of piezoelectric energy harvester: a comparison between EullerBernoulli and Timoshenko theory, in Proceedings of the ASME 2011 Conference on Smart
Materials, Adaptive Structures and Intelligent Systems, Phoenix, Arizona, USA, September
18–21 (2011)
57. P. Ribeiro, Non-linear free periodic vibrations of open cylindrical shallow shells. J. Sound
Vib. 313, 224–245 (2008)
58. J.N. Reddy, Geometrically nonlinear transient analysis of laminated composite plates. AIAA
J. 21, 621–629 (1983)
25
37. J.N. Reddy, A refined nonlinear theory of plates with transverse shear deformation. Int. J.
Solids Struct. 20, 881–896 (1984)
38. N.F. Hanna, A.W. Leissa, A higher order shear deformation theory for the vibration of thick
plates. J. Sound Vib. 170, 545–555 (1994)
39. V.M.F. Correia, M.A.A. Gomes, A. Suleman, C.M.M. Soares, C.A.M. Soares, Modelling
and design of adaptive composite structures. Comput. Methods Appl. Mech. Eng. 185(2),
325–346 (2000)
40. I.F.P. Correia, C.M.M. Soares, C.A.M. Soares, J. Herskovits, Active control of axisymmetric
shells with piezoelectric layers: a mixed laminated theory with a high order displacement
field. Comput. Struct. 80, 2265–2275 (2002)
41. J.S. Moita, P.G. Martins, C.M.M. Soares, C.A.M. Soares, Optimal dynamic control of laminated adaptive structures using a higher order model and a genetic algorithm. Comput. Struct.
86, 198–206 (2008)
42. B.A. Selim, L.W. Zhang, K.M. Liew, Active vibration control of fgm plates with piezoelectric
layers based on reddy’s higher-order shear deformation theory. Compos. Struct. 155, 118–134
(2016)
43. M.A.R. Loja, C.M.M. Soares, C.A.M. Soares, Higher-order B-spline finite strip model for
laminated adaptive structures. Compos. Struct. 52, 419–427 (2001)
44. C.M.M. Soares, C.A.M. Soares, V.M.F. Correia, M.A.R. Loja, Higher-order B-spline strip
models for laminated composite structures with integrated sensors and actuators. Compos.
Struct. 54, 267–274 (2001)
45. M.C. Ray, J.N. Reddy, Active control of laminated cylindrical shells using piezoelectric fiber
reinforced composites. Compos. Sci. Technol. 65, 1226–1236 (2005)
46. C.M.A. Vasques, J.D. Rodrigues, Coupled three-layered analysis of smart piezoelectric beams
with different electric boundary conditions. Int. J. Numer. Methods Eng. 62, 1488–1518 (2005)
47. S. Kapuria, An efficient coupled theory for multilayered beams with embedded piezoelectric
sensory and active layers. Int. J. Solids Struct. 38, 9179–9199 (2001)
48. S. Kapuria, P.C. Dumir, A. Ahmed, An efficient coupled layerwise theory for dynamic analysis
of piezoelectric composite beams. J. Sound Vib. 261, 927–944 (2003)
49. O. Polit, M. D’Ottavio, P. Vidal, High-order plate finite elements for smart structure analysis.
Compos. Struct. 151, 81–90 (2016)
50. E. Carrera, L. Demasi, Classical and advanced multilayered plate elements based upon PVD
and RMVT. Part 2: numerical implementations. Int. J. Numer. Methods Eng. 55, 253–291
(2002)
51. E.F. Crawley, J. Luis, Use of piezoelectric actuators as elements of intelligent structures.
AIAA J. 25(10), 1373–1385 (1987)
52. H.S. Tzou, W.K. Chai, Design and testing of a hybrid polymeric electrostrictive/piezoelectric
beam with bang-bang control. Mech. Syst. Signal Process. 21, 417–429 (2007)
53. I. Kucuk, I.S. Sadek, E. Zeihi, S. Adali, Optimal vibration control of piezolaminated smart
beams by the maximum principle. Comput. Struct. 89, 744–749 (2011)
54. S. Narayanan, V. Balamurugan, Finite element modeling of piezolaminated smart structures
for active vibration control with distributed sensors and actuators. J. Sound Vib. 262, 529–562
(2003)
55. M. Marinaki, Y. Marinakis, G.E. Stavroulakis, Vibration control of beams with piezoelectric
sensors and actuators using partical swarm optimization. Expert Syst. Appl. 38, 6872–6883
(2011)
56. Y. Zhu, J.W. Zu, Modeling of piezoelectric energy harvester: a comparison between EullerBernoulli and Timoshenko theory, in Proceedings of the ASME 2011 Conference on Smart
Materials, Adaptive Structures and Intelligent Systems, Phoenix, Arizona, USA, September
18–21 (2011)
57. P. Ribeiro, Non-linear free periodic vibrations of open cylindrical shallow shells. J. Sound
Vib. 313, 224–245 (2008)
58. J.N. Reddy, Geometrically nonlinear transient analysis of laminated composite plates. AIAA
J. 21, 621–629 (1983)