Closed-form solutions for the free-vibration problem of multilayered piezoelectric shells

Computers and Structures

Volumn 84, Issue 22-23, 2006, Pages 1506-1518

  D'Ottavio, M ^a   Ballhause, D ^a   Kroplin B ^a   Carrera, E ^b  

^a UNIVERSITY OF STUTTGART   (Germany)

^b POLITECNICO DI TORINO   (Italy)

Author keywords

Closed form solution; Higher order formulations; Multilayered structures; Piezoelectric materials; Unified formulation; Vibrations of shells

Indexed keywords

COMPUTATIONAL GEOMETRY; ELECTROMECHANICAL DEVICES; EMBEDDED SYSTEMS; HIERARCHICAL SYSTEMS; LAMINATES; MULTILAYERS;

CLOSED-FORM SOLUTION; HIGHER-ORDER FORMULATIONS; MULTILAYERED STRUCTURES; UNIFIED FORMULATION; VIBRATIONS OF SHELLS;

PIEZOELECTRIC MATERIALS;

EID: 33745383816     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2006.01.030     Document Type: Article

References (32)

1. Noor A.K., and Burton W.S. Assessment of computational models for multilayered shells. Appl Mech Rev 43 4 (1990) 67-97
2. Carrera E. Historical review of zig-zag theories for multilayered plates and shells. Appl Mech Rev 56 3 (2003) 287-308
3. Reddy J.N. Mechanics of laminated composite plates and shells: theory and analysis (2004), CRC Press, Boca Raton
4. 0 requirements - models for the two dimensional analysis of multilayered structures. Compos Struct 37 (1997) 373-383
5. Koiter W.T. A consistent first approximation in the general theory of thin elastic shells. In: Koiter W.T. (Ed). The theory of thin elastic shells (1959), IUTAM, North-Holland, Delft 12-33
6. Mindlin R.D. Forced thickness-shear and flexural vibrations of piezoelectric crystal plates. J Appl Phys 23 (1952) 83-88
7. EerNisse E.P. Variational method for electroelastic vibration analysis. IEEE Trans Sonics Ultrasonics SU-14 4 (1967) 153-160
8. Tiersten H.F., and Mindlin R.D. Forced vibrations of piezoelectric crystal plates. Quart Appl Math 20 2 (1962) 107-119
9. Tiersten H.F. Linear piezoelectric plate vibrations (1969), Plenum, New York
10. Saravanos D.A., and Heyliger P.R. Mechanics and computational models for laminated piezoelectric beams, plates and shells. Appl Mech Rev 52 10 (1999) 305-319
11. Kapuria S. A coupled zig-zag third-order theory for piezoelectric hybrid cross-ply plates. J Appl Mech 71 (2004) 604-614
12. Ossadzow-David C., and Touratier M. A multilayered piezoelectric shell theory. Compos Sci Technol 64 (2004) 2121-2137
13. Heyliger P., Pei K.C., and Saravanos D.A. Layerwise mechanics and finite element model for laminated piezoelectric shells. AIAA J 34 11 (1996) 2353-2360
14. Rogacheva N.N. The theory of piezoelectric shells and plates (1994), CRC Press, Boca Raton
15. Gopinathan S.V., Varadan V.V., and Varadan V.K. A review and critique of theories for piezoelectric laminates. Smart Mater Struct 9 (2000) 24-48
16. Benjeddou A. Advances in piezoelectric finite element modeling of adaptive structural elements: a survey. Comput Struct 76 (2000) 347-363
17. Lammering R., and Mesecke-Rischmann S. Multi-field variational formulations and related finite elements for piezoelectric shells. Smart Mater Struct 12 6 (2003) 904-913
18. Benjeddou A, Andrianarison O. Extension of Reissner's mixed variational theorem to piezoelectric multilayered composites. In: Lipitakis EA, editor. Proceedings of the sixth Hellenic-European conference on computer mathematics and its applications, LEA, Athens, Hellas, 2003. p. 116-24.
19. Carrera E. Theories and finite elements for multilayered plates and shells: A unified compact formulation with numerical assessment and benchmarking. Arch Comput Methods Eng 10 3 (2003) 215-296
20. Carrera E. Single-layer vs multilayer plate modelings on the base of Reissner's mixed theorem. AIAA J 38 2 (2000) 342-352
21. Carrera E. Multilayered shell theories accounting for layerwise mixed description. Part 1: Governing equations; Part 2: Numerical evaluations. AIAA J 37 9 (1999) 1107-1124
22. Ballhause D., D'Ottavio M., Kröplin B., and Carrera E. A unified formulation to assess multilayered theories for piezoelectric plates. Comput Struct 83 15-16 (2005) 1217-1235
23. Kraus H. Thin elastic shells (1967), John Wiley & Sons, Inc.
24. Novozhilov V.V. Thin shell theory. 2nd ed. (1964), P. Noordhoff Ltd., Groningem
25. Ikeda T. Fundamental of piezoelectricity (1996), Oxford University Press
26. Murakami H. Laminated composite plate theory with improved in-plane response. J Appl Mech 53 (1986) 661-666
27. Carrera E. On the use of Murakami's zig-zag function in the modeling of layered plates and shells. Comput Struct 82 (2004) 541-554
28. Carrera E. A class of two dimensional theories for multilayered plates analysis. Atti Acc Sci Torino, Mem Sci Fis 19-20 (1995) 49-87
29. Carrera E. A study of transverse normal stress effect on vibration of multilayered plates and shells. J Sound Vib 225 5 (1999) 803-829
30. Drumheller D.S., and Kalnins A. Dynamic shell theory for ferroelectric ceramics. J Acoust Soc Am 47 (1970) 1343-1353
31. Benjeddou A. Modelling and simulation of adaptive structures and composites: Current trends and future directions. In: Topping B.H.V., and Mota-Soares C.A. (Eds). Progress in computational structures technology (2004), Saxe-Coburg Publications, Stirling, UK 251-280
32. Heyliger P.R., and Saravanos D.A. Exact free-vibration analysis of laminated plates with embedded piezoelectric layers. J Acoust Soc Am 98 3 (1995) 1547-1557