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Here is a cantilevered isotropic piezolaminated cylindrical shell as shown in Fig. 7. This problem was initially calculated by Tzou and Ye [59] for active control of small amplitude vibrations, later by Chrós ́cielewski and Schmidt [12] for control of large amplitude vibrations using full geometrically nonlinear beam theory. The host structure is a steel shell, covered by two piezolayers (PZT), the bottom one as distributed sensor and the top one as distributed actuator.
References [12] and [59]:
[12] Chrós ́cielewski J, Schmidt R (1999) Nonlinear static and transient response of smart beams and shells with piezoelectric layers. In: Anderson GL, Garg D, Wang KW (eds) Proceedings of the fourth ARO workshop on smart structures, Penn State, State College, Pennsylvania, Session 8: modeling and characterisation issues. U.S. Army Research Office, USA
[59] Tzou HS, Ye R (1996) Analysis of piezoelastic structures with laminated piezoelectric triangle shell elements. AIAA J 34:110– 115
The following three different analyses are performed for this numerical example
(1) Linear eigenvalue problem and convergence study
(2) Static analysis of geometrically linear and nonlinear
deformations
(3) Simulation of large amplitude vibrations and control
with distributed actuators
FROM:
M.N. Rao, R. Schmidt and K.-U. Schroeder, “Finite rotation FE-simulation and active vibration control of smart composite laminated structures”, Computational Mechanics, in press, 2015, DOI 10.1007/s00466-015-1132-7
ABSTRACT: The present article focuses on the nonlinear finite element simulation and control of large amplitude vibrations of smart piezolaminated composite structures. Full geometrically nonlinear finite rotation strain–displacement relations and Reissner–Mindlin first-order shear deformation hypothesis to include the transverse shear effects are considered to derive the variational formulation. A quadratic variation of electric potential is assumed in transverse direction. An assumed natural strain method for the shear strains, an enhanced assumed strain method for the membrane strains and an enhanced assumed gradient method for the electric field is incorporated to improve the behavior of a four-node shell element. Numerical simulations presented in this article show the accurate prediction capabilities of the proposed method, especially for structures undergoing finite deformations and rotations, in comparison to the results obtained by simplified nonlinear models available in references and also with those obtained by using the C3D20RE solid element for piezoelectric layers in the Abaqus code.
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