Keywords: free vibration, state space method, adaptive structure, piezoelectric, laminated composite cylinder, fluid-structure interaction.

This paper presents a three-dimensional exact mixed state space solution, as well as a parametric analysis, for the free-vibration of a simply-supported arbitrarily thick laminated piezoceramic cylinder completely filled with fluid. The piezoelectric layers of the laminated cylinder are supposed to be polarized in the radial direction and the fluid is considered inviscid and either compressible or incompressible. The proposed formulation, inspired by that one developed for the free-vibration analysis of laminated plates with embedded piezoceramic layers [1], retains, as state variables, the standard mechanical displacements and transverse stresses. These variables are augmented, for the piezoelectric case, by electric transverse displacement and potential, and for the fluid-structure coupled problem, by the fluid pressure. The effect of internal fluid is taken into consideration by imposing a relationship between the transverse stress and the radial displacement deduced from the classical continuity conditions at the interface. Frequency and mode shapes are computed for different electrical boundary conditions at the inner and outer cylindrical surfaces of the piezoelectric layers. A detailed parametric analysis is then conducted to show the influence of the radius-to-thickness and the length-to-thickness ratios, the electric boundary conditions and the fluid effect. Concerning the piezoelectric aspect, it was found that the distribution of the electric state variables across the thickness of the cylinder depends strongly on the electric boundary conditions and the mode type. Moreover, contrary to the common practice of the mechanical community, the weak difference between short- and open-circuit natural frequencies should not be neglected. It might be used to assess the piezoelectric effect through the so-called effective modal electromechanical coupling coefficient whose level was found to depend on the mode type. This exact solution and the corresponding results can be used to validate other analytical or numerical solutions. Moreover, such a formulation can be used (i) to develop accurate piezoelectric shell finite elements, and (ii) to investigate the effects of various parameters on the natural frequencies and mode shapes of the fluid-piezoelectric structure coupled system.

1

J.F. Deü and A. Benjeddou, "Free-vibration analysis of laminated plates with embedded shear-mode piezoceramic layers", International Journal of Solids and Structures, 42(7), 2059-2088, 2005. doi:10.1016/j.ijsolstr.2004.09.003

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